I.: Occasion of this Address.

The matchless excellence, as well as novelty, of the New Instruction System, is a matter too universally recognised, to need mention in any other way than that of simple allusion. Of its applicability to the higher, not to say the highest, branches of intellectual instruction, the fullest persuasion is, over and over again, expressed in the works of its illustrious inventor, whose anticipations have, in every point, received such ample and undisputed confirmation from experience.

In common with so many others, the proposed conductors, or superintendents, undermentioned, had for a long time been entertaining the wish, not unaccompanied with the expectation, of seeing, in some mode or other, and by some means or other, so desirable an extension carried into effect; meaning, of course, on the ordinary terms, and by professional hands; and that too, in respect of the extent of the field of instruction, upon such a scale as would be suited to the efficiency of the novum organum, now placed within the reach of human industry, and the amplitude of the prospect opened by it to the public view.

Upon a more attentive consideration it appeared, however, to several of them, that, for a first experiment of this kind, more requisites were necessary, than could naturally be looked for in any single hand, or even in any number of hands uniting together upon any such ordinary ground; and of this conception the result has been an Association entered into by them for this purpose.

II.: Proposed Conductors,—Who.

Not to speak of probity and pecuniary responsibility—qualities, of which, though both are so indisputably requisite, yet neither can, in such a case as the present, be spoken of as appropriate; a commanding acquaintance with the whole field of that intellectual instruction, the communication of which is the object of this design; a detailed acquaintance with the several distinguishable component elements and sources of public welfare (the great and universal end to which all art, all science, all language, is, or ought to be directed;) husbandry, manufactures, trades, money, and in particular with the practical details of trade as carried on in that vast metropolis, from which almost exclusively the destined partakers of the proposed benefit can, for some time, be expected: all these various endowments will at first view present themselves, if not as being in every instance indispensably necessary, at any rate as being eminently desirable. All these endowments, in common with the whole public in the most essential instances, and with an ample portion of it in every other instance, the Members of the Association, the proposed Conductors, had the satisfaction of seeing united in their whole body; a satisfaction which, upon inquiry, or without need of inquiry, an ample share will be received by every individual, who, either in the character of proposed patron of the institution, or parent, or guardian of a child to which the benefit of it is proposed, feels any interest in the design.

The person by whom, without the communicated Edition: current; Page: [55] desire of any one of them, and without the privity of any more than one, this paper has been drawn up and sent to the press, has not, nor can have, the honour of being of the number: he may, therefore, with the less difficulty and reserve, speak of the title, which on this occasion, and to this purpose they will, every one of them, be found to possess, to the requisite public confidence.

III.: Primary requisite, a SCHOOL-HOUSE: proposed to be built by Subscription.

In the nature of the case, the first requisite, on which everything depends, and in the non-existence of which the chief cause of retardation may be found, is a School-house, an appropriate School-house, and that, in its dimensions, of an amplitude suited to that magnitude of scale on which, not only in respect to cheapness and extent, but in respect of efficiency, the New Instruction System so essentially depends.

For the attainment of this requisite, a pecuniary advance, and that to no inconsiderable amount, was obviously necessary; and for this purpose the proposed Conductors all presently agreed to become contributors, in such proportions as should be suited to their respective circumstances and convenience at the time of the commencement of the expense: an agreement which was the more readily entered into, by reason of the assurance they all saw reason to entertain, that whatever should be there bestowed would be no more than an advance, of which the reimbursement (which was all that by any of them has ever been looked for, or will be accepted,) might not unreasonably be depended upon, on condition of a few years patience.

It is for the completion of the sum requisite for this purpose that the present proposal is put into circulation.

IV.: Proposed Field and Plan of Instruction.

This proposal has for its accompaniment a collection of papers, drawn up by a friend to the proposed Institution, who, though declining to take any part in the management, has in this manner, as well as by his contributions, manifested his desire to see it carried into effect.

These papers have for their general title, Chrestomathiá; and for their design, the giving a view of the field and means of Instruction, proposed for the proposed Chrestomathic Day-School.

Partly for the sake of compression, partly for the accommodation of any persons who may be disposed to look into it with attention, the main body of this Sketch is comprised in two Synoptic Tables, digested into the form of Text and Notes.

In Table I. the matter is arranged under the following general heads: viz. Advantages, from Learning as such, as well as from Learning in the particular shapes here in question; Stages of Instruction; Grounds of Priority, in relation to the branches herein included; and Grounds of Omission in relation to Branches not included.

In Table II., under the two following: viz.

I. Principles constitutive of the New Instruction System, considered as applicable to the several ulterior Branches of Art and Science-Learning (Language-learning included.)

II. Exercises, by the performance of which, such learning is obtained or obtainable. In the instance of these principles, by means of the simultaneousness of the view, which, as above, is given of them, the connexions and dependencies of the several parts of the admirable whole, will, it is hoped, be the more readily observed, and correctly and completely comprehended.

On these considerations, in the instance of this last mentioned Table, (this happening to be the first of the two that was completed,) the whole matter, Notes as well as Text, was, in the first instance, brought together, and compressed into one side of a single sheet; and in this form copies, to a considerable number, have been printed off. Observations, however, having been made, that, while by the unavoidable closeness, added to the smallness, of the type, it could not but have been rendered afflictive to many an eye, it was by its still unavoidable bulk rendered in no inconsiderable degree unwieldy and formidable, another impression has since been printed off, in which the Text alone is in the Tabular-form, the accompanying Notes being in the ordinary Book-form; and in this manner alone—viz., Text in the Tabular, Notes in the Book-form—has Table I. been printed.

To the principal matter as contained in these two Tables, other papers are added in the form of an Appendix. The contents have for their object, partly a statement of some of the promises of ulterior success which are already known to have been furnished by experience,—partly a view of some ideas, which to the hope of utility, are supposed to add in some degree the character of novelty, and which, such as they are, the present design has been the means of calling forth.

V.: Site for School-House secured.

A requisite, the procurement of which might naturally have presented still greater difficulty, than any that is expected to attach upon the raising of the comparatively moderate sum necessary for the expense, was a spot of ground, sufficiently adapted, in respect of situation as well as extent, to the purpose of serving as a site for the erection. But this difficulty they have the satisfaction of declaring to be already removed.

VI.: Females proposed to be received,—Why?

Their wish being as above, to give to so great a benefit, and that in every direction, the utmost extension in their power, the female Edition: current; Page: [56] sex could not fail of being comprehended in their views.

In the whole of the proposed field of instruction, as marked out in the above-mentioned paper, scarcely will there be found a spot, which in itself, custom apart, will not be, in respect of the information presented by it, alike useful to both sexes: some parts (and more especially those which concern Domestic Economy, and the care of health, as applied to the more delicate sex, and to both sexes, at the time of life during which they are almost exclusively subject to its care,) will even be found more useful to females than to males. By an experienced as well as eminently intelligent disciple of Dr Bell’s,* it is mentioned as a “well-known fact, that girls are more docile and attentive than boys;” and that accordingly, in that part of their school-time, which remains after subtraction of that which is applied to occupations appropriated to their sex, the degree of proficiency which, at the end of the year, they have attained, is not inferior to that which, in the whole of that same school-time, has, within that same period, been attained by the boys.

In the case of the middling classes, to whatsoever other branches of instruction the labour of female children be applied, needle-work will certainly not be regarded as one that can be omitted; and though, for the practice of this art, there would remain several hours of the four-and-twenty, yet what may naturally be expected is, a general wish to see some portion of the school-time allotted to such works.

Dancing, Music.—By these fascinating words are presented two accomplishments, the possession of which will, by all that belong to the higher classes, be regarded as indispensable; and, by many of those that belong to the middling, as being, if not indispensable, at the least desirable. For neither of these, it is evident, can any place be found in the proposed school. For uniting its benefits with those accomplishments, there remain therefore but two expedients; viz. the deferring of the accomplishments, either to a later hour, or a later age.

VII.: Number proposed to be built for.

Under the National Institution, the number built for in the Westminster Free School is observed to be 1000; viz. for males 600, for females 400. The same total, viz. a thousand, is, in case of a sufficiency of funds, the number here proposed to build for; in case of a deficiency, the number built for must of course be proportionably reduced.

As to expense, £5000, they observe to be stated as the expense of that building; furniture, as well as lodging, for Master and for Mistress included. That same sum, it is presumed, may be made to serve equally well for the here proposed school-house.

According to the indications afforded by experience, the above number of 600 is understood to be generally regarded as the greatest number that, in one and the same school-room, can be taught under the constant inspection of one and the same Master. But, on the plan on which it is here proposed to build, it will be evident, that, whatsoever be the dimensions of the apartment, in which that number can be sufficiently inspected by one person, several such apartments, containing, each of them, as much room as in that case, will in this case be inspectable by one and the same person, and that in a manner still more perfect than in that other case.

Moreover, in this same place, though no part of the room allotted to females, will, unless at some special time, or by special recorded order, and for special reason, be open to the view of any person stationed in the part allotted to males; yet, by means of a slight alteration, any redundancy in the quantity of room allotted to either sex may be applied to the supply of any deficiency which, in consequence of an increase beyond the calculated demand, may be found to have place in the quantity originally provided for the other.

Considering that, in the case of the Westminster Free School, a thousand was, in the judgment of the National Society, as large a number as it was advisable to build for; and this, although the class of scholars in view composed so much larger a portion of the juvenile population than that from which any scholars could be looked for to the proposed Day-School, a conclusion which may be liable to be drawn, is, that, in and for the here proposed School, no number so large, or nearly so large as the above, can reasonably be expected.

But, in the case of that Free School, free as it was and is, limits were set to the probable number of scholars, by several circumstances, none of which will, in the present instance, be found to have place. On the part of the parents, insensibility to the advantages of intellectual instruction, inattention to the future and lasting welfare of their children, inability to spare the time necessary to the conducting of the children, for the first part of the time, to and from the school, especially in the case of those whose abodes are in a considerable degree distant from it.

In the present instance, to obviate, as far as may be, the latter difficulty, an expedient, which the proposed Conductors have in view, is to comprise in one sitting the whole quantity of the school time; and by that means reduce to its minimum the time and attendance, consumed in the passage between school and home. In the Westminster Free School, the total quantity of school time,—in the season of longest light, six hours, in the season of shortest, light, five,—is divided into two portions, with an interval of one hour between the two. In Edition: current; Page: [57] private schools, however, instances are not wanting, in which, without any interval, the children are kept under instruction for so long a time as six hours. To so great a length, the proposed Conductors are somewhat afraid to stretch it; but to such a length as five hours they expect not to find any conclusive objection.

One circumstance they look to, as a source, though not of immediate, yet in case of success, of eventual, increase to the population of the proposed school. Against any such undertaking as that of a Boarding School, to be carried on, or commenced, under their own management or even superintendence, their determination is decided. But, in case of success, a result, which they cannot regard as by any means an improbable one, is, that parents, situated at too great a distance to admit of their sending their children from their own residences, may, for the purpose of taking benefit of the instruction there, and there only, to be obtained, find for their children, in the residence of some relative or other particular friend, or even of some person who may be disposed to afford the accommodation on the ordinary commercial terms, a residence sufficiently near to the School-House to admit of their receiving the instruction which it affords. On this plan it is, that, to the great public schools, scholars are sent from the remotest parts of the three kingdoms: and, should it appear that, in the proposed new school, useful instruction in much greater variety, as well as quantity, is to be had, than in any of those old established ones, and that too in much less time, and by every scholar without exception, instead of by no more than a portion more or less considerable of the whole number, they see not why, in the present instance, an equal, if not superior afflux, may not sooner or later be expected.

A circle of about two miles radius, having the site of the school for its centre, is the space, from the whole of which, on condition of keeping the length of school-time undivided, they regard themselves as entitled to look for scholars; and that without any change made for this purpose in their place of residence.

VIII.: Ages, looked for, at Entrance and Departure.

Fourteen is the age at or before which they hope to see their intended course completed, by the scholars in general, in all its branches; and this too, upon the supposition that seven, and no earlier, is the earliest age at which children will be sent to take the benefit of it; fourteen, that being the age at which it is common for apprenticeships to commence; for, though no such views are entertained, as that of confining the benefit to such children as their parents may have destined to apprenticeships, yet it would be altogether repugnant to their wishes, if any child so destined should, on any account, find himself excluded from it.

The seven years, reckoning from seven to fourteen, is the length of time, within which, as above, they expect to see the aggregate course completed; and, as a ground for that expectation, one of their endeavours has been to collect from the various education and intellectual-instruction establishments, in which instruction on any of the proposed subjects of the proposed scheme of instruction is administered, Public Schools, Universities, Hospitals, Public Institution-rooms, and Private Lecture-rooms not excluded—an account of the number of hours actually occupied in each; and this, to the end that the sum of the times so expended in all of them together, may be compared with the sum of the times capable of being allotted to the same subjects, in the proposed school; and though, of the information desired on this ground, the whole has not as yet been obtained, yet enough has been obtained to enable them, and with the requisite degree of confidence, considering the experienced force of the new instrument with which they will have to work, to speak of the above proposed length of time, as being fully sufficient, viz. for the aggregate of all the courses, according to the plan exhibited in the accompanying sketch; matters being, at the same time, as far as may be, so arranged, that, at several different stages, the scholar may take his departure, without leaving his instruction imperfect, in relation to any subject, in which he has begun to receive it.

When seven years was thus looked to as the probable duration of the aggregate course, the occupation had, however, for its basis the supposition that, at that age, in the situations in life in question, scholars might in general be found already in a sufficient degree instructed in those branches to which, in the free schools at present established, the New Instruction system is applied. But, consistently with that principle of universal comprehension, which they could not but adopt, no child whose parents, being desirous of obtaining for it a share in the benefit, were able and willing to pay for it at the necessary price, could, by the conditions of the undertaking, be excluded.

By this consideration it is, that they have been led to the persuasion which they entertain, of the necessity of comprising in their plan those arts of primary necessity and continual and universal application, (viz. reading and writing, and common arithmetic,) which are comprehended in the New Instruction system, in so far as already brought into practice. To this determination, an ample confirmation has been observed to be afforded by the observation made and repeatedly brought to view by Dr Bell himself (and which is no more than upon an attentive consideration of the case, might from the first have been previously expected,) viz., that in any of those arts, an imperfect degree of proficiency, obtained by instruction, administered in the ordinary mode, operate rather as an obstacle, than as a help Edition: current; Page: [58] to, an useful foundation, for instruction administered in this, incomparably more advantageous mode: learning, in the improved mode, having to an undefinable degree, for its necessary preliminary, the unlearning what has been learnt in the other ordinary, and ordinarily imperfect, mode.

Of one rule the necessity is, by the bare mention of it, rendered indisputable, and that is, not to admit or continue to receive any child who, whether on account of immaturity of age, or on any other, is so circumstanced as to require, in the school-room, more care and attendance than the quantity of each, which is at the command of the Establishment, can supply. As on so many other occasions, so on this, a rule which, while it thus bears on the face of it its own reason, and thereby its own explanation, is applicable with equal propriety to every individual case included in it, they cannot but regard as preferable to any rule, in which, by means of fixt and inflexible quantities, invariable provision is, in the Procrustes style, made for indefinitely varied exigencies.

In the Barrington School at Durham, at an age as early as three years, the New Instruction System, as is to be seen in the instructive and interesting account for which the public is indebted to Sir Thomas Bernard, has been found applicable with advantage;* and if, at an age still earlier, any child should be offered to the reading and writing form of the Chrestomathic School, there seems no reason why it should be rejected, on any other ground than that of an exclusion put upon it by the irrational rule just mentioned.

IX.: This but an Experiment—expected Sources of Continuance and Extension.

The proposed undertaking being but an experiment, the period which the proposed Conductors look to, as that of the completion of the experiment, is the time at which the whole of the proposed field of instruction, as marked out in the Chrestomathia, shall have been travelled over, by the whole number of such of the scholars, as have gone through the aggregate course. At that time, if not earlier, the expectation of the proposed Conductors is, that such of them as are then alive, will have the satisfaction of beholding a number of fit persons willing, and in every respect well qualified, each of them by himself, to take the whole of the business out of their hands. Well may it be—and this was the very consideration by which the association was produced—well may it be, that, at present, any such undertaking is too great, considerably too great, for any single individual. Accordingly, the engaging in no inconsiderable number, as well as variety, a set of Masters, for the administering of the instruction in the several branches, is among the measures, the necessity of which is in full view.

But, at the period here in question, scholars, by dozens and by scores, may not unreasonably be expected to have learnt, in the Chrestomathic School, all the things whatsoever that will have there been taught. Viewing the matter at large, whatsoever it be, that a large number of persons have themselves learnt, supposing it well learnt, some proportion or other of the number will, by that same time, be not altogether unqualified to teach. But, at the period in question, under the New Instruction System, the scholars—no inconsiderable proportion of them—not only may reasonably be expected to be qualified to teach what they have learnt; but, during a length of time, more or less considerable, antecedent to that of their departure from the school, will actually have been employed in this same all-comprehensive work. At this time, if, in point of legal maturity of age, as well as in all other points, any one of them should be found competent to such an undertaking, so much the better. But even if, in respect of those requisites, the school should not happen to afford any individual who was, at that time, competent; yet, if so it were, that in point of intellectual maturity, as well as appropriate proficiency, any one such scholar should be found sufficient, the temporary legal deficiency might, as under the care of the already established Societies, find an adequate supply in the assistance of some trust-worthy friend.

X.: Terms of Contribution, &c.

For the erection, fitting up, and furnishing of the School-house, with the necessary out-buildings and other out-works, the following are the terms and conditions on which the contributions of well-wishers are solicited:—

1. Contributions to be in shares of £10 each.

2. By any person any number of such shares may be subscribed for: several such shares are subscribed for by each of the above proposed Conductors.

3. For every such share, interest, at the rate of 5 per cent. shall eventually be allowed, as per Article 13.

4. Of the money, received as per Article 7, after defraying charges, as per Article 7, together with House expenses, and pay to Master, Mistress, and paid Teachers, the whole surplus, except such as shall be deemed necessary to be kept in hand for the contingencies of the year, shall, in the first month of every year, be invested in Government Securities, to serve as a sinking fund for the reimbursing to Subscribers, in equal proportions, the money respectively advanced by them: such reimbursements to be made, each time, by instalments of 10 per cent., so soon as the aggregate of the money so applicable shall have risen to that amount.

5. Any sum, of less amount than a share, will, if offered, be thankfully received: but, whether by itself, or added to the amount of a whole share, on no such additional sum will Edition: current; Page: [59] it be understood to be expected, that interest, or unless required at the time of the advance made, reimbursement money shall be paid.

6. Upon the amount of their respective contributions, the proposed Conductors of the Institution reserve to themselves, in the shape of interest and reimbursement money, the same advantages as, and no other than, those which, as per Articles 3 and 4, are promised to all other Contributors.

7. Of the School-money to be required, the exact amount cannot as yet be fixed. Four pounds is at present looked to as a minimum, eight as a maximum. The amount must, of course, be different, according as, in the terms of the undertaking, the expense of slates, pens, books, ink, paper, maps, charts, and other implements of instruction, together with the hire of such as need not, or cannot, be purchased, is or is not included. In general, parents would, it is presumed, be desirous of seeing themselves at a certainty, in regard to this and every other expense.

8. With or without subscribing for shares, another mode in which encouragement may be afforded is—by an engagement to send to the School, for and during a specified length of time, in the event of its being opened, one or more Scholars. In this way, with or without sending a child of his own, any person of opulence may, by engaging for the child of another, confer, at one and the same time, a public and a private benefit, at one and the same expense.

9. To afford to Contributors, and eventually to Parents and Guardians, the assurance, that the undertaking will not be hastily abandoned,—for the term of the first three years, to be computed from the time when the Parents or Guardians, of any number of scholars not less than fifty, shall have signed an engagement to pay, at such rate as shall at that time have been fixed, for and during such time as shall have been fixed, for the schooling of their respective children, the proposed Conductors engage, jointly and severally, to carry on the proposed School, and in case of loss, to charge themselves with such loss.

10. For this purpose, so soon as the School-house, with the appurtenances, shall be in readiness for the reception of scholars, notice of such readiness will be given by advertisements in the London daily papers. A space will be provided, in which, without interruption to the business, subscribers and parents of scholars, being recognised as such by recollection of their persons, or by transferable tickets, which will be given for that purpose, will have a perfect view of the whole business of the School as it is going on. If, from any persons at large, any admission-money be accepted, the amount will be no more than may be judged necessary to keep out noisomeness and mischievous wantonness; and will be applied to the use of the Institution, as above, Article 4.

11. Of all moneys received, and the disposition made of them, accounts will be published yearly, or oftener, and at any rate within the first week of each year, in some one or more of the London daily papers.

Section I.: Plan of this Essay.

Deplorable it surely is, and, to a first view at least, not less extraordinary, that, for some of the most extensive, and most frequently mentioned, divisions of the field of Art and Science, even at so advanced a stage as that to which the human mind has already reached in its travels on that field, no tolerably expressive denominations should be to be found in the appropriate part of language.

Of language:—meaning, of course, the one which is here made use of; and which will Edition: current; Page: [64] not be denied to be one of the best cultivated languages which the present time affords; nor, in this particular, will the present state of any other language be found, it is believed, much more favourable.

That this unaptness has really place in the language, that real and practical inconveniences are among the actual results of it, and that, although not perhaps completely susceptible, it is, however, not altogether unsusceptible, of a remedy: such are the positions which it is the object of the following pages to present to view.

But, on the part of the intellectual subject or object in question—viz., the nomenclature of the aggregate body of the arts and sciences, in other words, the system of Encyclopedical nomenclature—this unaptness, in what does it consist?—Answer. In this: viz., that the nomenclature in question is not, either in the degree in which it is desirable that it should be, or in the degree in which it is capable of being made to be, subservient to those useful purposes, to which an instrument of this sort is capable of being rendered subservient.

In respect of any such useful purposes, to what immediate cause will any such failure, on the part of the subject in question, be to be attributed?—Answer: To its being deficient, in respect of one or more of those properties, which, ere it can be in a complete degree rendered subservient to those same useful purposes, it is necessary that it should possess.

In so far as, in any degree, it fails of being possessed of those same properties, and thereby of being capable of being rendered subservient to those same purposes, it will be found chargeable with certain correspondent imperfections, or points of imperfection.

To these several imperfections, if in the correspondent purposes, there be anything capable of entitling them to any such appellation as that of useful, it cannot but be desirable, that correspondent remedies should be applied. What then are they respectively, those purposes, those properties, those imperfections, and, if any such there be, those remedies? To find such answers as can be found, for this string of connected questions, is the object of the ensuing pages.

To a disquisition of this sort, inserted in such a work as the present, one very obvious objection presents itself. This is—that it is too abstract and abstruse; too logical; too metaphysical; or by whatever other epithet, for the purpose of condemnation, it may happen to it to be designated—too abstruse for the generality of readers, even of those by whom a course of education of the literary cast, carried on upon any of the customary plans, has been completed.

For this objection, however, an answer—which (it is hoped) will be found neither in point of fact incorrect, nor in point of argument irrelevant—is in equal readiness; at the conclusion of the Chrestomathic course, it will not be too abstruse for the comprehension of a Chrestomathic scholar.

What is there in it that, even to these striplings, should render it too abstruse? Is it the nature of the subject? Those parts excepted, which respectively regard general Ontology and Pneumatology—subjects, which for reasons already intimated, it has been found necessary to forbear including in the course—no one of all the subjects touched upon in it can be pointed out, which will not have been rendered altogether familiar to their view.

Is it then the language, from which, for giving expression to some of the leading ideas, words have been borrowed? Not to speak of its being the language constantly and universally drawn upon for such purposes, long before the scholars are arrived at this concluding stage, this same language will, in their eyes, have been stripped of all its terrors. Of those appellatives, for which custom has concurred with abstract convenience in resorting to a dead and foreign language, the interpretation will here be found all along subjoined; and in this very interpretation may the scholars, long before the conclusion of the course, have found matter for one of their exercises. True it is, that, as there has so often been occasion to observe, a hard word—a word belonging to a family of words, of which no other member is as yet known, constitutes, in every field over which it hangs, a dark spot; a spot, to which no eye, among those in which it excites the notion which that word is employed to express, can turn itself, without giving entrance to sentiments of humiliation and disgust. But, at the time in question, to the eye of a Chrestomathic scholar, in no part of the whole expanse of the field occupied by this sketch, will there be any such thing as a dark spot: to the original darkness, light will, in every instance, have been made to succeed.

Such is the objection, and such the answer. Here, however, if not before, comes another question: Of such an exhibition where is the use? But, to a question of this sort, in the present instance at least, the answer will obtain a much better chance for being satisfactory, if postponed till after the thing itself has been brought to view, concerning which it is asked, what is the use of it?

Section II.: Purposes to which a denomination given to a branch of Art and Science may be applied—viz., Ordinary and Systematic: Properties, desirable in it with a view to these purposes.

Ordinary and Systematic, applied to the purpose which, in the giving a denomination to a branch of art and science, has been in view, these adjuncts will, it is supposed, be found tolerably explanatory of themselves. Ordinary purpose, the presenting to view the contents of the particular branch which it denominates. Systematic, the purpose which is in Edition: current; Page: [65] view, where the denomination in question is one of a number of denominations, brought together in such manner as to exhibit to view certain relations, which the several branches so denominated, and thereby their respective contents, bear to each other: relations, for example, of agreement and diversity, or relations of dependence.

Accordingly, for the designation of the purpose, just described by the name of the ordinary purpose, the term non-systematic might, with equal propriety, be employed.

From the purposes to the accomplishment of which it is directed, follow the properties which it is desirable it should possess.

I. On the part of the denomination in question, for both the above-mentioned purposes, the two following properties may be stated as requisite.

1. Of the contents of the branch of art and sicence which it denominates, it should present to view—to the view of as many persons as possible—a conception as clear, correct, and complete, as by, and in the compass of, a single denomination,* can be afforded.

2. By this means, in relation to every less extensive branch of art and science that can be proposed, it should obviate the question—whether, within the compass of the more extensive, such less extensive branch is or is not included: it should obviate this question—i. e. in case of doubt, it should furnish the means of removing it, or, (what is better,) prevent the rise of any such doubts.

II. For the systematic purpose, the following is an additional property which presents itself as requisite.

It should (i. e. the denomination should) be so constructed, as, in and by its conjunction with other denominations, to display upon occasion, and that in as clear, correct, and complete a manner as possible, the several relations which it bears to the several other branches of art and science included in the same system: the relations, viz. in respect of identity of properties, on the part of the respectively contained particulars, on the one hand, and diversity of such properties on the other: that so, in the instance of every branch of art and science, comprehended in the system, it may, to the greatest extent possible, be apparent in what particulars they respectively agree with, and in what they differ from, each other.†

By these means, and by these alone—on these terms, and on these alone—is any conception that has been framed, delivered, received, or entertained of the whole system of arts and sciences, the whole encyclopædical system, as it is called, capable of being rendered a clear, correct, and complete one.

Thus, and in this way is shown, not only identity, in so far as identity, but diversity, in so far as diversity, has place. In this way, therefore, is performed, in regard to each branch of art and science, that, and more than that, which is performed by algebra, in regard to numbers. The wonders exhibited by that mysterious art, by what means is it that they are wrought? Only by showing, in each individual Edition: current; Page: [66] instance, the identity which has place, as between the import, conveyed at the outset by those extraordinary signs, which, as the instrument of its discoveries it employs, and some one or other of the always manifest imports, conveyed by those ordinary signs, of which common arithmetic makes use.

By the mutual lights, which these words are thus made to reflect upon the import of each other—by this means is, and by this means alone can be conveyed, in relation to the subject which they are employed to bring to view, the maximum of information: the greatest quantity of information capable of being brought to view, in and by the number of words thus employed:* the maximum of information in the minimum of space.

Section III.: Imperfections incident to a denomination of this sort: viz. 1. Unexpressiveness; 2. Misexpressiveness.

Correspondent to the properties, which it is desirable that a denomination attached to any branch of art and science should possess, are the imperfections of which it is susceptible. An imperfection will be imputable to it, in so far as, by failing to possess any one or more of the above-mentioned properties, it fails of being applicable with advantage to one or more of the above-mentioned purposes.

Imperfections, exhibited by this or that one, of the several denominations, considered by itself; imperfections, exhibited by the whole assemblage of them taken together, considered as a whole—to one or other of these heads will all such imperfections, it is believed, be found referable.

Unexpressiveness and Misexpressiveness—to one or other of these two heads, it is believed, will be found referable all such imperfections, of which any such denomination, taken singly, and considered by itself, will be found susceptible.

The purposes, to which it is desirable that a denomination of the sort in question should be capable of being made subservient, have just been brought to view: in so far as it simply fails of being subservient to those purposes, it is unexpressive, simply unexpressive.

Of the name, employed for the designation of any branch of art and science, the design and use is, to convey a conception, as correct and complete as by so narrow an instrument can be conveyed, of the nature, and, to that end, thereby of the subject, or subject-matter, of that same art and science: and this, in such sort as, when and as often as, in relation to any subject that happens to be proposed, a question shall arise, whether it does or does not belong to the branch in question, to suggest a true and clear answer, either on the affirmative or on the negative side.

If, instead of simply failing to convey any such instructive conception, it does indeed present a conception, but that conception altogether foreign to the subject, and thereby, in so far as it is actually entertained, erroneous and delusive, then it is, that, instead of being negatively and simply unexpressive, it is positively misexpressive.

Be the subject in its own nature what it may—and, on the other hand, the name applied to it, what any one will—true it is, that, in the course of time, the name, how completely unexpressive so ever, and even misexpressive, will become expressive.

To this observation no denial, or so much as doubt, can be opposed; and hence it is that, by names in the highest degree, not merely unexpressive but misexpressive, the functions of names are performed, the purposes which are in view in the use of names to a certain degree answered.

If the misexpressive name in question be a name, by which, when first brought to a man’s view, the branch of art and science in question is presented—much more if it be the only name by which it is ever presented to him—on this supposition, a question (it must be confessed) altogether natural is, of this supposed original misexpressiveness, what, if any, is the inconvenience? At first mention (continues the argument) true it is, that the conception it presented was, by the supposition, an erroneous one: but moreover by another part of the supposition, the conception which has at the long run come to be conveyed by it, conveyed to the very person in question, is a correct one: for, by this name it is, that whatsoever conception he has cause to entertain of the subject, has been conveyed to him; and, in point of fact, by names originally as unexpressive as can easily be imagined, have conceptions no less correct than those which have been conveyed by the most expressive names, actually, as it will be easy to show, been conveyed.

Plausible as it is, to the objection opposed by this question, an answer, which it is believed will be found no less plain and clear, than decisive and satisfactory, presents itself.

1. In the first place, by the supposition, a length of time there is, during which, instead of the subject, of which it is desirable that it should convey the conception, the subject which it actually presents is a different one. So long as this state of things continues, every proposition, in the composition of which the misexpressive name in question has a place, is a self-contradictory one. So long then as this self-contradictoriness, and the confusion, of which it is essentially productive, continues, so long the inconvenience, nor is it an inconsiderable one, continues to be felt: and it is only after a lapse of time, more or less considerable, that, the new conception having at length in a manner Edition: current; Page: [67] wormed out the original one, the inconvenience ceases to be felt.

2. In the next place, of the sort of name in question, another use, it has been already observed, is, to obviate doubts in relation to the extent of the field belonging to the branch of art and science in question: i. e. whether such or such a less extensive district, in whatsoever manner designated, especially if it be a newly discovered, or newly distinguished district, be included in it. In this case, by what rule or mark shall the answer be guided and determined? By the name, considered in itself, i. e. considered in its original import merely, no true light, but instead of it a false light, is afforded; and, as to the light afforded by mere usage, by the supposition, no light of this sort hath as yet begun to show itself.

Attached to the use made of misexpressive names, here then are two inconveniences; two distinguishable and undeniable inconveniences, which will be found to have place, in so far as, for the designation of any of the leading branches of art and science, any such improper and unfortunately chosen denominations continue to be employed.

Natural History, Natural Philosophy.—It will presently be seen, in how flagrant a degree both these denominations, both of them names, by which two main branches of art and science are wont to be designated, names in constant and almost universal use, are misexpressive.

By this imperfection, if any credit be to be given either to experience or to report, the amount of the inconvenience produced is by no means inconsiderable. Great is the length of time, during which it is not without extreme difficulty, nor till after great perplexity, that, in the mind of the beginner, especially if he be a very young beginner, the connexion between the misexpressive general name, and any of the particular matters meant to be designated by it; viz. the subordinate branches included under it, or any of the subjects appertaining respectively to those branches, can be formed.

So likewise as to the other inconveniences: to this likewise the like observation will be found applying with equal truth. This or that less extensive branch, is it to Natural Philosophy that it belongs, or to any, and what other more extensive head? No criterion, no source of guidance, being to be found in the name itself—viz., in its original import—mere accident determines. But in the instance of different persons, the determinations made by accident are different. Accordingly that less extensive branch, (Chemistry for example,) which in the view and language of some persons, is a branch of Natural Philosophy, in the view and language of other persons, is not a branch of it.

Thus it is that, the boundaries of the main compartments being indistinct, the conception entertained of the whole field of art and science is, in the instance of every mind, more or less inadequate, and either indeterminate or erroneous.

Thus much as to the imperfections, incident to the denomination of any branch of art and science, considered by itself. Now as to such imperfections, as do not apply but to the case, where the whole multitude of them, or a considerable part of that multitude, are collected together, and considered together, in the character of an aggregate.

As often as they are thus considered in conjunction and with reference to one another, the purpose for which they are thus considered may be termed a scientific, or Encyclopedical purpose; and with reference to this extraordinary purpose, all others may be distinguished by the appellation of ordinary.

In so far as it is to an Encyclopedical purpose that these several objects, the several branches of art and science, are considered, it is for the purpose of obtaining and communicating a view, as clear, correct, and complete as possible, of the whole field of thought and action, and therein of the whole field of art and science; and, to this purpose, a view of the several characters, i. e. characteristic circumstances, by which the several component branches of that ideal whole, are on the one hand assimilated to, on the other hand distinguished from, each other.

Learners and teachers (shall we say) or Teachers and learners? for, on the occasion of the mention now to be made of them, it seems not altogether easy to say, which of these two correspondent classes should be put foremost. Be this as it may, to the situation of both these two correspondent and contrasted classes it is, that in the framing of a sketch for the purpose in question, in a word, for the framing of an Encyclopedical sketch, the attention of the operator should be directed. As far as any separation can in practice be made, it is by the situation of learners that the principal demand for attention is presented: for all teachers must in the first place have been learners; nor, at any subsequent period can teachers exist without learners; whereas learners may exist, and, in so far as individuals are self-taught, do exist, without teachers; and, where both classes have place together, and at the same time remain distinct from one another, the class of learners may, and naturally will, be much more numerous than the class of teachers.

Nor will the class of persons, to whom, in the character of learners, an apposite and expressive system of Encyclopedical nomenclature may be of use, be found to be so narrow as might at first sight be imagined. To any one, whose subsequent pursuits were destined to be confined within the limits of ever so narrow a branch of the field, if not the whole, various other parts of such a system will be found, of which a conception more or less detailed will not be found to be altogether useless. Of no one part can a man’s conception fail of being the stronger and the clearer, Edition: current; Page: [68] the stronger and clearer his conception is of such or such other parts, which, by means of those properties, whereby they are respectively assimilated to it, and contrasted with it, contribute to reflect light upon it, and by this means place it in the clearer point of view.

To this class (to speak more particularly) will be seen to belong all those persons, by whom the benefit of the proposed system or course of Chrestomathic education will have been partaken of. With few if any exceptions, initiated, as they will be, in every useful branch of art and science,—strange would be the inconsistency, were any such determination taken, as that of forbearing to present to their view those relations of mutual agreement and distinction, by means of which these several branches receive each of them light from, and reflect it upon, every other. For, it is thus, and thus alone, that the mind can be endowed with, and rendered conscious of, that animating vigour, by means of which it feels itself able, with an assurance of success and mastery, to enter and operate with effect, upon any and every part of it, towards which the course of its pursuits may at any time happen to be directed.

But, on the proposed plan, along with the class of learners will be augmented the class of teachers: and that in a much larger proportion, than any which till of late has been in view. For, in the instance of every one of the branches of science thus taught, so it is that, by a very considerable proportion of the class of learners, the function of teachers will, even before their own term of learning is in respect of that same branch fully expired, be taken in hand and exercised: so that, to the extent of this large portion of the whole number of learners, the only line of separation between the two classes, is that which will have been drawn by the hand of Time.

Of the imperfections, of which a system of nomenclature for the various branches of art and science may be seen to be susceptible, when considered with a view to none but the ordinary purposes, as above explained, a conception may presently be formed, and has accordingly been already endeavoured to be conveyed. But, of the imperfections, of which the like system may be seen to be susceptible, when considered with reference to Encyclopedical purposes, as above explained,—no conception can be formed, till a conception has been formed of the particular form, which it is necessary a system of this sort should be made to wear, in order to possess—and that in the highest possible degree of perfection—those properties, a general intimation of which has just been given: viz. that in which, in relation to each branch, are brought to view the circumstances, in respect of which it agrees with, and those in respect of which it disagrees with, every other.

Of a system of this sort will here be given a general idea; and that followed by an exemplification, which, though particular, will be a very extensive one,—not embracing merely, but outstretching, the whole of the proposed field of Chrestomathic education. But, in the meantime, that the nature and existence of the demand, for a reform of some sort, in the nomenclature employed upon the subject, may be the more distinctly perceptible,—an exemplification will be given of its inaptitude, even with reference to the purposes, above distinguished by the name of ordinary purposes:—viz. in the instance of those names which are in most frequent use.

Section IV.: Inaptness of the appellatives Natural History, Natural Philosophy, and Mathematics.

1. The branch of art and science for the designation of which the compound appellation Natural History is as yet the only one in use, is that which has for its subject matter, in general, including bodies of all sorts, considered in respect of those modifications, which are found exemplified by it, before any operation has been performed upon it by human art, under the direction of human science:* or in other words, (if, for familiarity’s sake, notwithstanding the unapt floridness of the expression, it should be deemed advisable to employ, as usual, the name of the well-known fictitious personage, Nature,) in the condition in which it has been found placed by the hands of Nature—uncontrolled and unassisted Nature.

Of these bodies—i. e. of matter, in all such of its forms with which we have in any way or degree any acquaintance,—the aggregate is composed in the first place of our Earth, in the next place of all the other bodies, of which our World is composed: of our Earth in the first place, no others being of any importance to us, otherwise than with reference to that, “in which we live, and move, and have our being.”

Of this earth of our’s, the matter is either in the form of matter altogether lifeless; matter endowed with life, but without feeling; or matter endowed with life and feeling both. In and by the several appellatives, Mineralogy, Botany, and Zoology, all of them single-worded—all of them in familiar use,—the primary divisions of the branch of art and science here in question, are aptly enough expressed. And if, for the designation of that remaining branch of the art and science in question, which has for its subject the remainder of those modifications of matter with which we have any acquaintance, the term Uranology, as above,† or even the term Astronomy, be employed,—in either case, to the nomenclature thus bestowed Edition: current; Page: [69] upon these primary branches of the stock of art and science in question, no considerable objection presents itself as opposable.

Not so in the case of the whole aggregate, of which these are the divisions. Of the two words,—the first an adjective, the other a substantive,—of which the compound appellation Natural History is formed,—it found, at the time of its formation, the substantive History already appropriated to the designation of a branch of learning, having for its subject those states of persons and things of all sorts, and those events of all sorts, that have been known or supposed to have had place in times past: present time either being altogether excluded, or its history being but as it were a point, in comparison with the time of history which it closes. Adding the word natural, say Natural History, the result is, that, for the import, designated by this appellative, antecedently to the establishment of that usage from which it has received an import so widely different, we have this, viz. the natural account of those states of persons and things, and so forth, and of those events, and so forth, which had place in times past.

Now, with what propriety, to any one of the above-mentioned so aptly denominated divisions, of the branch of art and science itself thus unaptly denominated,—with what propriety, to Mineralogy, to Botany, to Zoology,—can the term Natural History, consideration had of its original and proper import as thus developed, be applied?

II. The branch of art and science, for the designation of which the compound appellation Natural Philosophy is in use, is that which has, for its subject, matter in general, considered in respect of such modifications as it has been made, or may be expected to be made, to undergo, by human art, under the guidance of human science: with the addition, perhaps, of such properties, as, by means of changes made in it by the application of that same mental instrument, have been discovered to have been already belonging to it.

Taken by itself, Philosophy is the love of wisdom. Adding the word natural, say Natural Philosophy, and, for the import designated by this appellation, antecedently to the arbitrary usage, established in this case as in that other,—we have this, viz. the natural love of wisdom.

That either in the study of Mechanics, or in that of Chemistry, or in the study of any of those particular branches of art and science, which are formed by the application of these general and theoretical branches to the various practical ones to which they are subservient, is there any want of capacity to afford gratification to an affection so laudable as that of the love of wisdom,—is not here by any means meant to be asserted, or so much as insinuated. But, not to speak of Oratory, Poetry, or any of the Fine Arts,—in the study of the art and science of Legislation, or in the study of the art and science of which Private Morals is the subject, is there any less room for the manifestation of the love of wisdom, or of wisdom itself, than in the study of machines, or in that of the various methods of compounding, decompounding, and recompounding, the matter, of which stones, plants, and animals, are respectively composed?

III. The branch of art and science, for the designation of which the term Mathematics is in use, is that which has for its subject quantity in general, considered with or without relation to form or figure: quantity in general, that is to say, as well matter as void space, they being considered respectively in relation to quantity, with or without relation to figure: void space—that is, space considered as void, or rather without consideration had of its contents: for, as to any determinate portion of space, determined by determinate boundaries,—and, within those boundaries not containing any the least particle of matter whatsoever,—an example of any such object would not, it is believed, be very easy to find.

Taken in its original import, Mathematics denotes anything that is learnt, or considered as capable of being learnt. It therefore is—or at least in that its original import was, capable of being, with no less propriety, employed in the designation of any one of those existing, or those about to exist, branches of art and science, comprehended or not, in the most comprehensive and copious Encyclopedia,—than in the designation of the particular branch, to which, by long and learned usage, it has thus, in these later times, become appropriated:—of the art of legislation, or the art of push-pin, no less than of Geometry and Algebra.

Upon all the above-mentioned three denominations, will not only the imperfection of inexpressiveness, but, in the instance of the two first of them, that of misexpressiveness, be found chargeable.

Running on in perpetual contradiction to the original import, a false account of the subject is the account, which the two appellations, Natural Philosophy and Mathematics, are, both of them, continually giving of it.

But, though in all these instances the proposition involved in the appellative is equally false, yet the falsehood so involved is not, in all these instances, equally pregnant with practical inconvenience.

In the instance of Mathematics, no very considerable practical inconvenience seems observable.

To such persons as are altogether unacquainted with the primary general import of the word, it conveys not any import at variance with that which, in the instance in question, it has acquired from particular usage; and, even to the eyes of persons acquainted with such its primary import, that general import Edition: current; Page: [70] has to such a degree been covered as it were, and by degrees even pushed aside, by the particular import attached to it by particular usage, as to be scarcely ever in use to present itself.

In the case of Natural Philosophy, the inconvenient effects of unexpressiveness, coupled as it is with misexpressiveness, have manifested themselves in a manner much more conspicuous and incontestable. To the same branch of art and science to which some attach the name of Natural Philosophy, others attach the name of Experimental Philosophy. In the present instance, both these terms being, as above, misapplied, are they—in the modern import of the former of them,—are they, or are they not, synonymous with each other? In relation to the subject to which they respectively apply, no intimation being given by either of these appellatives,—this being the case, to a question to the above effect, who shall undertake to furnish an answer?—thus much being pretty clear, viz., that for no such answer are any data afforded by the primary import of either of these appellatives.

Astronomy—though, properly speaking, it should in part be considered as referable to Natural History (viz., in so far as it consists in simple observations, unaccompanied with those observations and calculations, which, as in the case of Chronological Geography and Uranological Chronology,* are applicable, and actually applied, to practical use,) seems commonly to be considered as referable to Natural Philosophy, and to that alone. Be it so; but is it then referable to Experimental Philosophy? The light that issues from them, yes; but the stars themselves, are they, like the star-fish named from them, are they taken, can they be taken, for the subjects of experiment?

Chemistry, this branch of art and science does it, or does it not, belong to the domain of Natural Philosophy? Yes, say some; for, under that appellation they include it. No, say others; for, under that appellation they do not include it.

Belonging, or not belonging, to Natural Philosophy, does it not at any rate belong to Experimental Philosophy? In the whole of Chemistry, not to say any more, taken from beginning to end, is not there full as much of experiment as in any part of Mechanics?

Once more, does it, or does it not, belong to Natural Philosophy? On any such ground as that of reason and analogy, the question is manifestly unanswerable, and any dispute produced by it interminable. Why? Because, while one of these names—viz., Natural Philosophy, is not only unexpressive but misexpressive, the other, Chemistry, is also unexpressive. By Chemistry—an Arabian word, of which the origin has always been covered by a cloud—no intimation whatever, either of the subject-matter, of the sort of operator, or of the nature of any operations performed, is afforded.

By some Institutionalists, Chemistry, as above observed, is not considered as included in Natural Philosophy. Why? Because, before Chemistry had begun to find teachers, before any more than a few scattered fragments of the art and science could be so much as said to have existence, Natural Philosophy had, for a long time, been in use to be taught. Therefore, when Chemistry came to be taught, this new branch was considered as a branch of art or science, wholly distinct and independent, not included in that old one.

Section V.: Cause or Origin of this Inaptitude.

Of the thus extensively prevailing inadequacy, should the source be asked for, it may be found, it is believed, at no great depth beneath the surface. It may be descried in the difference between the respective extents of the several divisions of the field of art and science,—i. e., of the respective masses of their contents,—in the state in which they now present themselves to view, as compared with the extents respectively possessed by them when, for the first time, the degree of cultivation, which they had respectively received, suggested the convenience of employing a certain name, for the purpose of binding together in the mind such of their contents, with which at that time an acquaintance, more or less correct and extensive, had been formed. In each instance, numerous, insulated, and dispersed, must have been the particular observations and experiments made, before it occurred to any one to give to the aggregate assemblage of them a common name of any kind, and thus to bind together the contents of that aggregate by one common tie. Even when this instrument of connexion and elucidation came at length to be employed, it would at first be either altogether uncharacteristic of the objects which it served to designate, or, if amongst them there were any, at all, to which it bore any such natural relation, the number of them would, in comparison with the number of those to which it bore not any such relation, be very small.

Take, for instance, that branch of art and science which still bears the name of Electricity. Of the word Electricity, the root or basis is a Greek word, which signifies amber: had it been from the Latin that the word had been derived, it would have been Amberism. Why Electricity or Amberism? Only because, of such a multitude of sorts of substances as that by which, at present, upon the subjecting them to the same sort of operation (viz., rubbing,) the same appearances (viz., the causing light bodies first to move towards them, and then to recede from them) are exhibited, amber happened to be the first, in which the existence of this property was observed.

Even Magnetism, though to the purpose of Edition: current; Page: [71] calling to view, by means of its original signification, the phenomena, for the designation of which it has now for a long time been employed,—though to this purpose it is so much less inadequate than Electricity, has had its original boundaries far outstretched by observations made at various later dates. By the import originally attached to it, the intimation given is, that the properties, of which it takes cognizance, belong exclusively to the naturally existing mineral, termed, in Greek and Latin, Magnes, and, in English, the Loadstone.

Since those days the same properties have, however, been found to be capable of being given to iron,—a simple metallic substance, which is but one of two or more ingredients of which the loadstone is composed,—and to belong naturally to nickel, another metallic substance, which, with the exception of this property, and those that are common to all metals, has not been found to have anything in common with either of those two other substances.

In the instance of these two branches of art and science—both of them included in the domain so unexpressively denominated by the compound appellative Natural Philosophy—we have two names, which, however imperfectly, are still in a certain degree characteristic and expressive; designative of a portion, though not of the whole, of the contents of the branch of art and science which they are respectively employed to denominate. In the instance of Galvanism, the sign is altogether uncharacteristic, with relation to every one of the objects which it is employed to signify. By an Italian of the name of Galvani, within the memory of multitudes now living, observation was made of certain phenomena, in which no analogy to any other class of phenomena was for some time discovered. No other object, to which they could be said to bear any particular relation, being known,—at the same time that the person, by whose sagacity and ingenuity they had been in part observed, and in part discovered, being known,—it was from him they took their name. The phenomena observed or discovered by Galvani, and presently, for shortness, Galvanism, was the name given to them by the Natural Philosophers of that day.

This imperfection is not peculiar to the physical branch of art and science:—in a large proportion it is shared with it by the ethical.

From like causes proceed everywhere like effects. Hence, in the field of Government, the multitude of Offices, by the names of which not any the slightest intimation is conveyed of the nature of the operations performed by the possessors.*

Section VI.: Course to be taken for framing the most perfect and instructive System of Encyclopedical Nomenclature that the Nature of the Case admits of.

The nature of the subjects themselves, and the nature of the words or terms employed in giving to the aggregate mass of them, in all its diversifications, a system of nomenclature, and, by means of such nomenclature, a set of divisions, and thereby a scheme of distribution and arrangement—on these two circumstances, it is believed, will the aptitude of the work, with reference to its purposes, be found to depend.

I. As to the subject, for the particular purpose here in question, it is only in so far as concerns its primary and most extensive divisions, that an acquaintance with it will be found to be very material: with its details no other acquaintance will be found necessary, than that, by the want of which a man might be led into misconceptions concerning the general nature of the compartments and divisions in which they are comprehended: viz. in such sort, as, by means of some ill-chosen appellative, to ascribe to this or that one of the contents, this or that property, of which in reality it is not possessed.

In the choice made of the words, will be found to be included, two intimately connected indeed, but perfectly distinguishable particulars: viz. in the first place, the choice of such appellatives—single-worded and many-worded together—as, by the extent respectively belonging to them, shall be suited to the purpose of giving expression to all such divisions or parts of the subject, or aggregate, as, at each step in the progress of the division, shall be proposed to be marked out; in the next place, the tongue or language, of which choice shall have been made, for the furnishing the assortment of words required for the supply of that demand.

1. As to the extent covered by the respective appellatives, it will, in the ensuing sketch at least, for all but the last step taken in the course, be such as, when they are arranged one after another, in appropriate order, will be seen to give to the mode or scheme of division marked out by them, the character of an exhaustive one, and that, in respect of the number of the parts produced by each act of ideal division of the aggregate, considered for that purpose as a divisible whole,—the sort of scheme, which has been styled sometimes, from the Greek, dichotomous; sometimes, from the Latin, bifurcate; literally rendered in English by the word two-pronged, as applied to a fork: for, as will be seen, it is in and by this mode, and this alone, that all the purposes, which, on this occasion are of a nature to afford a practical use, can be accomplished. As to the considerations by which the choice made in Edition: current; Page: [72] favour of this mode was produced, a view of them will presently be given: but, that they may be the more clearly apprehended, it has been deemed advisable to bring to view, in the first instance, an exemplification of the sort of work to which they will have to make reference.*

Small, it is true, is the number of steps to which, accompanied with a correspondent system of nomenclature, this transcendently instructive and useful scheme of division can, consistently with any net balance on the side of advantage, be pursued: the number of words being so great, and not only the labour necessary to the forming of such a system, but even the labour of following it up when made, being such, as, after a comparatively small number of steps taken in this career, to threaten to become intolerable. But, against the carrying it on to whatever length it is capable of being followed up to with clear advantage, every impracticability, that may be found to attach upon an ulterior pursuit of it, will not be found to oppose any reasonable objection: and a task, for which neither the mind of the writer, nor the mind of the reader, may be ripe at one period, may find both minds sufficiently prepared for it, at a more advanced point in the line of time.

As to the language, the Greek presents itself as being, upon the whole, beyond comparison, the best adapted to this purpose: and this so clearly, as to be the only one which, on this occasion, there can be any use in holding up to view.

Reason and Custom—Reason, in this instance, the parent of Custom—join in the affording of this assurance. Of all known languages, the Greek is assuredly, in its structure, the most plastic and most manageable. To such a purpose as the present, upon a scale of any extent, it is the only language which it has been customary for men to draw upon for this purpose: customary, not only in the English language, but in the language of every other nation forming a part of the European system: or, in a word, as, to this purpose, may be said for shortness, and without any very material injustice, in the language of every well-instructed nation upon earth.

Of the sort of work proposed to be executed, the subject has already been brought to view, and its limits marked out, it is hoped, with that degree of precision which the nature of the case admits of: viz. of the whole field of thought and action, that part which constitutes the field of art and science: the field itself, or, what comes to the same thing, (both expressions being necessarily figurative, names of fictitious entities,) the aggregate of its contents.†

Of the division to be made of this field, or, (what comes to the same thing,) the distribution to be made of its contents, where shall we look for the source?—the primary source, by the choice of which the choice of all ulterior sources, should any such be added, will naturally be influenced at least, if not determined? Where, but in the different natures of different parts of this field—of different portions of its contents?—in a word, in the nature of the subject—the common subject of all these branches of art and science—and in the different natures of the several different parts of that subject, on which these several branches have to operate? So far as it is from this source that the division is made—the principle of division deduced—correspondent to each branch of the subject is the branch of art and science, by which it is operated upon: and, conversely, correspondent to each branch of art and science is that branch of the subject on which it operates.

In the preface, written by D’Alembert, and prefixed to the French Encyclopædia, under the title of Systême figuré des Connoissances Humaines—Figured System of Human Knowledge,* a systematic Table or Map is given, accompanied with a paper, entitled, Explication détaillée du Systême des Connoissances Humaines.

In that sketch, what is the declared subject of the work?—Art and Science in conjunction?—No: but sciences alone, to the exclusion of arts; for surely, under the French word connoissances, arts are no more included than under the English word knowledge, or the English word science. Yet in the Table itself the words Art and Arts occur in many places.

Again, the source of division, or, to begin with the first division which presents itself—the source of that leading division—what is it? Is it the nature of the subject—the different natures of the several different branches of the subject—on which the corresponding branches of art and science have to operate?—No: but the nature of the faculties, by means of which the subject, in its different parts, is (it is supposed) operated upon.

Lastly, the plan or scheme of division,—considered in respect of the number of branches, which are respectively the results of the several successive acts of partition or distribution, performed upon it,—what is it? Is it, as above proposed, regular and bifurcate? the number, at the first step, two, and at every step the same?—No: but at the first step trifurcate: and, after that, the number at each step varying, to the number of half-a-dozen or more.

Such is the scheme, or plan of division, pursued in that justly celebrated work: in these may be seen a part, and but a part, of the whole number of its incongruities: and, of some of the practical inconveniences resulting from some of these logical incongruities,—if, on the ground of science, confusion, and on the one part misrepresentation, and on the other Edition: current; Page: [73] part misconception, belong to the category of inconvenience,—it will be the endeavour of the next section to give a view.

Section VII.: D’Alembert’s Encyclopedical* Map or Tabular Sketch—its Imperfections.

Of the sketch given by D’Alembert, the leading principles are—as he himself has been careful to declare, taken from that given by Lord Bacon. Had it been entirely his own, it would have been, beyond comparison, a better one. For the age of Bacon, Bacon’s was a precocious and precious fruit of the union of learning with genius: for the age of D’Alembert it will, it is believed, be found but a poor production, below the author as well as the age.

Prudential considerations suggested to the French Philosopher the precaution of seeking shelter under the mantle of the foreign sage. But of this perhaps in another place.

Ingenious as, in several parts, and in several respects, it would, upon a particular examination, be found,—smoke, rather than light, will, upon the whole, be seen to be the result of it. At the very first step, the whole field, it will be seen, is involved in an all-obscuring cloud: a cloud too thick for any ulterior operation to be capable of dissipating.

Its principal merit and use will, it is believed, be seen to consist in the having formed, and presented to view, a general conception of a work of this sort,—and the having placed together, under one view, the whole stock of the materials, at that time known, to belong to it and to require to be employed in the composition of it.

Taking the work in the form in which it is exhibited by D’Alembert, the following are among the imperfections, which have presented themselves as chargeable upon it,—

1. The very subject of the work, inadequately designated.

2. The primary source of division, unhappily chosen.

3. The scheme of division, loose and irregular.

4. The appellations, in several leading instances, inapposite.

5. The distinctions, in several instances, groundless; distinctions, without any determinate and assignable difference.

6. Repetitions abundant:—under different names, the same object repeated a multitude of times.

7. The texture of the discourse incomplete: no verbs; consequently no propositions; nothing but substantives, with here and there an article or an adjective.

Section VIII.: Specimen of a New Encyclopedical Sketch, with a correspondent Synoptic Table, or Diagram.*

Directly or indirectly, well-being, in some shape or other, or in several shapes, or all shapes taken together, is the subject of every thought, and object of every action, on the part of every known Being, who is, at the same time a sensitive and thinking Being. Constantly and unpreventably it actually is so; nor can any intelligible reason be given for desiring that it should be otherwise.

This being admitted, Eudæmonics, in some one or other of the divisions of which it is susceptible, or in all of them taken together, may be said to be the object of every branch of art, and the subject of every branch of science. Eudæmonics,† the art, which has for the object of its endeavours, to contribute in some way or other to the attainment of well-being, and the science in virtue of which, in so far as it is possessed by him, a man knows in what manner he is to conduct himself in order to exercise that art with effect.

Considered in the character of an edifice or receptacle, Eudæmonics may, therefore, be termed the Common Hall or central place of meeting, of all the arts and sciences: change the metaphor, every art, with its correspondent science, is a branch of Eudæmonics.

If the above observation be correct, it is only in one or other of two shapes or characters—viz. that of a source of happiness, or that of a security against unhappiness that being can in

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Eudæmonics being the name for the universally practised art, the pursuit of happiness, being in some of its various shapes, will be allowed to be an indispensable means, without which the object of that art cannot in any instance be pursued and attained. Sensitive being is the only seat of happiness: being, in that and other shapes, is the universal instrument of happiness. To the attainment of happiness in any shape or degree, an acquaintance, more or less considerable, with the seat of happiness, and with such beings as, in each instance, afford a promise of serving in the character of instruments of happiness, is more or less conducive, or even necessary. For the designation, of whatsoever portion of science may be regarded as capable of being attained, concerning being taken in its utmost conceivable extent, the word Ontology has, for ages, been employed.

Eudæmonics is the art of well-being. Necessary to well-being is being. In every part, therefore, of the common field, concomitant and correspondent to Eudæmonics considered as an art, runs Ontology,† considered as a science.

For the expressly declared subject of division, let us take the science: art and science running along everywhere together, every division performed on the one, may, on any occasion, be considered as applying to the other.

By means of this joint consideration, as often as, on looking at the name of a branch of art and science as it stands in the Table, we come to consider its nature, our attention will be pointed to the only source and measure of its value.

Familiar as is the name Ontology, the idea commonly attached to that appellation has hitherto been subjected, by usage, to a restriction, which is not exactly conformable, either to the present purpose, or even to the etymology and original signification of the word, as above. The case is, that, by all those philosophers, by whom, under this name, any instruction has been undertaken to be given, those properties alone have been either considered, or professed to be considered, which have been regarded by them as incident to all beings without distinction: such as actuality, possibility, necessity, impossibility, probability, improbability, certainty, simplicity, compositeness, power of causation, derivation from a cause, and so forth.

Coenoscopic‡ and Idioscopic,§ by successively Edition: current; Page: [84] attaching to the subject Ontology these two adjuncts, the field of art and science may thus be divided, the whole of it, into two portions; in one of which, viz. the coenoscopic, shall be contained the appalling and repulsive branch of science, to which the no less formidable, and to many a man intensely odious, appellation of metaphysics, is sometimes also applied; while to the other, viz. the idioscopic, all the other branches of art and science, may, without distinction, be consigned.

Division the 1st. Division of Ontology into 1. Coenoscopic, and 2. Idioscopic.

Matter and mind—into these two portions, being in general, considered as an aggregate, is wont to be considered as divided. Hence arises,

2. Division the 2d. Division of Idioscopic Ontology into Somatology,* or Somatics, and Pneumatology,† or‡ Pneumatics, synonyms Psychology and Psychics.§

In the consideration bestowed upon body, the mind may confine itself, or not confine itself, Edition: current; Page: [85] to that property which belongs alike to all body, and even to every determinate portion of space unoccupied by body, viz. quantity. Hence arises

Division 3d. Division of Somatics into Posological* [Pososcopic] Somatics, and Poiological† [Poioscopic] Somatics. To avoid an inconvenience above brought to view, for an equivalent to Posological Somatics, may be employed the single-worded appellative Posology.

In the consideration of quantity, that of figure may be either taken into account or neglected. Hence arises

Division 4th. Division of Posology into Morphoscopic‡ Posology, and Alegomorphic or Alegomorphous§ Posology. By Morphoscopic Posology is denoted the same branch of art and science, for the designation of which the not altogether unexpressive, yet but inadequately expressive, term Geometry is the word in use.

In so far as it is without relation to figure that quantity is considered, the only diversification of which it is susceptible, is of that sort, for the expression of which the several modifications of which number is susceptible are employed. By Alegomorphic or Alegomorphous Posology, is here designated the same branch of art and science, for the designation of which the single-worded and adequately expressive appellation Arithmetic is the word in universal use.

Of a quantity, for the designation of which no more than one numerical figure,—or one line of such figures, no matter how long, so it be an uninterrupted one,—is employed, the amount is considered as known: i. e. by itself; the conception of it being, in so far as it is capable of being conveyed, conveyed in a direct way, and without need of the intervention of any other set of signs, to the mind of every person, by whom the import of those same figures, placed in that position with relation to one another, is understood.

Of a quantity, for the designation of which any two or more such lines of numerical figures, or one or more single figures, together with one or more such lines of figures, are employed, the amount is not, in a direct way, as yet known: for practical purposes it is not sufficiently known, until the composite expression, composed as above, has been transformed, or translated as it were, into a simple expression, consisting, as above, of some one single numerical figure, or some one single line of numerical figures, the elements of which are free from all such interruption as is produced by the interposition of any other sort of sign. To substitute to any other more complicated mode the simple mode of notation thus described, is what every operation of simple arithmetic has for its object.

In and for the designation of numbers, a convenience has, comparatively speaking, of late years, been found in the employing, in addition to numerical figures, and even on some occasions, or during some part of the operation, in lieu of numerical figures, signs of another kind, not varying in their signification, according to the order in which they succeed one another, in the same way as do the component elements of a line of numerical figures: of these newly devised signs, such as are capable of being ultimately translated into those which are composed of numerical figures, have, for a Edition: current; Page: [86] long time past, universally and exclusively been composed of the letters of the alphabet. But by none of these recently employed signs can any quantity ever be expressed in a direct manner: in any other manner than by reference to some single numerical figure, or line of numerical figures, ranged in arithmetical order, as above. Hence arises

Division 5th. Division of Alegomorphous posology, into Gnosto-symbolic,* or say Delo-symbolic,† and Agnosto-symbolic, or say Adelo-symbolic:‡ Gnosto-symbolic or Delo-symbolic being the term employed for the designation of the branch, for the designation of which the term common Arithmetic is in use to be employed, Agnosto-symbolic, or Adelo-symbolic, is the term, employed for the designation of that, for the designation of which the inadequately expressive composite appellation Algebraical Arithmetic,—or, much more frequently, the single-worded and completely unexpressive appellative Algebra,—is employed.

II. To return to Poiological Somatology [Poioscopic Somatics,] or Somatology at large.—Where bodies are considered, it may be either with, or without, reference to any operation, performed upon or in relation to them, by human art, by the help of human science. Hence arises

Division 6th. Division of Somatology, or Somatics at large, into Physiurgic§ [Physiurgoscopic] and Anthropurgic∥ [Anthropurgoscopic.] This division has for its source the consideration of the absence or presence of human art and science, applied to the purpose either of discovering latent properties already belonging to the subject, or of investing it with new ones. Physiurgic Somatology has for its synonym the above-mentioned misexpressive appellation—Natural History.

Anthropurgic Somatology has for its synonym the still more flagrantly and perplexingly misexpressive appellation Natural Philosophy, taken in one of the two or more different degrees of extension, which, as above, have been given to it.

Applied to bodies, alias portions of matter, in their natural, or say physiurgic, state, human art—or say elaboration by human art—has two distinguishable objects: sometimes it is to the one, sometimes to the other, sometimes to both, that it is directed. These are, 1. The discovery of such properties, as—already, and before it has, by the application of human genius and industry, been endued with any new properties—it is in possession of, having been put in possession of them, as it were, by the hand of Nature. 2. The giving to it, in addition to, or instead of, any such properties as it is found endued with by the hands of Nature, some new property or set of properties.

Intimately connected, and, in many instances, inextricably blended and intermingled, are, it is evident, these two functions: the detection of an already existing property or set of properties, being very often a condition precedent,—and always, in so far as it affords suitable indications, an encouragement,—to the engaging in any such operations as are found conducive to the faculty of investing the subject with new ones.

Of Physiurgy, alias Natural History, the object and business is—to discover and observe the properties possessed by objects, in the state into which they have been brought by the powers of unassisted Nature. But, to the bringing them for that purpose to view, and presenting them in a state as little changed as may be, new properties are, in many instances, requisite to be given to them: nor, in general, would the labour necessary to the accomplishment of this purpose be bestowed upon them, but in the view of investing them with new properties:—properties, by which they will be brought into some state or other, better adapted to human use, than any, into which they had been brought by the hand of Nature.

Division 7. Division of Physiurgic Somatology, or say Physiurgics into Uranoscopic¶ and Epigeoscopic** Physiurgics.

Uranoscopic Physiurgics has for its single-worded synonym the adequately expressive appellative Astronomy.

Division 8. Division of Epigeoscopic Physiurgics into Abioscopic†† and Embioscopic‡‡ Edition: current; Page: [87] Physiurgics: say Abioscopic and Embioscopic Epigeoscopics.

Abioscopic Physiurgics has for its synonym the adequately expressive and single-worded appellative Mineralogy.

Division 9. Division of Embioscopic Physiurgics into Azooscopic,* Azoologic, or Azoic, and Zooscopic or Zoologic Physiurgics.

Azooscopic Embioscopics has for its synonyms the adequately expressive and single-worded appellations already in use—Botany and Phytology.

Zooscopic Embioscopics has for its synonym the adequately expressive and single-worded appellative already in use—Zoology.

Beyond this point, no adequate advantage seems to be promised, at least on the present occasion, by the task of carrying on, in this direction, that track of dichotomous or bifurcate division, which, at the expense of much labour to the workman,—and not less perhaps to the small number of amateurs that can reasonably be looked for,—has thus far been persevered in. By the words Zoophytology, Entomology, Erpetology, Ichthyology, Ornithology, Tetrapodology, and Amphibiology, having for their respective subjects, Plant-Animals, Insects, Reptiles, Fishes, Birds, Beasts, alias Quadrupeds, and Amphibious, alias Land-and-Water Animals,—so many divisions of Zoology have for this long time actually been, or, in virtue of powers granted by Analogy, may, at any time, be in use to be designated.

Division 10. (1.) Division of Anthropurgics, or say Anthropurgoscopic Somatology or Somatics, into Coenoscopic† or Phanerodynamic‡ Anthropurgics, and Idioscopic§ or Cryptodynamic∥ Anthropurgics.

Coenoscopic or Phanerodynamic Anthropurgics has for its single-worded synonym the inadequately expressive appellative Mechanics: viz. when taken in the most extensive sense of the word, i. e. that in which it is employed to include whatsoever portions of Anthropurgic Somatics are not comprehended within the domain of Chemistry.

Idioscopic, or Cryptodynamic Anthropurgics. has for its single-worded synonym the unexpressive appellation Chemistry.

The properties, of which Mechanics—or, as the phrase is, Mechanical Philosophy—takes cognizance, are for the most part such as belong to all matter, taken in all its forms and species; by this circumstance it is that this branch of Art and Science is entitled to the appellation of Coenoscopic Anthropurgics, or Somatics.

These properties are, moreover, in comparison with those which belong to the subjects of the other just-mentioned branch, manifest, or say conspicuous, of themselves; not requiring the aid of human art to bring them out to view: in this circumstance it is that this same branch founds its title to the appellation of Phanerodynamic.

These properties being mostly, if not altogether, such as, in the common course of scientific language, come under the denomination of powers; hence, in speaking of this division of art and science, it has been thought that, on this occasion, a word corresponding to powers might, by contributing to clearness of apprehension, be not altogether without its use.

The properties, of which Chemistry takes cognizance, are for the most part, such as belong, not to all matter, nor to matter in general, but to this or that particular species of matter, as distinguished, each of them from the rest, by such a collection of these properties as, taken in the aggregate, belongs peculiarly to itself. By this circumstance it is that this branch of art and science entitles itself to the appellation of Idioscopic Anthropurgics.

These properties are, moreover, in comparison with those which belong to the branch just mentioned, recondite and unconspicuous; requiring—to the production, and, in some instances, as it were, to the creation of them—more or less of human art and elaboration, consisting chiefly in mixture, and in the application of different degrees of temperature: changes, which, in so far as the phenomena of heat and cold are considered as being the result of the absence or presence, the influx or efflux, of a particular species of matter, termed caloric, or the matter of heat, may also be considered as referable to the head of mixture.

Accordingly, in the adequately expressive appellative, Mixiology, or Symmictology, should any clear advantage be ever found derivable from the use of it, the originally unexpressive term Chemistry might at any time find an equally single-worded, and by no means unexpressive synonym.¶

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Division 10 (2.) Division of Anthropurgics into Anapirical, or Anapiric,* and Catastatical, or Catastatic,† [Catastatico-chrestic.‡]

This division has for its source the application or non-application of those newly discovered or created properties, which Art, in conjunction with Science, has had for its fruits, to the purposes of common life, through the medium of commercially established Art and Manufacture: Art and Manufacture, established upon such a footing that their produce is become an object of commerce.

Anapirical Anthropurgics has for its synonym the familiar compound appellative Experimental Philosophy.

Catastatical, or Catastatic Anthropurgics, has for its synonym the expressive, already established, and not altogether unfamiliar, appellative Technology.§

This tenth division, it is manifest, is not with reference to the last preceding one, subordinate, but co-ordinate: the aggregate being in both cases the same; only the source, from which the principle of division is derived, different.

It comprehends accordingly, and with equal propriety applies itself to, the mechanical branch and the chemical.

The demand, which in practice, there seemed to be for this division, viz. Experimental Philosophy and Technology being considered, the appellatives, which constitute the two branches of it being already in use, a place in this sketch could not be refused to it. True it is that, from the first of these ideal receptacles, as the newly produced fruits of art and science are converted into articles of commerce, individual objects are continually passing into the second; but of the appellations respectively given to the receptacles themselves, the propriety remains unchanged.

Beyond this point in the line of bifurcate division, there seems not, at present at least, any adequate use, in carrying on the investigation in this direction. Of the genus Mechanics, the species, according to a list more or less approaching to completeness, will be found ranged in a vertical line in a column of Table I., and so of the genus Chemistry.

III. To return to Pneumatology or Pneumatics.

Division 11. Division of Pneumatology into Alegopathematic∥ [Nooscopic¶] and Pathematoscopic** [Pathoscopic.††]

Alegopathematic, or say Alego-æsthetic Pneumatology has, for its single-worded synonym, the not unexpressive appellation Noology.‡‡

It has for its subject spirit or mind, considered apart from all feeling, whether of the pleasurable or painful kind: considered that is to say with reference to the purely intellectual part of the animal frame; including simple perception, memory, judgment, reasoning, abstraction, imagination, &c.

Pathematoscopic Pneumatology may have for its synomyn Pneumatic, or Psychological∥∥ Pathology.

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Division 12. Division of Pathematoscopic, [Pathoscopic] Pneumatology, or say Pneumatic or Psychological Pathology,* into Aplopathematic,† [Aplopathoscopic,‡] and Thelematoscopic.§

Aplopathematic Pneumatology or Pathology has for its subject the aggregate of Pleasures and Pains of all kinds, considered apart from whatsoever influence, in the character of motives, the prospects of them may have upon the will or volitional faculty, and the acts, as well purely mental and internal, as corporeal and external, of which those prospects may become the causes.∥

Thelematoscopic Pneumatology or Pathology, Edition: current; Page: [90] has for a syonym the single-worded appellative Ethics,* taken in its largest sense.

In the character of synonyms to Ethics are also used, in some circumstances, the words Morals and Morality.

Division 13. Division of Nooscopics or Noology Edition: current; Page: [91] into Plasioscopic* and Coenonesioscopic:†—Plasioscopic, i. e. Formation—regarding; Coenonesioscopic, i. e. Communication—regarding.

To the head of Plasioscopic Noology may be referred the art of thinking, with the correspondent science of what belongs to the formation of the matter of thought, in so far as the work of formation can be kept in view, and carried on in a state of separation from the work of communication, as applied to the same individual portion of that ideal species of matter.

To the word Logic, considered as the name of a branch of art and science, the conception that has been attached, seems never to have been altogether so determinate and definite as could be wished. But in one at least of the senses, in which it has been employed, it may be considered as the single-worded synonym of Plasioscopic Noology, as above characterized.

Division 14. Division of Coenonesioscopic Noology, or say Coenonesiology, into Aplo-didactic, or say Didactic, and Pathemategeretic, [Pathocinetic‡] or say Egeretic. Aplo-didactic, i. e. simply information affording; having, for the end or object of the communication in question, that and nothing more: Pathemategeretic or Egeretic, i. e. Affection-exciting, or in one word excitative.

Of the word Grammar, if not exactly coextensive with, the import will (it is believed) be recognised as comprehended under, the import of the word Aplo-didactic, as above explained.

To the head of Grammar seem commonly to be referred those rules, and no others, which have for their subject, among the words employed for the communication of thought, such relations between word and word as are still the same, whatsoever may be the particular purpose and occasion of the communication, and the nature and subject of the thoughts communicated.§

To the head of Rhetoric seem commonly to have been referred those rules, which have for their subject the choice capable of being made of words and combinations of words, on occasions on which the communication made, has for its purpose, or in the number of its purposes, the exercising an influence on the Affections, on the Affections, whether considered as having place in a calm state, or as in that state of intensity and perturbation, in which they receive the name of Passions.∥

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Division 15. First Division of Ethics (taken in the largest sense of the word) viz. into Edition: current; Page: [93] Dicastic,* i. e. Censorial, and simply Exegetic,† i. e. Expository, or Enunciative. Dioastic, or Censorial, i. e. expressive of a judgment or sentiment of approbation or disapprobation, as intended by the author of the discourse, to be attached to the ideas of the several voluntary actions, (or say modifications of human conduct,) which, in the course of it, are brought to view: in other words, his opinion, in relation to each such act, on the question, whether it ought to be done, ought to be left undone, or may, without impropriety, be done or left undone.

Simply Exegetic, i. e. Expository or Enunciative, viz. in so far as, without bestowing any such mark of approbation, disapprobation, or indifference, the discourse has for its object the stating what, in the opinion of the author, has, on each such occasion, actually come to pass, or is likely to have come to pass, or to have place at present, or to be about to come to pass in future,—i. e. what act is, on the occasion in question, most likely to have been done, to be doing, or to be about to be done.

This division has for its source the nature of the mental faculty, to which the discourse is immediately addressed. In so far as the discourse is of the Censorial cast, the faculty to which it addresses itself, and which, in so doing, it seeks to influence, is the volitional—the will, or at any rate the pathematic. In so far as it is of the simply Expository, or Enunciative, cast, the only faculty to which it immediately applies itself, viz. by seeking to afford information to it, is the intellectual faculty, the understanding.

For a synonym, Dicastic Ethics may have the single-worded appellative Deontology.‡

The principle of division, deduced from this Edition: current; Page: [94] source, will be seen to be applicable, and accordingly applying itself, severally to all the following ones.

Division 16.* Division of Ethics (whether Expository or Dicastic) into Genicoscopic,† i. e. general matters-regarding, and Idioscopic,‡ i. e. particular-matters-regarding.

Synonyms to Genicoscopic, as applied to Ethics, are, 1. Theoretical; 2. Speculative. Synonyms to Idioscopic, as applied to Ethics, is the word practical.

In this, as commonly in other cases, the limits between general and particular not being determinate, so neither are those between what, on the one hand, is theoretical or speculative, on the other, practical. Of the observations expressed, such part as is allotted to the explanation and fixation of the import of general words—words of extensive import, the use of each of which is spread over the whole field, or a large portion of the whole field, of the art and science—will belong mostly to the genicoscopic, theoretical, or speculative branch; and, under the name of principles, to the above observations will naturally be added any such rules, whether of the expository or the censorial cast, as in this respect are most extensive.

The deeper it descends into particulars, the more plainly it will be seen to belong to the idioscopic. In so far as, with the incidents exhibited in the fictitious narrative, any rules of a deontological nature (as in modern productions is frequently the case) happen to be intermixed, the matter of novels and romances comes to be included in, and the immense mass of it forms but a part of, the matter of practical ethics.

Division 17. Division of Ethics—whether Exegetic or Dicastic, and whether Genicoscopic or Idioscopic, into Apolioscopic,§ i. e. political-state-not-regarding, viz. private ethics, Ethics in the more usual sense of the word,—and Polioscopic, i. e. political-state-regarding,∥ viz. Government,¶ alias Politics.**

Division 18. Division of Politics and Government into Esoscopic,†† i. e. internal or interior-concerns-regarding, viz. Internal Government,—and Exoscopic,‡‡ i. e. external-concerns-regarding,—viz. Inter-national Government and Politics.

By internal Politics, may be understood that branch of Ethics which has for its subject the conduct of Government, i. e. of the ruling members of the political community or state in question, as towards the whole number of the members of that same community; by Inter-national Politics, that branch of Ethics, which has for its subject the conduct of Government, as above, as towards the members, whether rulers or subjects, of other such communities.

Division 19. Division of Internal Government and Politics, into Nomothetic, [Nomothetioscopic,§§] i. e. legislative, viz., Legislation,—and Aneunomothetic, [Aneunomothetioscopic,∥∥] i. e. without legislation,—viz. Administration.

In so far as it is by the establishing of laws that the business of government is carried on, it is carried on in the way of legislation;¶¶ in so far as it is carried on otherwise than by the establishing of laws, it is carried on in the way of Administration.

Division 20. Division of Administration Edition: current; Page: [95] into Aneristic,* [Aneristicoscopic,†] i. e. Uncontentious, viz. Administration in the more common import of the term,—and Eristic, [Eristicoscopic,‡] i. e. Contentious—viz. Judicature.

Division 21. Division of Judicature into Autothetic,§ [Autothetoscopic,∥] i. e. self-established, viz. Judicature, according to Common alias Unwritten Law,—and Catanomothetic,¶ [Catanomothetoscopic,**] i. e. according to Legislation, viz. Judicature according to Statute alias Written Law.

Section IX.: Explanations, relative to the above Sketch and Table.

In the sketch thus attempted, the following particulars present themselves as having, in a greater or less degree, a claim to notice. Subjoined to them, respectively, are a few questions, in relation to which some satisfaction may not improbably, it is supposed, be looked for, and will accordingly be here endeavoured to be afforded:—

1. In the Tabular Diagram, and accordingly in the Explanation given of it, the division or ramification professes all along to be exhaustive.—Question 1. What are the uses or advantages derivable from a tabular sketch, exhibiting in one view a number, more or less considerable, of the branches of art and science? Answer. See § 10.—Question 2. Why branches of Art and Science, and not Arts and Sciences? Answer. Because, in every part of the field, Art and Science are found together: no branch of art without a correspondent branch of science—no branch of science without a correspondent branch of art. It is not that in one part of the field you have an art, in another a science, in a third both; but that in whatever part you have either, you have both. See Chrestomathia, Table I. Note (32.) supra, p. 24.—Question 3. Why exhaustive? What are the uses and advantages resulting from its being so? Answer. See § 11.—Question 4. Can it, by any and what means, be proved to be so? Answer. See § 12.—Question 5. The idea of the utility of exhaustiveness, as applied to logical division—is it new to the scientific, and in particular to the logical world? Answer. Far from new; but at the same time not as yet quite so clear as it might be, and it is hoped will here be rendered. See § 13.—Question 6. Can any directions be given, by the pursuance of which, the exhaustiveness of a systematic sketch, of the subdivisions and contents, of any branch of art and science may be secured? Answer. See § 12.

2. The ramification is all along dichotomous, alias bifurcate, i. e. two-pronged.—Question 1. Why bifurcate rather than multifurcate? Answer. To secure its being exhaustive; concerning which, see § 12.—Question 2. Is the idea of the necessity of bifurcation to exhaustiveness Edition: current; Page: [96] new, as above? Answer. So it is supposed to be. See § 13.

3. Of the first partition of this kind that occurs, the result is composed of two, and no more than two, branches of art and science, which are thereby represented as included in that one, the division of which has thus been made; and as containing between them the whole contents of it. And so in the case of any other.

4. Of those two condivident branches, the names are respectively formed by, and composed of, the name of the immediate trunk,—which, grammatically speaking, is a noun-substantive,—followed, in each of the two instances, by a noun-adjective. Question 1. Of this two-worded name what is the use? Answer. To afford a definition, and, by means of the definition, an explanation, of the name constituting the immediate trunk.

5. Being thus composed of two words put together, each such name may, in Greek-sprung language, be termed a poly-epic, and in particular a biepic, name; in English-sprung language, a many-worded, and in particular a two-worded name.

6. In every instance, for reasons that have already been brought to view, (§ 6.) this two-worded name is, in the first instance, a Greek-sprung, and in most instances a newly-framed denomination. Question. Why Greek-sprung? Answer. See above, § 6.

7. In several instances, in the character of synonyms, subjoined to this principal biepic and Greek-sprung name, are other such names, one or more in each division; for which see the Notes. Question. Why these synonyms? Answer. 1. That, in each such group of names, the identity of import between the several names may be established; and in so far that error prevented, which would have place, if, from diversity in the sign, diversity in the object meant to be brought to view were inferred. 2. That by each of these names the object may in future be made known—not by that name only, but by any one or more of the others:—so that, on each occasion, that one of them may be employed, which, with reference to that same occasion, appears most convenient.

8. In most instances, to those Greek-sprung two-worded names, are added one or more two-worded, or many-worded, English-sprung names. Question. Why these names? Answer. To make known the import to such readers of English, to whom the import of the Greek-sprung names, new as they mostly are,—especially to English readers,—would not explain itself. By the unavoidable awkwardness of these compound English names, will be afforded the only justification that could be afforded for the practice of employing any such names, as, being borrowed from a foreign language,—and that a dead one,—are, until explanations of them have respectively been given and received, not intelligible to any but the comparatively small number, of those by whom the import of the corresponding foreign words happens to be understood.

9. Also, in several instances, new-coined, mono-epic, or single-worded Greek-sprung, names. Question 1. To what purpose are they thus added? Answer. To show by what means, in these several instances, the facility, afforded by the use of single-worded appellatives, may be substituted to the entanglement and embarrassment produced by the use of many-worded ones.

10. Also, in several instances, appellatives already in familiar use. Question 1. For what purpose are these added? Answer. For the purpose of contributing to the fixation of the import of these most familiar terms, viz. by presenting the clearest and most correct conception that can be afforded, of the mutual relations of the objects respectively designated by them,—and thus giving the greatest extent that can be given, to whatsoever benefits may be derivable, from the use of a Table constructed in this mode.

11. The first single-worded names that occur, viz. Eudæmonics and its associate Ontology (both of them Greek-sprung,) are so many names of that trunk which, with reference to the several pairs of branches,—products of successive acts of partition or ramification,—may be styled the universal trunk:—Eudæmonics, the universal trunk of Arts; Ontology, of Sciences.

12. With reference to the two branches into which it is divided, the name of every branch of art and science, which here presents itself, may, as above, be termed the name of the immediate trunk. Every such immediate trunk may, with reference to the universal trunk, be styled a particular or partial trunk.*

13. Any number of trunks, intervening between the universal trunk and the partial trunk in question, may, with reference to these two trunks, be styled intermediate trunks.

14. The trunk, which stands next to the universal trunk, may be styled the partial trunk of the first rank or order: that which stands next to it, the partial trunk of the second rank or order: and so on.

15. In some instances, several partial trunks are of the same rank or order. This is the case, as often as, from different sources, the same trunk is successively subjected to so many different divisive operations. In this case, whatsoever be the number of these operations, the divisions performed by them may, in every instance, be equally exhaustive. Be the numbers of sets of branches (viz. in so far as the bifurcate mode is conformed to, pairs of branches) ever so numerous, the operations themselves, and the pairs of branches, which Edition: current; Page: [97] are respectively their results, are all, with reference to each other, co-ordinate: with reference to the results of a division, performed on any trunk of a higher rank, (the highest rank being expressed by the smallest number) subordinate: with reference to the results, of a division performed on a trunk of a lower rank, superordinate.

16. The relation which, by the lesser aggregate designated by the name attached to any such subordinate trunk, is borne to the greater aggregate designated by the name attached to its immediate superordinate, is the same as that which, in the language of the current logic, a species bears to its next immediate genus—the genus of which it is the immediate species. The trunk, here styled the universal trunk, corresponds to the genus generalissimum of logicians.

17. Contrarily to the usage, which seems chiefly, if not exclusively, prevalent,—for giving intimation of the relation which, in each instance, is represented as having place between the trunk and its two immediate branches, the word is—instead of being omitted, and left to be supplied by the reader, is inserted.*

Question 1. Why thus depart from the most usual, it being also the most simple, mode?

Answer 1. To exclude obscurity unless the sign of this instrument of connexion is brought to view, no meaning is fully and adequately expressed:—unless the import of it is present to the mind, no meaning is comprehended. True it is, that, to the mind of one, to whom Tables of this kind are to a certain degree familiar, the import of this necessary bond of connexion may, at the first glance, and at the same instant, have been presented by those words of the proposition, which are inserted: and thus far no obscurity has place. But, other minds there may be, by which, though through the above-mentioned means, this same conception, will, sooner or later, have been obtained by them, yet for some time it will not have been obtained: and, till it is obtained, the undesirable quality of obscurity remains in the object, and the unpleasant sense of fruitless labour in the mind to which the object is presented.

Answer 2. To exclude ambiguity.—By the sort of omission here in question, it may be, that, in the individual sketch in question, framed as it is here framed, the imperfection thus denominated would not have been found produced. But, in a Table, framed in the manner, in which, to say the least, most Tables constructed for the sort of purpose here in question have been framed, the imperfection would, it is believed, be apt to have place. Two cases may be mentioned, in either of which it has place: 1. In so far as, between any two nouns that have place in the Table, a doubt arises, what is the copula intended, viz. whether the simple copula—the verb substantive—or this or that complex copula, that is, any verb, other than the verb substantive.† 2. In so far as, this simple copula being the one fixed upon, so it is that of the nouns, for the connexion of which it is capable of serving, the number is greater than two, a doubt arises for the connexion of what two or more it was intended to serve.

In the Table of D’Alembert, these doubts—one of them at least, if not both—will frequently, it is believed, be found presenting themselves.

Answer 3. To exclude misconception.—As often as of two conceptions, by the simultaneous existence of which ambiguity is presented, one alone is that which was intended by him whose discourse the discourse is, here the ambiguity has two issues or modes of termination, either of them capable of taking place. In so far as that which happens to be embraced by the reader, is different from that which was intended by the writer, misconception is the result.

17. For presenting to view so many different classes of the words of which the Table in question is composed, so many different types are, it may be observed, employed:—viz. 1. for the designation of the Greek-sprung words, which, in conjunction with the name of the immediate trunk, constitute respectively the two-worded names of its immediate branches, Italics, and these in a comparatively large type, are employed.

18.—2. For the familiar English words, which, when strung together in the form of one composite word, form those appellatives which, to the English reader, are designed to afford an explanation of the, in most instances, new, and, in every instance, Greek-sprung epithet,—the common Roman types, and in a comparatively small size, are employed.

19.—3. For the words, which form respectively those single-worded appellatives, which, Edition: current; Page: [98] being of Greek origin, and for the most part new, have on the present occasion been framed for the present purpose,—the sort of type called black-letter is employed.

20.—4. For those words, which, being respectively names of so many branches of art and science, are already in the English language, and in familiar use,—for these appellatives, whether single-worded or two-worded,—capital letters are employed.

21. As the trunks, which they respectively designate, recede further and further from the universal trunk, the types employed for these capitals are smaller and smaller.*

Section X.: Uses of a Synoptic Encyclopedical Table or Diagram.

By the name of an Encyclopedical Sketch, two perfectly different, however nearly related, objects may, with equal propriety, be designated, and under that common appellative thereby comprehended. The one is, a continued discourse, expressed in the forms of ordinary language: the other is a Systematic Table or Diagram, so constructed as to be in some degree emblematic. In the continued discourse, the relations in question are expressed at length in words and words alone: in the emblematic diagram some image is employed, by reason of which, while by their respective names, the objects in question are presented to the eye, all of them in the same place, and at the same time, certain relations* Edition: current; Page: [99] which they bear to one another, are at the same time held up to view. As to the image, that of a tree, with its trunk and branches, is that which, in the earliest example known,* was thus employed; nor does it appear that the nature of the case affords any object better adapted to this purpose.

To the form of a continued discourse the advantage attached is, that the quantity of explanation given by it is not restricted: but with this advantage is connected a disadvantage, viz. that, if it be of a certain length, it is only in succession that the several parts of it are presented to, and can be taken cognizance of by, the eye; so that, unless it be under the constantly repeated trouble and embarrassment, of turning backwards and forwards, leaf after leaf, or that of a constant strain upon the memory, or both, no comparison of part to part can be made.

In the systematic diagram, the advantage is, that, for the purpose of uninterrupted and universal comparison, continued to any length, after the objects with their several relations have been respectively explained, each of them, at whatever length may have been deemed requisite, in and by the continued discourse, the whole assemblage of them is, or at least, as above-mentioned, may be so brought together, as to be kept under the eye at once, forming as it were so many parts of one and the same picture.

Thus it is, that to this form two perfectly distinguishable, howsoever closely connected, advantages, both of them of a practical nature, are attached: in the first place, of the whole matter taken together, conception is facilitated and expedited; in the next place, comparison—reciprocal comparison—the articles being capable of being run over for all purposes, in all directions, and in all imaginable orders of succession, without interruption, and with that rapidity which is proverbial as being among the characters of thought.

To set against these advantages, no disadvantage has place, except that to the quantity of matter, to which this form is capable of being given, there are limits which apply not to the other. But, within these limits, here, as in a map or an assortment of maps, it is seldom that, be the purpose what it may, within the quantity of space capable of being thus employed, a quantity of matter sufficient for the purpose will not be capable of being displayed.

Anterior to the time of Bacon, were the profit worth the trouble, Encyclopedical Sketches might, even in the tabular form, it is believed, be found, and in both forms in no inconsiderable abundance. But, by the true lights, shed upon the field of thought and action, and thence upon the field of art and science, by that resplendent genius, all those false lights have been extinguished.

Of the two above-distinguished forms, of which an Encyclopedical Sketch is susceptible, the only one, however, of which the works of Bacon afford an exemplification, is that of a continued discourse, the purely verbal form.

In like manner, in no other than the purely verbal form, and that, too, wrought in a looser texture, may be seen the Encyclopedical Sketch prefixed by Ephraim Chambers to his Dictionary of Arts and Sciences.

With the two Encylopedical Sketches of Bacon and Chambers before him, D’Alembert prefixed to the French Encyclopedia his Encyclopedical Sketch, in the purely verbal form, taken, as he says, chiefly from Bacon: and, moreover—and for the first time reckoning from the days of Bacon—that correspondent sketch, in the form of a systematic diagram, which is here copied,† and which has been the subject of the remarks given above.

This diagram is exhibited by him in the character of the principal object; and it is in the character of an Explanation of that principal object, that the continued and purely verbal discourse attached to it, is delivered by him.

Notwithstanding the imperfections above held up to view, to which others might have been added, signal was the service which, in the estimation of the author’s collaborators, among whom were numbered almost all the men of any literary eminence whom France at that time afforded, was rendered by the instrument Edition: current; Page: [100] so constructed as hath been seen. In it they beheld, nor with other eyes has it been beholden (it is believed) in that or other countries, by their contemporaries or their successors, a sort of novum organum in miniature: a sort of instrument, which every man, to whose lot it has fallen, to labour, upon a scale of any considerable extent, in any part of the field of art and science, ought to have constantly in his hands and before his eyes.

To what instruction soever may have been extractible from that diagram, whether any and what addition has been afforded, by the remarks herein above made on it, together with the subjoined sample of another, executed upon a plan considerably different, the reader will judge.

A Table of this sort may be considered as an instrument in the hand of Analogy.

Scarce will the art be found, from which, through the medium of Analogy, assistance may not, in some shape or other, be borrowed by some other art, not to say by every other.

By Analogy, scarce will the article of knowledge be found, by which, in some shape or other, light may not be received from some other, not to say every other.*

Conception, retention, combination, generalization, analysis, distribution, comparison, methodization, invention—for all or any of these purposes, with an Encyclopedical tree in his hand, suited to the particular object which he has in view, skipping backwards and forwards, with the rapidity of thought, from twig to twig, hunting out and pursuing whatsoever analogies it appears to afford, the eye of the artist or of the man of science may, at pleasure, make its profit, of the labour expended on this field.

Yes, true it is that, no otherwise than through individual objects, can any clear ideas be imbibed, from the names of those ideal aggregates or bundles, of different sorts and sizes, into which, by the associating and dividing power of those appellations, they are collected and distributed. But, from a comparatively small number of individual objects, may be obtained very instructive and practically serviceable ideas, of very extensive aggregates. Many years age, forty thousand, or thereabouts, was supposed to be the number of species of plants at that time more or less known: forty thousand, the number of those ideal aggregates, designated by the name of species: millions of millions the number of the individuals at each moment designated by those same specific names. Yet from any one of those individuals may be abstracted a tolerably adequate idea of the species in which it is considered as contained; and how small is the number of species necessary to plant in the mind the prodigiously extensive idea designated by the word plant!

By attention, applying itself all along with still closer and closer grasp, by this faculty it is that advances, fresh and fresh advances, all of them so many conquests, are continually made in the field of art and science. Each laborious and inventive adventurer proceeds on in the wilderness, as far as his inclination and the force of his mind will carry him. Sooner or later, the same man or another, more frequently another, makes a road, whereby, to succeeding travellers, the quantity of labour necessary to the reaching of that farthest point is more or less reduced. By successive labourers of this pioneering class, the road is made gradually smoother and smoother. Where one ends, another begins; and hence it is that the veriest pigmy is at present able to look down, from a point, which, by his utmost exertions, the giant of anterior times could never reach.

That, of the branches of Art and Science, which, by the denominations here employed are thus endeavoured to be brought to view, the distinctness is, in a multitude of instances, far from corresponding to the distinctness of the denominations themselves, is but too true, and presents to view an imperfection no less undeniable than it is believed to be irremediable. In this tract, approximation is, throughout, the utmost that can be hoped for. But, unless and until some other scheme of distribution shall have been found, such as shall be exempt from, or at least in a less degree exposed to, this imputation of indistinctness, than that which is here submitted, the imperfection, so long as the work has any use, will not afford any sufficient reason for leaving it unattempted. That no scheme will be found altogether exempt from the imperfection, may be asserted with full assurance; and, if any scheme less tinctured with it than the present one is, could on this occasion, and by these eyes have been found, that and not this would have been the scheme in this place brought to view.

Let it not at any rate be said, that, by reason of this indistinctness, it is no more than upon a par with those other Encyclopedical Sketches, in the hope of superseding which it has been framed. Between the degree, and even the species of indistinctness, which has place in the two cases, wide indeed (it is believed) will be seen to be the difference. In this sketch (to borrow a phrase from Scottish history) in this sketch, may here and there be found (it is true) a small proportion of debateable land, concerning which it may be dubious to which of two contiguous districts it may with most propriety be said to belong: but in those cases, many are the instances, in which the whole of the territory, which is represented as belonging exclusively to one of two districts, may, with equal propriety, be said to belong to either or to both.

Section XI.: The Mode of Division should, as far as may be, be exhaustive—why?

If, of a sketch of the kind in question, the utility is by any person recognised, to satisfy him of the utility of its being rendered exhaustive, not many words can, it is supposed, be necessary. To be exhaustive, the parts which, at each partition or division so made, are the results of the operation, must, if put together again, be equal to the whole; and thus, and in this sense, exhaust (to use the word employed by logicians) the contents of the whole. It is only in so far as the divisions which it contains are, in this sense, respectively exhaustive, that the information, contained in a work which is composed of them, can be complete—can be what it appears to undertake for being, can be what it might be, and what, if it might, it ought to be. This being the case, if it be not exhaustive, every proposition, in which the exhaustiveness and completeness of the division is assumed, will, in so far as the assumption is proceeded upon, be, pro tanto, erroneous and incorrect; and, if received and acted upon, delusive: and, in whatsoever stage of the division the incompleteness has place, the consequence is, that, in every sub-division, the original imperfection is repeated, and the correspondent part of the work tainted with it.

But it is only by means of a system of division, carried on in the thus declaredly exhaustive mode, that any assurance can be afforded or obtained, that the survey taken of the field of thought and action, and therein of the field of science and art, or of whatsoever portion of that field is proposed to be comprehended, in the survey, is complete; any assurance, that, in the course of the progress made through it, a number of parts, in unlimited abundance each to an unlimited extent, may not have been omitted.

It is only in this way, that, even supposing the whole to have been actually embraced and comprehended in the survey, it can, in the mind that has embraced it, wear the aspect and character of a whole: instead of that of a regular tree, the form in which it presents itself will be no other than that of a confused heap of unconnected fragments,—each of them, in respect of form and quantity, boundless and indeterminate.

In the body of this work, intimation was given of what presented itself as the chief use, derivable from an insight, more or less extensive into those foreign languages, ancient and modern, in which the vernacular language has its roots. It consists (it was said) in this, viz. that, to an eye thus instructed, in the whole field of the language, there being no hard words, there shall be no absolutely dark spots; nothing that shall have the effect of casting a damp upon the mind, by presenting to it the idea of its ignorance, and thence of its weakness.

Correspondent to the sort of consciousness of power so obtainable in the field of language, is that which, by means of a set of systematic sketches,—and, an particular, by means of a set of systematic and tabular diagrams,—always supposing the mode pursued to be exhaustive, may be obtained and exercised over the field of art and science. No parts in it, from which through the medium of these appropriate denominations (the relations of which, as well those to one another, as to the matter of the body or branch of art and science, are determined and brought to view) ideas, more or less clear, correct, and complete, are not radiated to the surveying eye: in a word, no absolutely dark spots: no words that do not contribute their share towards the production of so desirable an effect, as that of substituting the exhilarating perception of mental strength, to the humiliating consciousness of ignorance and weakness.*

Desirable as this property will, it is hoped, be acknowledged to be, with reference to the purpose at present in question,—a purpose will now be mentioned, to which it must be acknowledged not to be applicable. Relations of logical identity and diversity, and relations of practical dependence, as between branch and branch, both these sets of relations have already been mentioned, as capable of being, with good effect, brought to view in the form of a synoptic Table. But, for the exhibition of relations thus different, neither can any one Table, nor any number of Tables, upon this same plan, be made to serve. In the plan, of division and correspondent distribution, pursued in the view given of the logical relations as above explained, exhaustiveness will indeed always be an essential feature. But where the relations to be exhibited are the practical sort of relations just spoken of, viz. those of dependence, or say, of subservience, (whether the subservience be mutual or but unilateral,) the nature of the subject admits not of any such regularity and all-comprehensiveness. From branches of art and science, the most remote from one another in the logical tree, one and the same art may be seen looking for Edition: current; Page: [102] assistance. Natural History, Anatomy, Chemistry, Architecture, Political History, Ethics—all these, not to mention any more, the Painter, not to speak of the Poet, may have occasion to summon to his aid.*

Exercising dominion over almost every branch of art and science, sometimes in furtherance of the interests of the professors of that particular branch, more frequently and more necessarily in furtherance of the interests of the whole community, the legislator, on pain of acting blindfold, has need of an insight,—the more clear, correct, and extensive the better,—into the matter of every such branch of art and science. For his use, therefore, to the Table of logical relations, exhibited upon an exhaustive plan, a Table of relations of dependence or subservience, as above explained, constructed upon a plan in which particularity and copiousness should be the ruling objects, would be an essential accompaniment.

Section XII.: Test of All-comprehensiveness in a Division how constructed—Additional Advantages, Distinctness and Instinctiveness. Bifurcation why necessary.

A problem is here proposed, and undertaken to be solved. A logical aggregate of any kind, as designated by any appropriate name, being given, required to divide it into a number of parts, each in like manner designated by a distinctive name, in such sort, that, in the sum of these parts, shall be contained the same individuals, and all the individuals which, and no other individuals than those which are contained in the whole.

Such is the problem, the solution of which is requisite for the present purpose. In other words, the solution of it consists in securing to the parts, into which the sort of whole in question is to be divided, the property of all-comprehensiveness.

For the accomplishing of this solution, what has been found necessary, is, the construction of an instrument, such as, being employed in the divisional operation in question, and thereby in the conformation of the parts, which are the results of it, shall serve as a test, in such sort, as to demonstrate, if such be really the case, that the division thus effected is in fact an all-comprehensive one: call it accordingly, the test of all-comprehensiveness.

An instrument of this sort has accordingly been constructed;† and, on turning to the Encyclopædical Table, will be seen to have, in every part of it, been explicitly or implicitly employed. It consists in what may be called the contradictory formula: the essence of which consists in the sign of negation, employed or employable in the designation of some one in each pair of branches, and not in that of the other. But of this presently.

In and by the word pair, as applied to the branches thus produced, what is already implied is, that, by the instrument in question, it is only in the way of bisection that the problem can be solved. But in this mode, it will be seen, that every desirable purpose may be accomplished: that it cannot by any other mode; and that on any occasion at pleasure, by division into two parts, division into any other number of parts may, if there be any use in it, be accomplished.

Of the desirable property, which, on this occasion, stands as the principal object, and occupies the fore-ground,—all-comprehensiveness, having for its synonym, as already explained, the word exhaustiveness,—is the name. But, by the same means by which to the scheme of division in question this property is secured, two other desirable properties, as it will be seen, are, at this same time, secured, viz. distinctness and instructiveness.

Intimately as they are connected with the principal property, and, by the same docimastic instrument, secured to the scheme of division executed by means of it, what will at the same time be seen is, that these two subsidiary properties are not, either of them, inseparable from it. Instances require to be shown, and will accordingly be shown, in which a scheme of division is or may be all-comprehensive without being distinct, and all-comprehensive and distinct without being instructive.‡

For securing clearness to the ideas attached Edition: current; Page: [103] to the names of those three properties, a few words of explanation may have their use.

1. Of all-comprehensiveness, with its synonym exhaustiveness, enough has in this view been said already.

2. By distinctness, as applied to the division in question, (whether by the word division what is here meant be the operation or the result,) by distinctness what is meant is, that, of all the individuals contained in the subject of the division, viz., the trunk or say, the major aggregate, it shall, when the division has been performed, be, in the instance of every such individual, clear and manifest to which of the several branches it belongs.

3. By instructiveness is meant a property which bears relation, and applies to both the others. It consists in this; viz. that the words, employed for giving denomination to the branches, shall be such, as to declare and announce, that the division is all-comprehensive, as also that it is distinct.

Of this property, it will be seen, that neither is it useless, nor is the warning, thus given to secure to the scheme of division the benefit of it, superfluous. 1. The property is not useless. For from the property of all-comprehensiveness no use can be derived, but in so far as the scheme of division is understood to be possessed of it: and so in the case of distinctness. 2. Neither is the warning superfluous. For, various, it will be seen, are the instances, in which these properties, though really possessed by the branches, into which, by the current names employed in the designation of them, the trunk has been divided, yet (such is the structure of those names) are not held up by them to view, and are therefore of little or no use.

Thus much as to the desirable properties, which, by the test above alluded to, viz. the contradictory formula have been secured, it is supposed, to the scheme of division here employed:—now as to the contradictory formula itself. Examples of it have been in existence as long as the logical tree of Rames, improperly (as will be seen) attributed to Porphyrius, has been in existence.* Examples of it are, as above, the matter of which the Encyclopædical tree here attempted is composed. What remains to be done here is, to point out the precise part to which the appellation is meant to be applied, and the ground on which it has been thus applied.

In the instance of each trunk, observation has been made, of a particular property, as being possessed by every individual, to which the name of the generic (say the major or comprehending aggregate, employed to represent the trunk) is applied: possessed, moreover, in like manner, by every individual, is a property to which the name of the minor or comprehended aggregate (the relatively specific appellative, employed to designate one of the two branches) is applied,—but as to the other of the two branches, not possessed by any one of the individuals, to which the appellative employed to designate that branch is applied.

Having thus the effect of giving, as it were, birth to, and, at any rate, indication of, the distinctness supposed to be possessed by the two branches, this property may be termed the distinctive property.

This subject (be it what it may) is possessed of this quality (be it what it may;) this subject (meaning the same subject)† is not possessed of the quality (meaning the same quality)—these two are—as the logicians call them, and as any body may see they are,—a pair of contradictory (viz. mutually contradictory) propositions the former of these may be termed the positive contradictory, the other the negative.

In regard to contradictories (such for shortness is the term employed, instead of saying a pair of mutually contradictory propositions) two observations have been made by logicians, and delivered in the character of axioms. One is, that, to whatsoever property, and with reference to whatsoever subject, these opposite assertions are applied, in no instance will they, both of them, be found true. The other is, that, to whatsoever quality, and with reference to whatsoever subject, they are applied, one or other of them will be found true.‡

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An example may here perhaps be required. Turning to the Encyclopædical tree (letter-press or diagram) take then for the dividendum, viz. the trunk or major aggregate, the branch of art and science therein denominated Posology, but commonly called Mathematics. It having been proposed, in an all-comprehensive and distinct manner to divide this major aggregate into two minor aggregates, exhibited in the character of branches, a property was looked out for, which, being possessed by every individual object comprehended in the major aggregate, as also by every individual in one of the two aggregates into which the major aggregate was to be divided,—and at the same time not possessed by any individual not comprehended in that same minor aggregate,—might, for the purpose of distinguishing each of the two minor aggregates from the other, serve in the character of a distinctive property. In the property of bearing relation to form, or say figure—i. e. in the property of taking for its subject form or figure—a property which seemed capable of being employed in the character of a distinctive property was found. Of the two minor aggregates, into which, by this means, the major aggregate, Posology or Mathematics, was divided; form-regarding, or figure-regarding Posology or Mathematics, in Greek-sprung language, Morphoscopic Posology, was the name given to the positive minor aggregate: this done, the name of the negative minor aggregate was thereby determined and given, viz. form-not-regarding, in Greek-sprung language, Amorphoscopic Posology, or, to exclude ambiguity Alegomorphoscopic.

But, in that portion of the matter of discourse, which in the Table, is employed for giving expression to these two minor aggregates, in the character of branches of the major aggregate, of the division of which they are the immediate results, is contained the import of the above-mentioned formula, brought to view under the name of the contradictory formula. The division, of which they are the results, is therefore, at the same time all-comprehensive (or say, exhaustive) and distinct. It is moreover instructive: for, in and by the terms of it, the all-comprehensiveness and distinctness, which really belong to it, are declared. Speaking of propositions, delivered on the subject of Mathematics.—This proposition does regard figure.—This proposition does not regard figure; of no one proposition,* delivered on the subject of Mathematics, will these two contradictories be found, both of them, to hold good: and if, of all the propositions, which do thus regard figure, one branch of Mathematics be (and there is nothing to hinder it from being) composed, and if of all those which do not thus regard figure, another, and the whole of that other branch, be composed; here we have two branches, in one or other of which every conceivable proposition belonging to mathematics will be found to be contained.

For each one of these minor aggregates or branches, when in the character of a major aggregate, in pursuance of the divisional process, it came itself to be divided, in lieu of, or at least in addition to, the many-worded appellative, which, in its character of a branch, is, in the first instance, employed to designate it, there should be a single-worded appellative. In the words Geometry and Arithmetic, two words in current use presented themselves as being,—and that without any violence done to their established imports,—capable of being employed in this character; i. e., as comprehending between them the whole of the import, which either is, or with propriety can be, Edition: current; Page: [105] comprehended in the import of the word mathematics: with propriety, i.e. without outstretching* the most extensive import, for the designation of which that appellative has ever been employed.

On this occasion, the pair of names, which, for these two branches of mathematics, have, on this occasion, been, in the first place, brought to view, are the two newly-devised many-worded ones. But the pair of names, by which those names, and the relation of which they are expressive, were, in the first instance, suggested, are the two old-established single-worded ones. Geometry and Arithmetic, considered as branches of art and science, in what particular, it was asked, do they agree? The answer was obvious enough:—as being, both of them, branches of Mathematics. So far so good. But, forasmuch as they are not the same branch, in what is it that they differ? Of a survey taken of the contents of each, with a view to this question, the result was that, to which, as above, the pair of many-worded appellatives have given expression. In one of them figure is regarded; in the other, not.

Now then, thanks to the Encyclopædical names,—of the two trivial names, viz. Geometry and Arithmetic, which are in use to be employed in the designation of these two branches of mathematical art and science, the all-comprehensiveness† will, it is believed, be readily enough, and generally enough recognised: nor will the distinctness,‡ it is believed, be found to be in any greater degree exposed to dispute.

At the same time, in regard to instructiveness, as above explained, the utter absence of this quality will, in the instance of both these trivial names, be found, it is believed, equally manifest: and thence it was, that, as soon as it did present itself, it was in the character of a sort of discovery, that the coincidence of these two imports, with the imports of the two many-worded appellatives to which they are here stated as being respectively synonymous, presented itself:—and, in this same character, howsoever it may be in the case of an adept, in the case of many a learner, there seems little doubt of its presenting itself.

Of the nature of the contradictory formula, the explanation above given will, it is hoped, be found tolerably intelligible. Its capacity of serving, in the character of a test of all-comprehensiveness and distinctness, in a logical division, will also, it is hoped, be recognised. In the formation of the Encyclopædical appellatives employed in the Table, this test will, in several instances, be seen actually and explicitly employed, included as it is in the composition of the words themselves. Other instances, however, there are, in which it is not thus employed. In the production of this omission, two considerations, whether sufficient or not, concurred: one was—that, by the employment of the two epithets, both in the positive form and independent of each other, instead of no more than one positive one, Edition: current; Page: [106] with the correspondent negative, a greater quantity of instruction might, in a given compass, be conveyed: the other was—that, in some instances, doubts seemed to hang over the question, which of the two contradictory properties should be presented in the positive form; which in the negative: and, on whichever side the determination might happen to fall, for explaining the grounds of such determination, more words might become necessary than could well be spared. Of the plan of nomenclature here pursued, the characteristic property accordingly is—not that, in the composition of either name of the pair, the criterion in question—the sign of the contradictory formula—has in every instance been actually employed; but that, in the character of a test of the all-comprehensiveness and distinctness of the division, in the expression of which these names have been employed, a pair of names, in one of which this sign is employed, may, without misrepresentation, in every instance in which it has not been thus employed, be added or substituted.*

Of the lights, which the nature of the work admits of and requires, the Encyclopædical names thus provided, though they are the only instruments, are not, it should be observed, the only objects. Other objects, for the illustration of which the demand, as being much more general, is accordingly still more urgent, are those current names, examples of which have just been brought to view; and which, wheresoever they could be found, have been sought out, and put by the side of those Encyclopædical names, with the imports of which their respective imports seemed to approach nearest to a coincidence.

Unfortunately, that this coincidence should be perfect, is in many instances plainly impossible: such it will be seen to be in every instance, in which the import attached to the current name is in any degree indeterminate; and the further this import is from being determinate, the further will the agreement be from amounting to a perfect coincidence. Unfortunately, again, these instances are at present but too numerous: of one of these mention has already been made; and, without need of looking elsewhere, among such of these names as are comprehended in this Table, other instances will, it is believed, be found observable.

To the satisfaction of the reader, that, in so far as it has place, observation of the impossibility in question should be taken, is highly necessary: otherwise, where everything has been done that can be done, it may appear to him that nothing has been done. To give determinateness to the import of an appellative of his own framing depends upon the author; not so as to that of any of those which he finds already made. Towards effecting that coincidence, which, as above-mentioned, is so highly desirable, all that depends upon him, is, in the first place, to give to the appellatives of his own framing that degree of determinateness which the nature of the case admits of; and, in the next place, among those which he finds ready made, to choose for synonyms to those of his own making, such trivial names, the import of which appears, upon the whole, to come nearest to that of his own, being at the same time, if in any, in the smallest degree indeterminate.

For securing determinateness to those of his own framing, the established logical expedient of the distinctive property afforded to the author of this Table an effectual means: for choosing out of the existing stock of trivial names such as should stand least exposed to the imputation of indeterminateness, no equal security could be afforded by the nature of the case.

In this way, though by no direct and immediate means can determinateness be given to the import of those current names, of which at present the import is indeterminate, yet in time, and by means of the instrument of fixation here brought to view, an object so desirable may gradually perhaps be accomplished. By the supposition, a standard of comparison and reference will have been set up; supposing it to be what it is intended to be, and, in the nature of the case, well capable of being made, supposing it to be in itself clear, and as near as may be to the range of the variable one, conformity to this standard will be found matter of general convenience; and in proportion as the fixed import comes to be adopted, the varying one, in all its variations, will drop out of use.

What if, in this way, and by these means, the import of all words, especially of all words belonging to the field of Ethics, including the field of Politics, and therein the field of Political Religion, should one day become fixed? What a source of perplexity, of error, of discord, and even of bloodshed, would be dried up! Towards a consummation thus devoutly to be wished, there does seem to be a natural tendency. But, ere this auspicious tendency shall have been perfected into effect, how many Edition: current; Page: [107] centuries, not to say tens of centuries, must have passed away!

All this while, on the nearness of the approach made to a perfect coincidence, depend the strength and utility of the mental light capable of being reflected upon each other’s import, by the two denominations, the Encyclopædical and the trivial. Hence comes the need of a memento, to which expression may be given by the following rule.—For determining the contents of the two branches, into which the trunk in question is to be divided, look out for that distinctive property, by the application of which such a pair of branches shall be produced, the imports of which shall come as near as possible to the imports of the two appellatives already in current use.

Of the above rule, in no instance will any neglect be followed by impunity. He who, taking up a word, gives a definition of it, issues thereby a requisition, calling upon as many as read or hear of it, to use the word in that sense. Let the word thus defined be a word of a man’s own creation, in this case, if so it be, that for this new-invented instrument an adequate use can be found—provided also that the newly-attributed import is not contradictory to any import already attached to it,—if both these conditions are fulfilled, then so it is that for any expectation he may happen to entertain of seeing the requisition generally complied with, a substantial ground has been laid. On the other hand, if it be a word in common use, in that case, if the import thus newly endeavoured to be attached to it be to a certain degree at variance with common use, the consequence is—what?—that, against the sort of law, which he is thus taking upon himself to enact, he finds (nor is there any reason why he should not find) as many rebels, as there are persons, by whom, in its old established sense, the word has been in use to be employed.

Fixation, yes: this may be endured: comparatively at least, the thing is not difficult: the use is manifest. Substitution, no: the difficulty is extreme; and that difficulty not atoned for by any the smallest use.

1. Define your words, says the capital rule, laid down, and so much insisted upon, by Locke.—Yes: define your words.—But, in addition to this rule, a subsidiary one there is, the demand for which will, it is believed, be scarcely found less imperative.

2. In defining a word, if it be a word in current use, be it your care, that the import you are thus endeavouring to attach to it, be not only determinate, but as near to the current import, as a determinate import can be to an indeterminate one.

In the character of a distinguishable addition to the mass of instruction afforded by means of the contradictory formula, may perhaps be mentioned the series of those definitions, which thus in substance, and almost in form, presenting themselves at every joint, give to the whole system a degree of precision and compactness, altogether incapable of being infused into it by any other means. So many pairs of branches or minor aggregates, so many pairs of definitions: major aggregate, at each joint, a genus: its two immediate branches the two minor aggregates, its species: the distinctive property, with its negative, the two specific or differential characters. To this advantage a brief reference has been already made, viz. in the section (§ 9.) in which the particular characters of the Encyclopædical tree are brought to view.*

Such being the advantages, indicated by the terms all-comprehensiveness, distinctness, and instructiveness, as applied to a scheme of logical division,—in the next place comes the question—in what way, if in any, is the existence of these advantages attached to the use of the bifurcate, as contradistinguished from the multifurcate mode?

To this question the answer has probably, in the mind of many a reader, already presented itself. To the bifurcate mode alone, to the bifurcate mode, and not to the multifurcate, is the test of all-comprehensiveness and distinctness, viz. the contradictory formula, applicable.

After the explanation above given, exists there any person, in whose eyes, when compared with the bifurcate, the multifurcate mode would be preferable? To a tree, or any part of a tree, once constructed in the bifurcate mode, might be substituted a tree constructed in the multifurcate mode, without trouble and almost without a thought. Throw out the Encyclopædical names, put together the current names—the thing is done. The plan of division pursued, suppose it all along all-comprehensive and distinct, the all-comprehensiveness and the distinctness would, after this change, Edition: current; Page: [108] remain to the matter as expressed in the multifurcate mode; but the proof of its being all-comprehensive, the proof of its being distinct, and the instruction afforded by the language by which this proof is expressed, all this would be gone. After these deductions made, by this means, out of a system constructed and exhibited in the bifurcate mode, you might have remaining a system equally good, constructed, or at least exhibited in the multifurcate mode. Constructed? Yes; but in what manner? Exactly in the manner in which, in his oration given to an audience of Shoemakers, Orator Henley showed them how, by one man, a gross of shoes might be made in a day: viz. by cutting them out of a gross of boots.

Of this conversion the converse would not be altogether so easy. Nor indeed, without addition, supposing the multifurcate tree to be, in any one of its ramifications, less than all-comprehensive, would it be possible. On the opposite supposition, however, i. e. if in every one of its ramifications it be supposed to be all-comprehensive, the converse would be possible. Of the required bifurcate tree, the matter would, on this supposition, in part, though only in part, be given; and, as to the mode of filling up the deficiencies it has already been explained, and may be seen exemplified in the Table.

Of a division, which in the article of all-comprehensiveness, is deficient, an example, should any person be desirous of it, may with equal facility be extracted from the same Table. Take, for instance, Natural History: branches, upon the multifurcate plan, supposing it in the execution all-comprehensive, three, viz. Mineralogy, Botany, and Zoology. Suppose any one of them left out, thus, instead of the all-comprehensive division, you have an imperfect,* or, as Euclid might have said, a deficient one.†

That, for obtaining a clear, correct, all-comprehensive and commanding view of the contents of any logical aggregate or whole, bifurcate, in contradistinction to multifurcate, is the only adequate mode, another consideration may perhaps help to satisfy us. Of two objects, and no more, can the eye of man, (whether it be of the bodily and real, or the mental and fictitious organ, that the word be understood as designative,) obtain any usefully distinct view at the same time. Vibrating, as it were, between the two; and at each vibration, applying (as Euclid might have said) to the impression made by the one, the still vivid idea‡ Edition: current; Page: [109] of the other, one by one it can compare them; but if any greater number, say three, be presented to it at the same time, then so it is, that, for any such purpose as that of obtaining a perception of those reciprocal points of coincidence and diversity, ere it can bestow upon them a steady and persevering consideration, it will find itself under the necessity of dividing them, in the first place, into two lots; in one of which it will place one of them, and in the other lot either it will place one alone of the two remaining objects, or if both, then, for the purpose of comparing the other object of the comparison, the two will be put together, and, by conjunction in the same lot, be in imagination reduced to one.

Endeavours are used (suppose) to consider and compare all three at the same time. What will be the consequence?—that, while any two of them are thus kept in comparison, the third, before any clear and decided judgment can be formed in relation to these two, will be obtruding itself. Confusion will thus ensue: and a necessity will be found of recommencing the comparison: and so toties quoties.*

One word more on the subject of instructiveness. In the exhaustively bifurcate mode,—in and by means of the ramified chain of virtual definitions which have been brought to view,—at each joint a pair or rather a triplet of relations, has been brought to view: viz. the relation of each minor aggregate to the immediate major aggregate, and the relation of each minor aggregate to the other: the two first, relations of identity and coincidence; the third, a relation of diversity and separation. But, of every object of the understanding, be it what it may, the nature is the more thoroughly known, the greater the number is of those relations† which it is seen to bear to other objects: and, were it only in virtue of its being an object of the understanding, every such object bears some relation—in truth a multitude of relations to every other. By Algebra, whatsoever riddles are solved, are solved—whatsoever is done, is done—by the converting of this or that unknown quantity into a known one: a conversion, which neither is, nor ever can be, effected in any other way, than by means of a relation which it bears, viz. the relation termed the relation of equality,‡ (which, in a case that affords nothing but quantity, is the same as the relation of identity,) to such or such other quantity or quantities, which were known already.

No object is known, but in so far as its properties are known: and, for every property, the manifestation of which depends upon any other object, a correspondent relation between Edition: current; Page: [110] the two objects must be acknowledged to have place.*

Section XIII.†: Exhaustiveness, as applied by Logical Division—the idea whence taken—Saunderson’s Logic—Porphyrian or Ramean Tree—Hermes.

To the author of these pages, the first object by which the idea of exhaustiveness, as applied to logical division, was suggested, was a chapter of Saunderson’s Logic, which has this operation for its subject. Much about that same time, viz. some four and fifty years ago, on the occasion of a set of College-Lectures, in which that book of Saunderson’s was employed as a text-book, the copy of it, now lying on the table, received in manuscript a copy of a diagram of a logical tree, therein called Arbor Porphyriana—the Porphyrian Tree—exactly

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in the state in which it is represented in Table IV., No. I. In Table IV., No. II., it is exhibited with some little alterations, which, on the present occasion, might serve, it was thought, to render it somewhat more readily intelligible.

In this same work of Saunderson’s, in a list given of the commentators of Aristotle, the very first place is occupied by this same Porphyrius. Yet, useful as it not only is in itself, but more particularly useful as it might have been made, to the purpose of affording exemplification and illustration to some of the instructions contained in that same work of Saunderson’s, in no part of that work is any reference to it to be found.*

By every eye, by which this prime and most ingenious example of logical analysis is glanced at, the divisions made by it may at one glance be seen to be, at each step, bifurcate. By every one who, in this point of view shall have had the patience to examine into it, it will be found to be at every such step exhaustive.

On the subject of Division, Saunderson has—for, in following out and paraphrasing the system of Aristotle, he could not fail to have—a chapter. Amongst other rules for the performance of this operation, he requires that it be exhaustive—that it possess this property. In that chapter, had it occurred to him to avail himself of the exemplification thus already given of this his own rule, he might have exhibited to his readers a specimen of division, which, being throughout bifurcate, is throughout exhaustive. In so doing, after causing his readers to observe, that it is bifurcate, he might have shown to them, in the first place, that it is exhaustive, in the next place, that it is by its being bifurcate that it is rendered capable of being proved to be so; and, lastly, that by the mutual contradictoriness of the two propositions, the import of which is suggested by the pair of denominations presented by each pair of branches, the proof of its being so is actually afforded.†

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Planted and firmly rooted, by the logical work of Saunderson, the conception of the necessity of the property of exhaustiveness to an adequate division, received, at a later period, further confirmation, as well as illustration, from the grammatical work of James Harris.

Upon reference now made to that work, no such word as exhaustiveness or all-comprehensiveness has been found in it; but by the word all, repeatedly decked out in emphatic capitals, and reinforced by the word whatever, together with the division made of the contents of it, by the words either and or, the idea was plainly meant to be conveyed, and was accordingly brought to view. Whether in the instance of every one, or so much as any one, of the divisions there exhibited, that quality is given to it, has not, for the present occasion, been thought worth inquiring into. What is certain is, that, for proof of the existence of that quality, neither the test here in question, nor any other, is there brought to view. What is also certain is, that, be they as they may in regard to exhaustiveness, or say all-comprehensiveness, in regard to distinctness, the divisions exhibited in Hermes are stark naught.

Under the name of attributives of the second order, adverbs—all adverbs,—are there given as being in their import, distinct from the three parts of speech following: viz. from substantives, for example place and time; from attributives of the first order, for example the pronoun adjective this, and from connectives, for example the preposition in. Unfortunately, to look no further, in the import of every adverb designative of place, and in that of every adverb designative of time may be found the several imports of the three several parts of speech, from the imports of which, the import of an attributive of the second order had, in that division of Harris’s, been represented as distinct. Adverb of place, here; i. e. in this place: adverb of time, now; i. e. in or at this time: and so in regard to quality, manner, and so forth.*

Section XIV.: Imperfection of the current Conceptions relatively to Exhaustiveness and Bifurcation;—ex. gr. 1. in Saunderson’s Logic.

Of the systems of logical division, which, for one purpose or other, are so abundantly framed, and so continually observable, many there are, which, in some of their ramifications, particularly those which are the nearest to the trunk, will be seen to be bifurcate; nor can it be doubted, but that of these again a large proportion would, upon the application of the above test, be found to be exhaustive: and, lamentable, indeed, it would be, if—in those arrangements, by which, on all sorts of subjects, men’s conceptions are settled and determined—a property which by all logicians, has been acknowledged to be the inseparable accompaniment Edition: current; Page: [113] of a good and adequate system of division, and thence indisputably necessary to a complete and sufficient comprehension of the subject, were not frequently to be found.

Not very frequently, however, in giving denomination to the component parts of the division, are those names employed, those correlative and contrasted names, by which, as above, the test of plenitude is actually applied.

On this occasion three institutes of logic have been referred to: viz. Bishop Saunderson’s, in Latin; Dr Watts’, in English; and the view given of the Aristotelian Logic, by Dr Reid, in Lord Kaimes’s History of Man.

Of all the views that have ever been given of Aristotle’s System of Logic,—concise, nervous, compact, methodical, well-divided,—Saunderson’s would, it is believed, be found by far the best; several others, which for this purpose were taken in hand, seemed far inferior to it.

In England, at any rate, Watts’, as being in English, and furnished with familiar illustrations,—Watts’, though diffuse, and teeming with anilities, appears, by the multitude of the editions, to have been the most in use.*

Posterior, by a generation or more, to Watts’, as that is by several to the Bishop of Lincoln’s, the view given in the work of Kaimes presents in conjunction the authority of two distinguished Scottish writers.

To no one of all these writers does the utility and excellence of the exhaustively bifurcate method, or so much as the use actually made of it in the Ramean tree, appear to have made itself sufficiently sensible. By all of them the bifurcate method is indeed mentioned.—Mentioned? But for what purpose? Scarcely for any other purpose than the being slighted. By Reid and Kaimes it is even taken for a subject of pleasantry: but of pleasantry (it will perhaps be seen) not very happily applied.

Section XV.: II. Watts’ Logic.

In his chapter, intituled Special Rules to direct our Conception of things, Sect. 8. Of Division and the Rules of it, Watts delivers on this subject a set of rules; of which, according to his numeration, the number is six. But in that which calls itself the sixth, may be seen two perfectly distinct ones.

By anything like a thorough examination of them, much more room would be taken up than can here be spared. The fourth, and the last part of the sixth, are the only ones that have any direct bearing on the present point.

1. “Let not sub-divisions (says the fourth) be too numerous without necessity.” Here we have anility in a still worse form, than as above in Saunderson. Anile tautology patent; self-contradiction latent. “Let them not be too numerous:” this is plain identicalism and nothing more: add, “without necessity,” the identicalism is now topped by self-contradiction. Good simpleton! what mean you by the word too? Know you then of so much as an imaginable case, in which there is a “necessity” that anything should be “too” anything? in which that which ought not to be done ought to be done?

2. Lastly, as to that second part of his Sixth Rule—“Do not,” says he, “affect Duplicities, nor Triplicities, nor any certain number of Parts in your Division of Things;” “For,” (continues he, and then come reasons, in which not much application to the subject has been perceived) “yet,” (continues he,) “some persons have disturbed the Order of Nature, and abused their Readers by an affectation of Dichotomies, Trichotomies, Sevens, Twelves, &c.”

The section then concludes with another Edition: current; Page: [115] effusion of anility, condemning what he calls “a too nice and curious attention to the mere formalities of logical writers, without a real acquaintance with things.”

What applies more particularly to the subject here in hand, is, that this division, into no more than two parts at each operation, is, in the scale of usefulness, placed by him upon a level, not superior to that of division into any other number of parts; to this or any one number, in comparison of any other, any preference that can be given is equally ascribed to no better a source than affectation. Thus what is plain is, that to his eyes, as already observed, the matchless beauty of the Ramean tree, the test which it affords of exhaustiveness, had not displayed itself.*

Section XVI.: III. Reid and Kaimes, in Kaimes’s History of Man.

In Lord Kaimes’s work, entitled Sketches of the History of Man, is contained “A Review of Aristotle’s Logic,” which he declares to have received from Dr Reid. In general, the account there given of that work, is, it may be presumed, correct. But, in the particular passage which now stands for consideration, his lordship’s froth seems, in a dose more or less considerable, to have mixed itself with the phlegm of Dr Reid.

On this occasion the exhaustive mode came under his review:—he begins with a declaration of its usefulness: he ends with an attempt to turn it into ridicule.

He acknowledges it to be good: but, at the same time, finding the use of it to be attended with some difficulty, and that a difficulty with which he did not feel himself in a condition to cope, he vows revenge, and, to accomplish his vow, applies to Momus.

Ascribing it, and as it should seem with reason, to the above-mentioned Ramus, he calls it new: in that character it becomes fair game for ridicule; and with ridicule it seems to him that he has completely and sufficiently covered it, by a proposal, that, for the purpose of exhaustion, in a series of divisions, carried on in this dichotomous mode, to one of the two members an et cætera should in each instance be substituted.

Here then, according to this pair of Logicians, the Latin phrase et cætera, in English, and the rest, might, on every occasion, and with equal advantage, be substituted to the name of either, or at least to that of one, of the branches in each joint of a system of logical divisions, framed and denominated in the exhaustively bifurcate mode. But is this so? No: not on any occasion, with any such advantage. Why not? Answer. Because, by an &c., substitute it to which of the two names you will, though you may make your division equally exhaustive, you can neither make sure of making it equally distinct, nor can you (see § 12.) render it equally instructive.

In the name, which, upon the Ramean plan, you give to each branch, viz. the two-worded name, be it positive, be it even negative, you bring to view two properties: one, in respect of which the individuals contained in both branches agree with one another; another in respect of which they differ from one another: those of the one having this latter property, those of the other not. But an et cætera?—what are the properties of an et cætera?

Let it not be said, that the name, the two-worded name, of a negative branch, shows no property. For, in the first place, it shows that property, which the individuals belonging to that branch possess in common with those that belong to the other: in the next place, it shows another property: for, to the purpose of instruction, concerning the nature of the object, even the non-possession of this or that property, is itself a property.

Under the assurance afforded by the bifurcate mode, when it is declaredly exhaustive, viz. the assurance, that, at each joint, in the composition of the two-worded name of either of the two branches, if the sign of negation is not actually employed, it may, without impropriety, be so employed at pleasure, under this assurance, so it is that they may either, or both of them, be employed as trunks, and, in that character, may be subjected to ulterior division. And in this way accordingly it is, that, in several instances, in the annexed sample of an Encyclopædical tree, both branches may be seen employed.—But an &c.?—the phrase et cætera?—in what way could these Logicians have made it serve in the character of a trunk? In what way could they have divided it into branches?

Of what one sort of aggregate is et cætera the name? Yet, according to them, with as much propriety as any given number of other names, an et cætera, if repeated that same number of times, is capable of giving denomination to all sorts of aggregates.

By the contradictory formula, which, in every ramification, if performed in the Ramean mode, is, as above, either expressed or implied,—an assurance is given, that the mode of division pursued is meant to be exhaustive, and to that end is rendered bifurcate. But if, in the instance of either branch, in the room Edition: current; Page: [116] of a significant name the insignificant name et cætera is employed,—in this way, what assurance is given that the mode employed will be bifurcate? True it is, that, in the case supposed by Reid and Kaimes, the mode (it seems to be taken for granted) is the bifurcate mode. But in the nature of their et cætera, there is nothing to hinder its being employed when the mode is multifurcate: whereas, as hath been seen, it is the property and excellence of the contradictory formula, that it cannot be employed but that the mode of division is, at the same time, bifurcate and exhaustive.

More misconception—more confusion. Of the confusion made by Watts, for want of his being sufficiently aware, that what belonged to the subject was, not a physical and real whole, but a logical and fictitious aggregate, notice has been taken in § 12. Exactly into that same inadvertence may Reid and Lord Kaimes be seen to have fallen in this place. “Division of England into Middlesex and what is not Middlesex:”* this is what they give as an example of the only sort of division here in question, viz. a logical one. But, agreeing in this respect with the vegetable body called a tree, the portion of the earth’s surface, called England, is a physical and real whole, not a logical and fictitious aggregate.

In a logical division, performed in the exhaustively bifurcate mode, the two-worded name of each branch gives intimation of two properties belonging to all the individuals contained in it: one, in the possession of which they agree; another, by the possession and non-possession of which they are distinguished. But, of no one property,—whether as possessed, either by all “England,” or by itself, or by anything that “is not” itself,—dees the word “Middlesex” give any intimation. “It is evident” (say they) “that these two members comprehend all England.” True. “In the same manner” (say they) “we may divide what is not Middlesex into Kent, and what is not Kent.” True again. “Thus,” (continue they) “one may go on by divisions and sub-divisions that are absolutely complete.” True, once more: but while, for your subject, instead of a logical aggregate, you take a physical whole, although those divisions will indeed be as trifling and useless as to yourselves they appear to be, being so, will they prove what you bring them to prove? Not they indeed. Why? Because they are nothing to the purpose. “This example” (they go on to say) “may serve to give an idea of the spirit of Ramean division.” How far this purpose is really served by it, the reader may now judge.

A curious circumstance is, that it is in the character of a source of objection to this mode, that his lordship brings to view the train of false “conclusions” that, in relation to this subject, “philosophers, ancient and modern,” have, according to him, in great abundance, fallen into: fallen into, and from what cause? From the having made use of this security against error? No: but from their having (says he) omitted to make use of it. To the “divisions” of their making, the fault he ascribes, is that of being “incomplete.” Of the mode of division, which he is thus holding up to ridicule, the distinctive character is, that it is capable not only of being rendered, but, wherever it is so, proved to be complete. Yet the mode is (according to him) a bad one. Why?—but because by pursuing it?—no: because, for want of having pursued it,—certain persons have made bad work.

So much for the objection, which, by this pair of Scottish philosophers, we have seen made to the scheme of logical division, which, in that age of comparative darkness, was invented, as it should seem, by the ingenious French Logician, Pierre Ramée.

As to any of those applications which by him (as we are told) were made of it, that at this time of day, unless it be from seeing how the instrument itself was managed by him, any useful instruction should be derivable, there seems no great reason to expect. Observation and experiment,—in these, as above observed, (§ 12.) may be seen the only sources of all real knowledge. In the days of Peter Ramus, anterior as they were to those of our Lord Bacon, scarcely, unless it were here and there by accident, had these funds been, either of them, so much as begun to be drawn upon. Of Logic with its divisions, all that it is in the power to do is, to arrange and display in the most instructive manner whatsoever matters have been extracted from those sources. What it can do is, to methodise; and in that unimmediate way promote creation:—what it can not do is, to create.

Section XVII.: Process of exhaustive bifurcation, to what length may and shall it be carried?

In the division of a logical aggregate, exhaustiveness can never fail to be useful and instructive: to afford assurance and demonstration of its existence, bifurcation can never fail to be necessary. By this time these propositions may, it is hoped, be assumed as truth. There remain however still, on every occasion, two questions: viz. how far this useful process can be, and how far it ought to be carried on.

By these questions the answers are suggested. Two bars present themselves, by either of which, where it has place, the employment of these instruments may be effectually opposed. One is impracticability, the impracticability of the operation: the other may perhaps be termed the uneconomicalness of it: being that which has place, where, whatsoever may be the value of the benefit, the value of labour necessarily attached to it—labour Edition: current; Page: [117] of creation, communication and receipt included—would be still greater.

I. As to impracticability. Of impracticability, in this case two causes present themselves as capable of having place: viz. uncognoscibility and unexpressibility.

1. As to uncognoscibility. It is only in so far as the properties, of the aggregates or classes of things in question, are known, that, for the purpose in question, or any other, any one such aggregate, with its branches, can thus be exhibited: this or that property being stated as having place in all the individuals contained in one of the two branches, and as not having place in any of those contained in the other. Take, for example, Natural History, and therein Botany. Forty thousand was, some years ago, stated as the number of supposed different species of plants (exclusive of varieties) at that time more or less known to the botanic world. But, at that time, the utmost knowledge obtained of them by any person was not, to any such degree clear, correct, and complete, as to enable him, in this way, to show, of every one of them, in any such concise mode, its points of agreement and disagreement with reference to every other. And even if, in and for any one year, the distinctive properties of the whole multitude of individuals contained in the whole multitude of species then known, could have been exhibited in this systematic form, the sketch given of them, if with regard to the whole number of species of plants then existing it professed to be, and even if it really were, an exhaustive one, would, in and for the next year, no longer possess that quality.

2. The quantity of surface necessary to the exhibition of such a diagram, presents another circumstance, by which, long enough before the number of the extreme branches had reached to any such number as forty thousand, as above, not to say the tenth or the hundredth part of it, the bar of impracticability would be opposed. Number of the extreme branches being 40,000; and this number, being the last term of a series of multiplications in which two is the common multiplier, what would be the sum required of the number of the intermediate branches, which being to be interpolated between the first term, viz. 1, and the last, viz. 40,000, would be to be added to the sum of those two numbers? To this question the answer is left to be found by any ready arithmetician, in whose eyes the profit would pay for the trouble.*

II. As to uneconomicalness. To perform the comparatively small number of ramifications exhibited by the annexed sample, was found to have imposed so heavy a labour, that over and over again, the thought of having undertaken it has been matter of regret. In comparison of the labour necessary to the execution of such a work, the mere labour of perusing it is obviously nothing. Yet even with this comparatively slight burthen, it is only in the instance of a very small proportion of the whole number of those by whom this volume may happen to be opened, that any expectation of their charging themselves with it can reasonably be entertained.

To those who have inclination and leisure, an assurance is here ventured to be afforded, that whatsoever may be the information derivable from the perusal of a work of this sort, to whatsoever subject applied, much greater will be the profit derivable in that same shape from the execution of it.

As to the length to which the operation shall be pursued, each individual will in both instances be determined by his own feelings in regard to net profit and convenience. But in one thing all persons, it is supposed, will be agreed, viz. that of the whole number of ramifications, which in this way it might be possible to exhibit, it will in most instances be no more than a part and that in most instances a small part, of the whole field, that will be found to afford adequate payment for the trouble.

On the other hand, the more extensive the universal trunk, the more extensive will be the quantity of information which, in and by each such ramification, will have been obtained and communicated; the more extensive the field, the greater will be the profit derivable from this mode of cultivation.

In the fields of Noology and Ethics it is, in contradistinction to that of Somatology (including Natural History and Natural Philosophy) that the nature of the field will, it is believed, be found to afford the greatest profit. Why? Because, for example, in Natural History, the knowledge of the utmost number of peculiar properties that could in this way be brought to view, would be but inconsiderable, in comparison with the number of such properties as are seen really to have place; and for which, though in each instance they might be exhibited, as they are actually exhibited in a simple list,—no place could be found in any such Table.

The objects, of which the words that belong to Noology and Ethics are the names, are chiefly the works of man, the products of his mind. In multitude and variety the works produced by this instrument are as nothing in comparison with those produced by the hand of Nature.†

Section XVIII.: How to plant a Ramean Encyclopædical tree, on any given part of the field of art and science.

Having, during a long course of years, and on a great variety of occasions, if his conceptions on this subject are not altogether illusory, derived much advantage from the use of the Ramean tree, the author is unwilling to quit this part of the field altogether, without having first thrown out a few hints, which have occurred to him, as capable of affording more or less assistance, to any other person,* who, on any occasion, may feel inclined to make trial of the old logical instrument, thus newly offered to notice.

1. As far as they go, employ such materials as you find ready provided to your hands. These materials are such words as, in relation to the subject in question, are to be found already existing in the language: the words, and thereby the relations, in the designation of which they are respectively employed. Set them down together, one after another, for example in columns, as many as in the first instance you can think of or find, adding from time to time others as they occur.

2. When you have got enough of them to begin upon, whatsoever be the field of which you were then endeavouring to take a survey, among the words the import of which is contained within the limits of it, look out for the one of which the import presents itself as most extensive. See whether it exactly covers the whole extent of the proposed field of your survey. If yes, employ it for your universal trunk; if not, you must frame some word which, by its import, shall, after what explanation may be found necessary, present to view, in the most effectual manner, the whole contents of that same field.

3. The universal trunk being thus found or made, for the first pair of branches look out for the two words, the imports of which present themselves as being both of them contained in the trunk, and at the same time the most extensive of all those that are; applying to them the test herein described, observe whether within their imports, taken together, the whole matter of the trunk be comprehended: if yes, there is your first pair of minor aggregates given, your first ramification made.

4. If no two such words can be found, then take the one the import of which—it being, (as it naturally will be,) the name of a positive property—appears, next to that of the above-mentioned trunk, the most extensive. Taking this for the name of one of your two minor aggregates, branches of the first ramification, the sign of negation added to it gives you the other.

5. The test always in hand or mind, proceed in the same way, carrying on your series of ramification as far as you find convenient: at every joint, for your two branches looking out for a pair of names, both of them in common use: taking up with only one such name, and for the corresponding name adding to it its contradictory, in those cases alone in which no such already existing pair of trivial, but at the same time all-comprehensive names are to be found.

6. For each such branch, if you see occasion, in addition to such its two-worded name, framed as last-mentioned, find or frame a single-worded name;† which will thus stand as a synonym to the just-mentioned Encyclopædical two-worded name, and will for ordinary use be a commodious substitute.

7. If, under any trunk, whether by finding them or by framing them, you provide yourself, in the first instance, with a pair of single-worded names, then, for purely Encyclopædical synonyms, you will have to frame for each a two-worded synonym: if, in the first instance, the pair of two-worded Encyclopædical names are those with which you provide yourself, then, for Encyclopædical use, or trivial use, or both, what you will have to do is, as above, to find or frame, as the case may be, one or two single-worded synonyms.‡

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8. On proceeding in this track, what will be very apt to happen to you is, the finding that, after you have thus found places in your system for a certain stock of appellatives, growing always in number greater and greater, but in point of import each of them less and less extensive as you advance, a number of appellatives, more or less considerable, the imports of which are more extensive than those of some to which you have given admittance, have been left behind. These imports, however, being, by the supposition, included, every one of them, within the limits of the field which you are thus surveying, will not present to you any new difficulty. By the imports of these words, as well as by those of the others, will the field be divisible: only, for the making of your divisions, you must look out for some one or more other sources.*

9. In these cases, as in those first mentioned, these sources will be furnished by so many distinctive properties: which accordingly you must be on the look out for, and for each of which, if it have not a name already, you must make one.

10. Having found or made names for all these several sources of division, set them down one after another in one list; which done, for exhibiting the relation which the objects so denominated bear to one another, you will probably find some means of comprising, in one and the same system of divisions, the whole list of those sources of division, in the same manner as you have comprised in one such system the results of the several divisions from the first of all these several sources.†

11. On looking over the stock of words, belonging to this your field, you will probably find, in a number more or less considerable, pairs or parcels of words, which with relation to one another are synonymous. These, as they occur, you will pick up, and, in that character, note them, and set them down. Examples of words thus related may also be seen in the Table.

12. Whatsoever they may be in other respects, it was impossible these directions should be made anything like complete for use, without some intimation given of the distinction between names of real entities and names of fictitious entities; a distinction which, in some of his Encyclopædical remarks, D’Alembert was, it is believed, the first to bring to view, and which will be found to pervade the whole mass of every language upon earth, actual or possible. Names of bodies, for example, are names of real entities;‡ names of qualities and relations, names of fictitious entities. The names, by which the branches of the Porphyrian or Ramean tree are designated, are names of real entities.§ The names of the branches of the Encyclopædical tree here submitted to view, are names of fictitious entities; though to a considerable extent included in them, as will be seen, are references made to correspondent names of real entities.

Names of real, names of fictitious entities, in the division thus expressed, may be seen one exhaustive division of the whole stock of nouns substantive. Strict, to the highest pitch of strictness, as is the propriety with which the entities here called fictitious are thus denominated, in no instance can the idea of fiction be freer from all tincture of blame: in no other instance can it ever be equally beneficial; since, but for such fiction, the language of man could not have risen above the language of brutes.

The above seemed as little as could be said, to prevent the whole field of fictitious entities from presenting itself to the eye of the mind in the repulsive character of an absolutely Edition: current; Page: [120] dark spot. More cannot be said, without wandering still further from the main subject, and trespassing beyond hope of endurance upon the reader’s patience.

The endeavour to trace out, throughout the whole of their extent, the principal relations between the field of thought and the field of language—comprising, of necessity, the leading principles of the art and science of universal grammar—have been the business of a distinct Essay, which it has been, and continues to be, the wish of the author to include within the limits of the present work. And in that work, in addition to the discoveries, half concealed or left unperfected, by Horne Tooke, the distinction, between names of real and names of fictitious entities, will constitute a capital and altogether indispensable instrument.* Almost all names, employed in speaking of the phenomena of the mind, are names of fictitious entities. In speaking of any pneumatic (or say immaterial or spiritual) object, no name has ever been employed, that had not first been employed as the name of some material (or say corporeal) one. Lamentable have been the confusion and darkness, produced by taking the names of fictitious for the names of real entities.

In this misconception may perhaps be found, the main, if not the only source, of the clouds, in which, notwithstanding all their rivalry, Plato and Aristotle concurred in wrapping up the whole field of pneumatology. In the phantoms generated in their own brains, it seemed to them and their followers that they beheld so many realities.

Of these fictitious entities, many will be found, of which, they being, each of them, a genus generalissimum, the names are consequently incapable of receiving what is commonly understood by a definition, viz. a definition per genus et differentiam. But, from their not being susceptible of this species of exposition, they do not the less stand in need of that species of exposition, of which they are susceptible.†

By any person,—should there be any such person to whom the ideas thus hazarded, present themselves as having a substantial footing, in the nature of things on the one hand, and the nature of language on the other,—it will probably be admitted, that a demand exists for an entirely new system of Logic, in which shall be comprehended a theory of language, considered in the most general point of view. For the construction of such an edifice, a considerable proportion of the materials employed in the construction of the Aristotelian system of logic, would be indispensably necessary. But in this very supposition is included the necessity of taking to pieces the whole mass of that most elaborate, and, considering its date, justly admired and venerated monument of human industry and genius.

As to Plato, when in the vast wilderness of words with which, by this spoilt child of Socrates, so many shelves and so many brains have been loaded, and in which so many wits, beginning with those of Cicero, have been lost, when among all these signs, so much as a single thought, which is at once clear and instructive, shall have been pointed out, it will be time enough to steal from the examination of Aristotle’s Logic, either a word or so much as a thought, to bestow upon his master’s eloquence.

With some modifications, which reflection will suggest, and which it would take up too much time and room here to endeavour to particularize, the method herein above proposed, as applicable to names of objects, to those elementary parts of propositions, which by logicians are distinguished by the name of terms, would be found applicable to propositions themselves: to those propositions, for example, by which, under some such name as Contents, intimation is given, in general expression, of the matter contained in any literary work, and more particularly in any work of the institutional kind: and thus it is, that to the view taken of any such portion of the field of art and science, may be given, in the promptest and most commodious manner, any degree of extent of which the existing state of the materials, collected by observation and experiment, has rendered it susceptible: and in truth, terms being the matter of which propositions are principally composed, by any arrangement given to those principal ingredients, an arrangement is already in some sort given to the whole matter of all the several propositions, into the composition of which those elementary articles are capable of being made to enter.

In the explanation above given of the manner in which, out of such terms as, in any given part of the field, the existing state of the language furnishes, a system of exhaustively bifurcate division may be formed—it has been seen how it is that, in a number of places more or less considerable, for want of such names, already in use, gaps will be left in the work: gaps, for the filling up of which instructions are thereupon given.

By the powers of the imagination, working with analogy for its instrument as well as its guide, words, especially where, in some orderly manner, spread out, a number of them, together on one and the same surface, before Edition: current; Page: [121] the eye, will bring to view, each of them, not only the particular object, which in common discourse it is employed to designate, but an indeterminate multitude of other objects which, by means of some relation or other, stand, each of them, in some way or other associated with it. In this way it is, that by means of some indication, afforded by the import of this or that article belonging to the existing stock of names, the filling up of a gap of the sort just described will be effected: and by every gap thus filled up, precision at least, and frequently extension, will, if the operation be properly performed, be given to the conception entertained of the contents of that part of the field: and thus may be seen, according to the nature of the branch of art and science which is in hand, one way at least in which inventions may be, and doubtless have been brought to light, and discoveries made. Quodlibet cum quolibet, is a motto that may serve for every discovering, and every inventing mind.

Section XIX.: Logical Mode of Division—its Origin explained and illustrated.

For facilitating the execution of a work of the sort here in question, viz. a system of logical division in the exhaustively bifurcate mode—a few instructions, such as they have been seen, have just been hazarded. The topic was upon the point of being closed, when, by a dip taken into Condillac’s little work on Logic, an addition was suggested, which now seemed indispensable. The only sort of analysis, which in the present work hath as yet been in question, is of that sort, of which not so much as the conception could have presented itself, but in a considerably matured state of the human mind. But in that little work of Condillac, under the same name analysis, was observed to be brought to view a sort of logical operation, to which that appellation could not, it seemed, with propriety, be refused, but of which it was at the same time evident, that it could not but have been in use in the very earliest stage of human existence: a stage so early, that although the operation must, in its extension, have kept pace with that of language, yet in part the existence of it must have been anterior even to that of the earliest formed raw materials, of which language was gradually composed: since those materials are not, any of them, anything but signs of ideas, and it is only by the sort of analysis now in question—viz. the primæval logical analysis, performed by the mind upon individual objects in the character of physical wholes, that those ideas were supplied.

Of every logical analysis—of every system of logical divisions—the subject is a logical whole. But, any such logical analysis, nowhere could it ever have had a subject, but for that system of primæval logical analysis, which has had for its subjects physical wholes, and for its results those ideas, which at the very moment of their conception, were respectively accompanied and fixed by so many names or denominations:—signs, by means of which, in so far as those signs were the sort of names called common names, those ideas were as it were tied up into bundles, called sorts, kinds, species, genera, classes, and the like: the connexion being effected by another sort of logical instrument, which, as will be seen, is not analysis, but its converse, synthesis.

Of this double course—a course of analysis, conjoined with a correspondent course of synthesis—the commencement must have had place in the very infancy of society; and neither to the continuance nor to the extension of it can any conceivable bounds be assigned, other than those which apply to the extension and continuance of society itself.

1. Difference between a physical whole and a logical whole; 2. difference between physical analysis and logical analysis, when both have for their subject a physical whole; 3. difference between logical analysis and logical synthesis; 4. operation and instrument by which logical synthesis is performed; 5. necessity of an antecedent logical analysis, performed upon a physical whole, to the previous formation, and thence to the subsequent analysis of a logical whole; 6. necessity of an act of logical synthesis to the formation of such logical whole: such are the points, on all which, as soon as the definitions of the two species of wholes have been given, a conjunct illustration will be attempted.

By a physical whole, understand any corporeal real entity, considered as being in one mass, and without any regard paid at the instant to any parts that might be observable in it: for instance, this or that individual plant.

By a logical whole, understand that sort of fictitious aggregate, or collection of objects, for the designation of which any one of those names which, in contradistinction to proper names are termed common names, are employed; for example, the aggregate designated by that same word plant. The common name plant is applicable to every individual plant that grows; and not only to those, but moreover to all those which ever grew in time past, and to all those which will grow in time future; and in saying, of any one of them individually taken—viz. of those that are now growing, this plant exists, there is no fiction. But the aggregate, conceived as composed of all plants, present, past, and future put together, is manifestly the work of the imagination—a pure fiction. The logical whole, designated by the word plant, is therefore a fictitious entity.

For the illustration of these several points, follows now a short history, which though at no time perhaps realized in every minute particular, must many millions of times have been exemplified in every circumstance, which, to the purpose of the present explanation, is a material one.

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Walking one day over his grounds, a certain husbandman observed a plant, which was not of the number of those which he was employed in cultivating. Overhanging some of them, it seemed to him to impede their growth. Taking out his knife, he cut the plant off just above the root; and a fire, in which he was burning weeds for the ashes, being near at hand, he threw it into the fire. In so doing, he had thus in two different modes performed, upon this physical whole, the physical analysis. By being cut as it was, it became divided into two parts, viz. the root, and that which was above the root: and thus in the mechanical mode was the physical analysis performed upon it. By its being thrown into the fire and there consumed, of the portion so cut off as above, part was made to fly off in the state of gas, the rest staid behind in the state of ashes: and thus in the chemical mode was the physical analysis performed upon it.

Not long after, came a daughter of his that same way, and a plant of the same kind which her father had thus cut down being left standing, her attention was caught by the beauty of it. It was a sweet-brier rose, of which one flower had just expanded itself. All parts of the plant were not alike beautiful. By one part her attention was more forcibly engaged than by the rest. It was the flower. To examine it more closely, she plucked it off, and brought it near her eye. During its approach, the scent of it became perceptible; and thus another sense received its gratification. To prolong it, she tried to stick the flower in a part of her dress that covered her bosom. Meeting with some resistance, the stalk to which, with a few leaves on it, the flower was attached, was somewhat bruised; and now she perceived and distinguished another odour, which though not less agreeable, was somewhat different from the first.

All this while she had been performing upon this physical whole the logical operation termed logical analysis: performing it not the less, though, as in Moliere’s Bourgeois Gentilhomme Monsieur Jourdan when talking prose, without knowing it. The instrument, by which this mental operation was performed by her, was the fictitious entity attention. By the attention which she bestowed upon the flower, while no equal degree of attention was bestowed upon any other part of the plant, she analyzed it—she mentally resolved or divided it—into two parts, viz. the flower, and all that was not the flower: and thus she distinguished part from part.

Again. By applying her attention, first to the beauty of the flower, composed as it was of the beauty of its form and the beauty of its colour, she performed in this same original subject another analysis, which though still a logical analysis, was productive of results somewhat different from those produced by the former; for thus, in the same part she distinguished two properties or qualities; viz that of presenting to the sense of sight a peculiarly agreeable appearance, and that of presenting to the sense of smell a peculiarly agreeable odour. The parts were both of them real entities: the qualities were, both of them, fictitious entities.

Eager to communicate the discovery to a little brother of her’s, she took him to the spot: she showed him the plant from which the flower had been plucked. The flower had already become a subject of conversation to them: that part had already received the name of flower: not having equally engaged her attention, the other part, like a sheep in a flock, or a pig in a litter, remained without any distinctive name.

Ere long her sweet-brier rose put forth two other blossoms; being so little different from the first, each of these became flower likewise. From a proper name, flower thus became a common name.

In the course of another social ramble, a mallow plant, with a flower on it, met her eye. At a distance the flower was not yet distinguished from that of the sweet-brier rose—“Ah,” (cried she,) “here is flower again.” The sweet-brier, on account of its scent, which continued after the flower was gone, had been preserved: the mallow, having nothing but colour to recommend it, was neglected.

These rambles had not continued long, before other sweet-briers and other mallows met her eye. The former being regarded with interest, the other with comparative indifference, the occasion for distinguishing them in conversation was not unfrequently recurring. The rose flower became a rose flower, the mallow flower a mallow flower.

When the flower first observed was named flower, as yet nothing but analysis—logical analysis—had been performed; no operation of the nature of logical synthesis: of one individual object it was and no other, that the word flower had been made the name. But, no sooner was the second flower observed, and the same name flower, which had been applied to the first, applied to this other, than an act of logical synthesis was performed. The proper name was thus turned into a common one; and the fictitious entity, called a sort, a kind, a species, or a genus, (call it which you please) was created.*

The fictitious entity being nothing at all, and the two real entities being each of them something, the fictitious entity itself did not contain within itself the two real entities, or either of them. But the name, which, after having occasionally been applied to each of Edition: current; Page: [123] the two real entities, became, by degrees, designative of the fictitious entity deduced from them, as above, by abstraction, continued to be employed for the designation of either of them, and occasionally for the designation of both of them together: and thus, in a sense, which, although not strictly proper, has the advantage of conciseness, the one fictitious entity, the species, may be said to have contained, and to contain, the two individual real ones: to contain, viz. though not in a physical, in a logical sense.*

The analysis thus unconsciously performed by the maiden on the first-observed sweet-brier rose, viz. by applying her attention to one part, while it was not applied to the other, had for its subject the real entity, the physical whole. It may be termed, the primæval or primordial analysis: for by no other sort of logical analysis will it be found capable of having been preceded. The analysis, by which the rose-flower became rose-flower, and the mallow-flower, mallow-flower, had for its subject no other than the fictitious entity, the logical whole, viz. the whole designated, fixed, and, as it were, created, by the denomination flower, so soon as, after having been employed merely as a proper name, it had come to be employed as a common, and thence as a specific or generic name. It may be termed the secondary analysis, or analysis of the 2d order. In her young mind, and in this its simple form, this secondary mode of analysis had nothing in it of science, nothing of system. But, in it may be seen the germ of all those systems of division, which, being framed by scientific hands, have spread so much useful light over every portion of the field of art and science.

The maiden had for her sweetheart a young man, who, though not a member of the Company Edition: current; Page: [124] of Apothecaries, (for the company had not yet received its charter,) had, on his part, been engaged in a little train of observations, to an improved and extended series of which, together with the experiments which they suggested, some thousands of years afterwards that most useful and respectable community became indebted for its establishment.

He had observed his dog, after a full meal, betake itself to a grass-plat, and gnaw the grass: a sort of article which, when hungry, it had never been seen to meddle with. To this sagacious swain the maiden was not backward in reporting her above-mentioned discoveries. It might, perhaps, have been not altogether impossible to obtain a communication of some of those observations and discoveries of his, for the purpose of adding them to hers. But, for the explanation of what has here been endeavoured to be explained, what has already been reported of the damsel’s will, it is hoped, be found to suffice, without any further trial of the reader’s patience.*

Some thousands of years after appeared Linnæus. In the course of that interval, not Edition: current; Page: [125] only in the language in which he wrote, but in every lettered language at least, not indeed with perfect steadiness, but still without much dispute or variation, a name corresponding to the word plant had been in use to be employed in the designation of any one of those physical objects, to which, when individually taken, that same denomination continues to be applied.

For the same length of time accordingly, a logical whole, possessing this vast extent—a logical whole, formed by the logical process called synthesis—had been in possession of the sort of existence which the nature of an object of this sort admits of.

For the purpose of distributing, according to such of these properties, as were at the same time most easily observable, most steady in their union, and most interesting to man, whether in the way of use or harm, such individual plants as from time to time should come under observation, and this to the end that such names might be given to them, whereby, for the purpose of putting to use their useful properties, or excluding the operation of their pernicious properties, they might, when seen, be recognised,—various sources of division had occurred to various scientific observers. By none of them had this useful object been completely accomplished. To Linnæus it appeared, that it was in the flower that the most apt source of division was to be found: inasmuch as, for the determination of the principal and most comprehensive divisions of a vast logical whole, certain differences, in respect of the form in which that part manifests itself, might be made to serve with as yet unknown advantage. Why? Because, with those differences in respect of the flower, other differences in respect of some of the properties most interesting to man—differences pervading the entire mass of each individual plant—had been observed to be conjoined. Thence, by seeing what sort of a thing the plant in question is, in respect of the flower, a guess may be formed, better than can be formed by any other means, what sort of a thing the plant is in other respects.

From this view a conception may be formed, of the disadvantage, under which every system of logical division comes to be framed. In this way no two things can be put asunder, but what have first been put together. To no other objects can this mode of analysis be applied other than to logical wholes—objects which are altogether the product of so many antecedent logical syntheses. But, in the first place, the primæval logical analysis, performed upon individual objects—this process, notwithstanding this its scientific name, having taken its commencement at the very earliest stage of society, cannot but have had for its operators the most unexperienced, the most Edition: current; Page: [126] uninformed, and unskilful hands. In the next place, the synthetic process, by which the results of that analysis, fragments detached, by abstraction, from these physical wholes, were placed as it were under so many different common names, and by those names bound together by so many logical ties,—this likewise was a work, which, though not yet concluded, nor in a way to be soon concluded, must in its commencement have been coæval even with that of the primæval process, to which it has been indebted for all the materials on which it has had to operate: coæval with the very first crude effusions, of the results of which the matter of spoken, and thence of written language, came, by continual additions, to be composed.

Thus stands the matter, in regard to those names of aggregates, in the signification of which are comprised such individual objects as are purely corporeal. How then stands it (says somebody) in regard to objects of the pneumatic cast, real and fictitious? The answer is—to apply to this division of the objects of thought the triple process, just above described, would require a full and detailed explanation of the nature of those fictitious entities, which, by reason of the similarity of the aspect of their names to that of the names of corporeal objects, all which names are real entities, are so continually confounded with real ones. But to suggest the question is almost all that can be done here. To attempt anything like a complete answer, would be to transgress beyond endurance the proper limits of this work. A few words, for the purpose of affording an indication, how faint soever, of the only track, by the pursuit of which, a satisfactory answer would, it is supposed, be to be found, may be seen in the concluding note.*

Section XX.: Proposed new Names—in what cases desirable—in what likely to be employed?

Among the new names, here proposed for Encyclopedical purposes, are there any, of which it is desirable that they should come to Edition: current; Page: [127] be employed for ordinary use? Among these again, are there any which present any chance of their being so employed?

In answer to both these questions, a very few words are all that can be afforded.

Geometry, Arithmetic, Algebra, Fluxions—for familiar use, what seems as far from being desirable as from being probable, is—that terms, of all which, though only one of them is exactly and originally expressive, the import is so well fixed, should be expelled by new ones.

To Mathematics, considered as a branch of art and science, in which all those others are included—to Mathematics, howsoever in its original import misexpressive, the same observation may be extended. Not but that Posology, should it ever be its lot to come into use, Edition: current; Page: [128] would form a more instructive, and, to all by whom its original import is borne in mind, a more satisfactory name.

Being in their original import so misexpressive,—and, even in respect of present import, one of them at least so indeterminate,—that Natural History and Natural Philosophy should give way to appellations fixed in their import, in some sort instructive, and at the worst not misexpressive, seems at any rate to be wished. Whether to be looked for seems not equally clear. To a grecianized ear in the first instance, and to an ungrecianized ear when explained to it, Physiurgic Somatology and Anthropurgic Somatology are expressive,—but then they are not single-worded. Physiurgics and Anthropurgics are, each of them, when separated from Somatology, single-worded. To the use of these, what seems to be the only obstacle, or at any rate the only assignable objection, is—that, being expressive of accidents without a subject—being substantives formed out of an adjective without a visible substantive—they might, for some time, fail of being sufficiently expressive. In themselves, (not to speak of Algebra, which, in its original import, is all darkness,) they are, however, in this respect, but upon a par with Fluxions. Even Physiurgic Somatics, or Physiurgic Somatology—Anthropurgic Somatics, or Anthropurgic Somatology—even these, though, as touching their two-wordedness, they are in no better case than Natural History and Natural Philosophy, yet in that respect they are in no worse case; and, in respect of determinateness and instructiveness, they stand in that so much better case, which in Section the fourth has been brought to view.

In all these instances, for presenting the import desired—the import for the presentation of which the demand is continually occurring—words, howsoever originally unexpressive or misexpressive, are—and without any very considerable inconvenience—already in universal use. Not so in the case of that branch of Ethics, for the designation of which the word Deontology has here been ventured to be proposed. Under the undiscriminating import of the word Ethics, a branch in itself so perfectly distinct, and which in practice so frequently requires to be distinguished from, and put in opposition to, that which joins with it in forming the two branches of the common trunk, is at present continually, and, but for those many-worded explanations, which are never given, and scarcely ever so much as thought of, irremediably confounded.*

For exemplification, thus much may perhaps have its use. To examine, in this same view, every new appellative which the Table furnishes, would surely be superfluous.

SOURCES OF MOTION.

Analytical Sketch of the several Sources of Motion with their correspondent Primum Mobiles.

Of Motion in general—its generation and extinction.

In the masses of matter with which man is conversant, and on which for his being, as well as his well-being, he is at all times dependent, whatsoever change is effected—this change is either itself some motion, or owes its origin to some motion of which it is the result.

Motion is the motion of some body or bodies; of some portion or portions of matter, of the aggregate mass of matter with which man is conversant.

Of this aggregate mass no particle can at any time, or in any place, in any direction, enter or be made to enter into a state of motion, without having to encounter a perpetual and indefatigable antagonist styled Resistance.

According to the commonly received distinction, this Resistance is susceptible of two Edition: current; Page: [129] different modifications; viz. 1. Counter Motion, i. e. active; and 2. vis inertiæ, or purely passive resisting force. But, perhaps, upon a closer examination it might be found, that that which presents itself in the character of a purely passive resisting force, is no other than an actively resisting force, produced by the elasticity of the mass to which the moving power is applied; that is, the repulsive power, the countermotion, or tendency to countermotion, of the particles of which the mass acted upon by the moving force is composed.

To one or other of these powers, if between them there can be any real difference, will be to be referred that cause, to the designation of which, when cessation of motion is considered as the effect of it, the word friction is applied.

For the purpose of rendering, in the best manner in which we are able, an account of the motion of such bodies as are in motion, and of the rest of such as are at rest, certain fictitious entities are, by a sort of innocent falsehood, the utterance of which is necessary to the purpose of discourse, feigned to exist and operate in the character of causes, equally real with, and distinct from, the perceptible and perceived effects, in relation to which they are considered in the character of causes.*

All bodies we are acquainted with, it is universally agreed, are compounds, as it were, of solid matter and empty space. All bodies, viz. the ultimate particles of solid matter which enter into their composition, are separated by intervals of space, in which no matter at all, at any rate none that we have any acquaintance with, is contained. To the different distances at which, in different states of its existence, the component particles of the same body are placed, are owing, in some degree, the different textures of which it is susceptible, and which, under different circumstances, it exhibits to our senses.

Take, for example, any mass of matter whatsoever: suppose an apple; the apple let it be from which Newton derived the first hint of the attraction of gravitation; the ever memorable apple which, as an object of worship to the latest posterity, ought to have been preserved from corruption in a hermetically sealed glass-case; ought to have been transmitted as an object of worship to the latest inheritors of this our globe:—the particles of solid matter of which this apple is constituted are, each of them at a certain distance from each of the several others. How happens it that they are not more distant. What is the cause of such their propinquity? The necessary fiction above spoken of provides an answer and says, the attraction of cohesion is the cause by the operation of which they are thus kept together. How happens it that they are as distant as they are? What is the cause of such their distance? Here again steps in the same useful respondent, and answers, It is by mutual repulsion that they are thus kept asunder.

It is to distinguish it from the attraction of gravity, of which presently, that the attraction, termed the attraction of cohesion, has acquired that name. Of this species of attraction, repulsion, it has been seen, is the constant companion, and antagonist; each of the opposite and mutually balancing effects have equal need of a fictitious cause. Repulsion is the generic name applicable to other cases. Attraction of cohesion is a specific one. To match with this its antagonist, the particular species of repulsion here in question requires its specific name. Repulsion corresponding to the attraction of cohesion, let this be that specific name; or rather an appellation thus multitudinously worded, being too cumbersome for use, say, the repulsion of cohesion: and though taken by itself, and without explanation, the appellative would, upon the face of it, be self-contradictory, yet by this explanation, to which by its texture it would naturally point, it may perhaps be found not altogether unfit for use. Instead of this appellation, or Edition: current; Page: [130] for variety along with it, if for attraction of cohesion, the appellation internal attraction, or intestine attraction, be employed; for repulsion of cohesion, the term internal repulsion, or intestine repulsion, may be employed.

In the Attraction of Gravity may be seen one of the fictitious entities, to the operation of which, in the character of causes or sources, the birth of motion, howsoever modified, may, as far as we are acquainted with it, be referred. To the repulsion of cohesion—to this one simple cause, will, it is believed, be found referable, with equal propriety, the death of all these several motions; which, at the conclusion of the conflict maintained by the various species of attraction, endowed with their several unequal degrees of force, remains, constituting the only force by which matter is retained in that state of composition above-mentioned, which seems essential to its existence; and by which the whole multitude of its particles are prevented from being crowded together into one mass.

To account for the difference of bodies in point of distance, a sort of nominal entity is feigned, to represent the cause of it, and Motion is the name by which this imaginary cause is designated. Motion is thereupon considered (for such are the shifts that language is reduced to) as a sort of receptacle in which bodies are lodged; they are accordingly said to be in motion, as a man is said to be in a house.*

By laying out of consideration everything that concerns the particular nature of these bodies respectively; everything, in a word, concerning them, but the difference between the distance or interval between them at the one time, and the distance or interval between them at the other, we obtain the abstract idea, for the designation of which the word motion is employed. In speaking of it, we speak of it as if it were itself a substance: a hollow mass into which the body, the really and independently existing body, whatever it be, and how vast soever it be, is capable of being put, and which is capable of being communicated to that body, and so in regard to bodies in any number.

A philosopher, says the old Greek story, denying the existence of Motion, another to refute him, got up and walked. Good for a practical joke, not so for a serious refutation. Of the existence of the faculty of locomotion, the denier of the existence of motion, was not less perfectly aware before the experiment than after it. What he denied was,—not the universally exemplified, and universally known, and acknowledged matter of fact, that the same body is at one time in one place, at another time in another, and in that sense the existence of motion—but the existence of any real entity, corresponding to the appellation motion; any entity real and distinct from the body or bodies in which the motion is said to have place.

Thus early (as appears from this story) had a conception, however narrow and inadequate, been formed of the distinction between names of real entities and names of fictitious entities;† a distinction by which much light has already been thrown, and by degrees much more will be thrown on the field of language; and through that medium, on the field of thought and action; and, in particular, on the nature of the relation between cause and effect. Cause, when the word is used in its proper signification, is perhaps in every instance the name of a fictitious entity; if you want the name of the correspondent real entity, substitute the word author, or the word instrument, to the word cause.

Rest is the absence, non-existence, or negation of this imaginary receptacle. When, after observation taken of the two bodies in question, at two different points of time, no such difference of distance is found, they are said to have been during that length of time each of them at rest. Rest is thus a sort of imaginary pillar, or anchor, to which, in the English language, they are considered or at least spoken of, as being fastened.‡

Enclosed in that receptacle, or fastened to this pillar or anchor,—one or other is at every point of time the condition of every object to which the name of body has been attached.

The truth is, that absolutely and properly speaking, in as far as observation and inference have extended, motion is the state or condition in which, at every point, every body is, and so for ever is likely to continue. Rest is not the state of our own sun, about which the planet that we inhabit moves. If a state of rest were predicable of anything, it would be of the ideal point in the expanse of space, the centre of gravity, as it is called, about which, the sun on the one part, and the planets on the other, are observed or supposed to turn. The observations and inferences thus applied, in the first instance, to our sun, have been extended to those other bodies to which, to distinguish them from those companions to our earth called planets, we give the name of fixed stars; but which, determined as they have been by these observations and these inferences, it has seemed good to our astronomers not to tie to the above-mentioned pillar, but to put all together into the above-mentioned receptacle.

So it is then, that, for the purposes of discourse, as well as of thought and action, the Edition: current; Page: [131] pillar is not less necessary to us than the receptacle. For this purpose, rest requires to be distinguished into absolute and relative. Absolutely speaking, as above, no one body is at rest; but on this our little planet, the theatre of all our little doings and sufferings, bodies in abundance are to be found, which, as between any two given points of time, having been at the same distance from each other, have, during these two points of time, together with the whole interval, if any, that has been between them, been at rest. Upon the whole, then, absolute rest is not exemplified anywhere; but, on the surface of our planet, exemplifications of relative rest may be found everywhere. These things considered, henceforward as often as rest is spoken of as having place, relative rest, and that alone, will be intended.

The motions in which the various effects, as yet observed by us to be produced by the powers of nature, modified or not modified by human art and industry, have their essential causes, are derived from various sources. Of these motions, obvious, as when once brought to view, the task of giving a list may seem to be—obvious, and, by its conduciveness to the purpose of instruction, presenting an incontrovertible claim to the notice of the institutional writer, who, for the theatre of his labours, has chosen the field of Natural Philosophy,—the task of giving such a list, hath, it is believed, as yet, been undertaken by no one. No work in which that task has been executed, or endeavoured to be executed, is as yet anywhere to be found.

Consideration had of the utter absence of all information from more competent hands, to the author of these pages, how little soever accustomed to apply his industry to this department in the field of science, it occurred that an attempt to afford, in a manner however inadequate, a supply to this deficiency, might have its use, were it only by attracting to so interesting a subject, which presents so strong a claim to their notice, the attention of those from whose more adequate learning and ingenuity it may receive more correct and complete explanation.

Of these various sorts of motions, some are, as far as we have reason to believe, in their nature perpetual, unintermitting, or, if a common figure of speech may be allowed, immortal. Others, and by far the greater number, in their nature mortal and perishable.

Of these two so materially different heads, Which come under the former? Which under the latter? In any attempt to give answers to these questions, an answer to the question concerning the existence of what is called perpetual motion, is necessarily involved.

Of the following sketch the design is, in the first place, to perform the enumeration of the several distinguishable sources of motion, considered as it is wont to be produced, or capable of being produced by human art, in some determinate direction, for the purpose of accomplishing some determinate object or end in view. In the next place, by means of a systematical sketch, to bring to view the several points of relation between these several sources of motion,—the points in respect of which they agree with one another, and those on which they differ.

By this means a facility, it is hoped, will be given to the decision on the question, whether, in the preceding enumeration all such sources, actual and possible, are included; or whether any, and what are omitted.

Primum mobile is a term already in use; and by it, in each instance, is designated that mass of matter, which, when from the particular source in question, motion is considered as derived, is considered as being of all the bodies by which the motion is experienced, which, at the time in question, issues from that source, the first in which it has place. Accordingly, corresponding to every distinguishable source of motion, a primum mobile will be to be brought to view.

Of the two expressions, viz. sources of motion, and primum mobiles; the latter is the one, principally, if not exclusively, in use. To the other the preference has, notwithstanding, here been given, and that on several accounts.

1. It is only in as far as it points to the source whence it is derived, that the question, what or which is the first mover? (the body which, on the occasion in question, is of all the bodies in which the motion is observed to have place, the first in which it makes its appearance,) is an object of regard. In the class of objects designated by the generic word motion, men behold the cause of every effect, desirable or undesirable, which they perceive to take place. But various are the sources whence this important agent is seen to be derived. An object of anxious and continual research cannot but be, the determining, on every occasion, from which of all these sources, the article thus in universal demand, may be derived to most advantage.

Of this inquiry, source is the only direct and intrinsically important object: the primum mobile is so no otherwise than either in respect of its affording indication of the source, or, in respect of the need there is of commencing with this article, the plan of the operations instituted, for the deriving down to the ultimate object, whatsoever supply there may be occasion to draw from this source.

2. In many instances in which the source is sufficiently distinguishable to admit of a separate name, the primum mobile is altogether undiscernible; or, to speak more properly, a primum mobile is a thing that has no existence,—two bodies, or sets of bodies, move each of them towards the other, both beginning at the same instant of time; as is plainly the case, for example, in all those minute motions or dances of atoms, which belong to the experience of the chemical branch of science.

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In a word, of the phrase, source of motion, the applicability will be seen to be universal; that of primum mobile, very confined; so much so that it is only in deference to usage, that any notice is here taken of it.

Sources of motion, enumerated with their corresponding Primum Mobiles: a sketch supposed to be all-comprehensive, and now, for the first time, attempted.

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MECHANICAL POWERS.

On this ulterior subject, a few loose hints are all that the writer can at present afford,—all that he can hope to find the readers, to whom he looks, disposed, on this occasion, to bestow any further portion of their notice.

To reduce to one and the same expression the description of the several sorts of instruments, which are in use to be included under the common name of the mechanical powers, seems to have been an object of desire, and, in some respects, of endeavour, with the authors of institutional works.

In any such desire, in any such endeavour, at least the notion of the practicability of the work is included.

That it may be practicable to reduce to a single expression some certain property, or certain properties common to all these several instruments, is a proposition which I see no reason, nor feel any disposition, to dispute.

But it is only in respect of the uses which they are capable of being put to, that for any purpose but that of barren speculation and solitary amusement or curiosity, they have any of them any claim to the attention of the ingenious, or any other part of mankind.

Now, howsoever it may be in regard to this or that speculative property, in regard to the practical applications made of them—those applications in respect of which alone they can lay any claim to the property of being of use—in reference solely to this property, what may be asserted with confidence is—that they are not capable of being reduced to any such common denomination.

Instruments for gaining force, at the expense of velocity, or velocity at the expense of force, were this a property belonging to all of them, the problem of reducing to one expression the advantage gained by them, might be a not unsolvable one. But out of the six or seven, it is to three only that this common property can justly be ascribed, viz. the lever, the axis in peritrochio, and the pulley or combination of pulleys: to the inclined plane, the screw, and the wedge, it is not applicable. In all these instances, the use derived from the instrument in practice depends upon other sources: upon properties in which the three before-mentioned powers do not any of them partake.

In the case of the lever, the axis in peritrochio and the pulley, the power of the machine finds not an assistance, but, in so far as it operates an impediment; whereas, in the case of the screw and the wedge, were it not for the power of friction, the effect aimed at would not, generally speaking, be produced.

Of the screw, though it certainly may be and actually is employed as well as the lever, axis in peritrochio, and pulley in the raising of weights, yet, the use to which it is applied with much greater frequency, and with a correspondent amount of advantage is that of connexion: binding for an infinity of different purposes, two or more masses of matter in a solid form into one.

So again the inclined plane. It is not for gaining force at the expense of velocity or velocity at the expense of force, that the instrument thus denominated is commonly, if ever, applied: it is for modifying direction; it is for producing in a certain direction certain results, which but for this instrument could not, in certain circumstances, by all the force obtainable by any of these instruments, be obtained.

Suppose a natural rock, or an artificial erection, having for its altitude that of one of the Egyptian pyramids, and for the boundaries of its upper surface, as well of those of its under surface, those of that same pyramid. By the application of force on one side of the paralleli-pedon with all the levers, wheels, and pulleys that could be collected, a man would not communicate the power of either himself mounting to the top of it, or causing a block of stone so to Edition: current; Page: [147] do. Applying an inclined plane to it, making an angle coinciding with any one of the angles made with its base, and the plane at the vertex of the pyramid by one of its present sides, the man may mount upon it, or the block of stone may be drawn up to it.

On this head the theoretical conclusion is, that in pursuing without sufficient scrutiny, and hence with too undeviating an adherence, the path chalked out by the ancients, and by them pointed out by the collective appellation of the mechanical powers,—the five or the six mechanical powers,—the progress of science has in this part of the field, as in so many others, been retarded.

So much for the theoretical conclusion: and the practical which corresponds to it, and is deduced from it, is, that some other principle of arrangement should be looked out for, and that a more comprehensive one—a principle which will afford an opportunity of placing upon the list many species of instruments which, though actually invented and in use, are not as yet put upon the list; many instruments actually known, and known to be in use, and, peradventure, other instruments which by a more correct and complete conception of the subject may continually be brought to light. What is the principle? It consists in substituting to the present arrangement, an arrangement which shall bear reference to the several distinguishable purposes or uses, for which mechanical contrivance is in demand; in one word, in substituting the idea of uses to that of powers. Gaining force at the expense of velocity,—gaining velocity at the expense of force,—are but two of those purposes,—are but two items in an indefinitely, in an hitherto indeterminately ample catalogue; changing direction is a third; forming connexion is a fourth; dissolving connexion is a fifth; and so on. But here, on pain of losing myself altogether in a field foreign to the present purpose, I must make an end.

PERPETUAL MOTION.

In the history of the generation and extinction of the birth and death of motion, is involved the question of perpetual motion.

One species of motion there is, which, as far as we can judge, may, with good reason, be pronounced perpetual. It is that by which the bodies which compose the perceptible part of the universe, are kept whirling in their orbits. Perpetual, as far as we can judge, it must be presumed to be. Why? Because there can be discerned no cause, the operation of which should tend to make it cease. This, however, supposes the spaces in which they respectively move to be so many vacuums: for suppose them occupied with matter in any shape,—in the shape of a gas how rare soever,—in the resistance opposed by friction, by the gaseous repulsion of the particles of which it is composed, in that resistance, how distant soever the term may be, may be seen a cause fully adequate to the production of its effect.

In the instance of the stereopiptic source, numerous, it is believed, have been the contrivances produced by the hope of converting a source of short-lived motion into a perpetual one.

One consisted of a wheel, in which, along a spiral channel, a quantity of mercury was to find its way in its fall from the axis to the circumference; the longer the semi-diameter of the wheel, the longer the lever with which, when arrived at the circumference, the mass of mercury would act upon any body situated nearer to the centre. Make the diameter of your wheel infinite, and the force you will thus acquire will be the half of an infinite force. But, long before you had been at the trouble of giving to it any such inconvenient extent, you would have acquired force enough to pump up into the annular reservoir contiguous to the axle-tree a supply of mercury sufficient to continue the motion, and thus your motion would be a perpetual one. Somewhat in this strain seems to have been the reasoning that gave birth to this contrivance.

By the time it had reached the circumference, subtraction made of the force destroyed by friction, the mercury would have produced an effect equal to the effect produced by the same mass of mercury in falling from its position near the axis to its position near the circumference, without the trouble of taking any such sweep.

In the course of its transit from the one end of the spiral to the other, it would have to make a number of descents, as also a number of ascents, proportioned to the number of convolutions or threads in the spiral: the descents would be so many motions having for their adequate cause the attraction of gravity; the ascents would be so many motions, none of which would have any adequate cause; friction sufficing of itself to prevent the cause which in the preceding descent they respectively had from being an adequate one.

All perpetual motions having for their source the attraction of gravity, would, it is believed, be found resolvable into this mercurial one.

Some five and forty years ago, Dr Kenrick, most known by an attack made by him on Dr Johnson the Great, in an 8vo volume entituled Lexiphonis, took in hand the subject of the perpetual motion, and on this subject read, and afterwards published, a few lectures of which the effect, if any, was to render the subject somewhat more obscure than he found it. The object was to render probable the possibility of the existence of this rival of the philosopher’s stone. One of the proofs consisted in some mention that was made of a certain mysterious wheel invented and manufactured by a person of the name of Orphyonis. By this wheel great were the wonders wrought; but, unhappily, the instrument being with prudent caution kept constantly enclosed in an Edition: current; Page: [148] opaque and well-locked box, the invention died with the inventor, and was thus lost for ever to the world.

Not being known to the world by any other work, the inventor, Orphyonis, has somewhat the air of having been in the way of eponthesis, derived from Orpheus.

If any such wheel was ever made, it may be affirmed, without much danger of mistake, that the principle upon which it was constructed, was either the mercurial principle just explained, or the magnetic, of which the idea has been already given.*

By the perpetual motion is designated a motion, which, how ill-grounded soever, has on various occasions been espoused, by men not altogether unconversant either with the practice or with the principles of mechanics. On this part of the field, one true use of science is to render clear, and hold up to view the delusiveness of all expectations entertained on this ground, and thereby prevent the disappointments and pecuniary losses with which all such expectations can scarcely in the event of their being acted upon fail of being productive.

For any motion of any mass or masses of matter, situated within the reach of human agency, to be in the literal import of the word perpetual, it would require that the masses of matter in question should be in every part indestructible, and the particles of which they are composed, unsusceptible of being, any one of them, by means of the motion or otherwise, separated from any other. A notion to any such effect being in opposition to universal and continual observation and experience, can scarcely be supposed to have ever found admittance into any human breast.

But, independently of the operation of any such manifestly and universally operating cause, by the word friction as above explained, is moreover designated a cause, in which no imaginable motion, from whichsoever of the above sources proceeding, can fail of experiencing, within a very short space of time, unless renewed, its inevitable death.

But in any case, in which the motion can be said to be renewed, the motion, when the case is more clearly looked into, will be seen not to be one and the same: it is a continually successive creation of fresh motions: viz. in the case of falling water, falling earth, or wind, the motions of fresh and fresh parcels of matter, receiving motion one after another, though in the same direction; in the case of motion produced by muscular exertion, fresh and fresh exertions of the will, and contraction of the same or other muscles, produced in consequence.

If in the import of the words perpetual motion, were included the idea of any internal source of motion, by which different particles of matter, after having in any never-interrupted series been put successively in motion, were so to continue without end, then and in such case there would at all times be as many perpetual motions as there are distinguishable purely physical sources of motion (meaning individual sources, not species of sources) operating and producing motion, as above. But, in no one of the cases, in which a perpetual motion has been said to be invented, or said to be capable of being invented, does any such state of things appear to have been in view.

SKETCH OF THE FIELD OF TECHNOLOGY.

To a course such as that here proposed, a not unapt conclusion may, it should seem, be afforded by a view of what has been termed Technology,—General Technology,—the aggregate body of the several sorts of manual operations directed to the purposes of art, and having, for their common and ultimate end, the production and preparation of the several necessaries and conveniences of life.

Of a view of this art, the amusiveness no less than the instructiveness, will receive no small increase, if to the exhibitive description, accompanied as far as may be, with the exhibition of the instruments and operations themselves, be added an indication of the rationale of the several operations.

By the rationale is here meant, an indication of the end most immediately in view, and the considerations by which, as between instrument and instrument, or operation and operation, the choice appears to have been determined.

By a familiar example, what is here meant will, it is believed, be rendered sufficiently apparent. For the purpose of making holes destined to give admission to threads employed Edition: current; Page: [149] for the purpose of junction, the instrument employed by the tailor is the needle; that employed by the shoemaker, the awl. When the needle is employed, the work, it is evident, may be made to go on with a degree of rapidity much beyond any that can be given to it by the awl. Why, then, in the case of shoemaker’s work, employ the awl?—Answer. Because the habiliment fastened by the shoemaker,—having for its principal object the exclusion of water, to the action of which it is continually exposed, at the same time that the material is of that sort which, when a hole has been made in it, has but little tendency to fill up the vacuity,—could not, if the needle were employed, be made to answer the intended purpose. The needle is capable of admitting the thread only by means of a slit called the eye, made at the thickest end of the needle into which the thread is passed, and, therefore doubled. The needle is a cone, of which the transverse section is a circle. The thread, without being in some part of its length double, cannot pass through the hole made by the needle, without passing in the form of two cylinders enclosed, both of them within the circle formed by the above-mentioned section of the needle. But, in this way, notwithstanding whatsoever elasticity may happen to be possessed by the substance into which the holes are made, it cannot be but that a part, and that a very considerable one, of the circle, will remain unfilled up; and, at this part, if the habiliment be a shoe and the material leather, the water will gain entrance. On the other hand, when, for making the holes, the instrument employed is the awl, the thread is not attached to it. The thread is a strip of leather, the section of which is a square, a form by which the hole will be more exactly filled up than by any other that could be given to it. Of this square, the central part is occupied by a hog’s bristle, a cylinder, which being comparatively inflexible, and of a diameter smaller than that of the hole destined for the strip of leather in which it is imbedded; a ready admission will be obtained into the hole as soon as the awl is drawn out of it.

For the purpose of such a conspectus, a work of indubitable use, would be a logical, i. e. an analytical arrangement of the several manual operations, employed and employable, for the purposes of the several arts considered on this occasion, and for this purpose, in conjunction: say, therefore, of art in general.

To any person by whom a work of this sort should be undertaken, very useful hints would be found afforded by a work of Bishop Wilkins. As a copy of that most ingenious work is not obtainable but by accident, an extract from it, containing as much as seemed applicable to the purpose in question, will be found in the Appendix to this present Essay.*

In the works of recent naturalists, chemists, and nosologists, and, in particular, in the Philosophia Botannica of Linnæus, the father, as he may be termed, of Somatological tactics, much useful instruction, many excellent patterns may be found applicable to such a work. That, in such a work, these patterns or standards of reference, cannot in any part be closely copied, will be evident enough; but that, by the aid of analogy, instruction in abundance will be derivable from them, will be found equally indubitable.

From the consideration of the purpose, together with other considerations subordinate to that leading one, mechanical instruments and operations, and their results or products, may, as well as plants or other natural bodies, be arranged into classes; those classes divided into orders, and sub-divided into genera and species; between orders and genera, other divisions, if found necessary, being interposed; and to these several aggregates, thus continued one within another, names taken for distinction sake, from one or other of the dead languages, may be attached.

Say, for instance, name of one of the genera of instruments, Terebræ—instruments employed for the boring of holes. Species—1, the awl; 2, the gimblet; 3, the augur; 4, the whimble, &c.

Name of another of the genera, Clavi—instruments employed for the effecting a connexion between two or more substances of a rigid texture, and for that purpose to remain inserted partly in one and partly in another. 1, The pin; 2, the bolt; 3, the nail; 4, the trenail; 5, the screwing nail, called for shortness, the screw.

Neither as being, in as far as it goes, complete, nor as being the most apt, that the nature of the case admits of; nor in any such hope as that of its being found to approach to perfection in either of these particulars, is this specimen brought to view; the object of it is merely to afford a general idea of the principles upon which it is proposed that it shall be formed.†

Not only to instruction, but moreover to improvement, to practical improvement, will be the assistances afforded by a systematical, or say an analytical, arrangement of this kind. Taking throughout, for its leading principle, the object or end in view, it will form all along, as the work proceeds, a bond of connexion, and, as it were, a channel of intercourse between art and art; artists of all sorts, how different soever the results and products of their respective arts, may thus receive instruction from each other’s practice; each may thus find his mind expanded—expanded in that direction in which, being prepared for it by antecedent practice, expansion will be most easy and pleasant.

For a work of this sort, in the French, Edition: current; Page: [150] “Descriptions des Arts et Metiers,”* materials will be found in abundance. But, conducted upon the systematic and all-comprehensive plan above brought to view, it will possess a degree of utility beyond any to which that work so much as aimed. Of that work, the compilers were philosophers, and in that character, something in this way might not unnaturally have been looked for at their hands. But of so vast and diversified an aggregate of materials, the collection and the arrangement—the arrangement in logical order, such as is here in question, was too much to look for, not only from the same hands, but, perhaps, from the same half century. In a case such as this, the particulars required had not only to be collected upon a most ample scale, but compared and confronted, one with another, in an infinity of directions before the work of classification could be entered upon with any very promising prospect of lasting use.

Bulky to a degree of unwieldiness is that justly celebrated work.† But, even with those ample additions which, by English practice, might doubtless be afforded to the stock of the materials, it follows not that, in point of bulk, a systematical work of the kind here proposed need, by a great length, approach to the bulk of that vast and elaborate performance. By apt aggregations, infinite is the number of particulars which in such a case may be found superseded. In different trades, an instrument which, in all these several instances, is of precisely the same use; an operation which, in all of them, is of precisely the same nature, may stand designated by so many different names.

For a course of Chrestomathic instruction, as here proposed, a work of this nature would form a necessary text-book. By the indication of such a work in the character of a requisite, the possibility of commencing such a course, may seem, at first view, to be thrown forward to an immeasurable distance.

1. But, in the first place, it is not till the very end of the proposed Chrestomathic course—viz., say for seven or eight years—that any such particular course is so much as proposed to be delivered.

2. In the next place, for a commencement, an extempore work, very far not only from the utmost attainable perfection, but from the degree of perfection of which an idea can be formed at present, will be of indubitable use, and as such, presents an undeniable claim to favourable acceptance. Be it ever so little, ever so imperfect, whatsoever will in this way have been done, will be so much more than will ever have been done before.

3. In the third place, by any one by whom, to the following sketch by the ingenious Bishop, a moderate share of attention will, in this case, be bestowed, no inconsiderable portion of that appearance of extraordinary difficulty, which the subject may, at first view, have presented, will, it is believed, be seen to vanish.

“VI.: Violent Motion.*

“The general kinds of Violent Motion, may be distributed according to the effects upon the thing moved, into such as denote

• Translation into a new place; comprehending
  • Motion together; when the Mover sustains the thing mored; to which may be annexed, by way of affinity, that other action, by which one thing sustains, or hinders the falling of another.
    • 1.

      Carrying, bring, convey, bear, serve, import, waft, weare about one, portable, portage, porter, baggage, vehicle, fare, bier, packhorse.

      Bearing, supporting, sustain, hold up, prop, shore up, stay up, uphold, carry, stand under, shoulder up, bolster up.

  • Amotion, when the Mover and Moved do at the beginning cease to be contiguous: or, admotion, when the thing moved doth end in a contiguity of something else.
    • 2.

      Casting, throwing, fling, hurl, project, inject, eject, ding, pelt, toss, coit, sling.

      Catching, apprehend, lay hold, snatch, lay hands on, grapple, grasp, scamble.

  • Often returns into the same place; according to greater or less degrees.
    • 3.

      Swinging, Vibration, waving, brandish, agitate, exagitate, to and fro, flourish, rock, sway, dangling, pendulous, wield.

      Shaking, Quassation, concussion, jogging, agitate, dandle, wag, swag, sway, jolt, totter, flutter, shatter, waving.

  • Some impression from the Mover; according to the more
    • General name; or that which is from an obtuse hard body.
      • 4.

        Striking, Percussion, smite, bang, beat, bast, buffet, cuff, dash, hit, swinge, thump, thwack, blow, stripe, slap, flap, rap, tap, kick, wince, spurn, bob, box, fillip, whirret, yerke, pummel, punch, rebuff, repercussion, collision, guash, skittish, interfere, let fly at.

        Knocking, beating, Blow, butt, Mallet, battering, jobbing, Ramm.

    • Particular kind; by the end of a thing, more obtuse, or acute.
      • 5.

        Pounding, braying, contusion, stamp.

        Pecking, Mattock, Pick-ax.

• Dissolution of Union in the same body, according to,
  • The Stiffness or Limberness of the body wherein it is made.
    • 6.

      Breaking, Fracture, Rupture, burst, Crack, Crash, Squash, Dash, Flaw, Shatter, shiver, crumble.

      Tearing, torn, dilacerate, rend, rent, ragged, tattered, flittered, jagged, pull in pieces.

  • The figure of the body by which it is made; either an edge or a point.
    • 7.

      Cutting, Incision, gash, slash, hack, hew, chop, rip, chip, snip, slice, section, segment, carve, dissect, whittle, barb, pare, top, lop, curtail, dock, sharp, keen, Hatchet, Pole-ax.

      Pricking, Stabbing, Goad, pungent, runn in, thrust in, goar.

“Operation.

“The Sundry kinds of works about which men of several callings use to employ themselves, are usually styled by the name of

Operation, Labor-ious Pains, Travail, Toil, moile, Turmoile, drudge, droil, work, handy-work, Ply, co-operate, take pains, lay about him.

Play, Sport, lusory, dally.

These are either,

• More common and general; relating to
  • Mechanical Faculties, I.
  • Mixed Mechanical operations, II.
• More Particular; belonging to the providing of
  • Food, Agriculture, III.
  • Houses, or Utensils, Fabrile Arts, IV.
  • Clothing, Sartorian Trades, V.
  • Physic, Chymical, Pharmaceutical Operations, VI.

Edition: current; Page: [152]

“I. Operations belonging to the Mechanical Faculties, are either such as do refer to the

• Lever; for the forcible motion of a thing upwards or downwards.
  • 1.

    Lifting, heave, hoise, advance, elevate, exalt, Lever, Crow, Crane.

    Depressing, strein, stress, weigh down.

• Balance; for trial of the weight of things, or the preponderating of one side.
  • 2.

    Librating, balancing.

    Biassing, preponderate.

• Wedge; for the dividing of hard tough bodies; to which may be opposed the thrusting of them close together.
  • 3.

    Cleaving, rive, slit, split, Cleft, Chink, Chat, Crevise.

    Compressing, crib, gripe, pinching, press, squeezing, straining, wring, nip, twing, throng, crowd, crush, constipation, bulge.

• Pully, when the mover and moved continue their contiguity in admotion, or amotion.
  • 4.

    Pulling, pluck, tow, tug, lugg, twing, twitch, draw, drag, Draught, hale, Revulsion, vellication, distract.

    Thrusting, push, shove, drive, rush, justle, repell, extrude, intrude, press, throng, crowd, cramm, farce, wedge in, vennue, run at, foin at.

• Wheel; by continued turning about, or rolling backward or forward.
  • 5.

    Vertiginating, turning round, Revolution, wheeling, Rotation, twirl, whirl, spinn, roll, round.

    Volutation, tumbling, rolling, wallow, welter, rock, trundle, waddle.

• Screw, to which may be adjoined for some affinity, the action of that concave Instrument used for the projection of water.
  • 6.

    Screwing, Winch.

    Syringing, squirting, spirt, spouting.

• Spring, wherein there is a motion of restitution; to which may be annexed for its affinity, the forcible putting a thing out of its natural tension and posture.
  • 7.

    Springing, elastical, fillip.

    Bending, bow, warp, crooke.

“II. Those are styled Mixed Mechanical operations, which are not appropriate to any one kind of art, but are general and common to many. These do concern the

• Uniting or separating of several bodies; considered more
  • Simply,
    • 1.

      Binding, gird, Band, Bond, Bundle, Packet, Fardle, sheafe, faggot, tack, lace, swaddle, swathing, trussing, girt, surcingle.

      Loosening, unbind, undoe, solve, lax, slack, relaxation.

  • Relatively to the affections of Binding, viz. fastning of the bond by a knot, or confused kinds of knots.
    • 2.

      Tying, Knot, Node, bracing, buckling, coupling, fastning, knit, furling.

      Tangling, entangle, hamper, ravel, perplex, snarled, felter, intricate, involved, Intrigues, extricate, complicate, insnare, Labyrinth.

  • Concealing, or manifesting; either more
  • Common.
    • 3.

      Covering, heal, Veil, shroud, hide, whelm, stop, Canopy, Hood, Lid, palliate, cloake, overlay, overrun, overshadow.

      Uncovering, open, expose, discover, shew, reveal, naked, unmask, unveil.

  • Special, relating to containing bodies.
    • 4.

      Shutting, stop, close, inclosing, immure, exclude, seclude, recluse, obstruct, Wink, fold up, pinn up, sowe up, seal up, corke up, lute up, lock up, put to the door.

      Opening, breaking up, disclose, display, Expansion, gap, Slade, Aperture, unstop, expose, lay or set open.

• Putting of things nearer together, or farther asunder; either
  • More general,
    • 5.

      Gathering, Collect-ion, assemble, convene, compeile, levy, raise men or money, Receiver, rake or scrape together, rally, glean, pick up.

      Scattering, discuss, disperse, dissipate, sprinkle, strew, inspersion.

  • More particular; with reference to the
  • Capacity of
    • Consistent bodies, and such as are not supposed to be contained.
      • 6.

        Heaping, accumulate, amass, lay up, stow, pile, Stack, Mow, Cock, Rick, Shock, Drift, Dunghill, mixen.

        Spreading, diffuse, Expansion, display, Suffusion, strew, run, plash, lay cloth.

    • Fluid Bodies, and such as are supposed to be contained in something.
      • 7.

        Filling, replenish, Repletion, full, plenary, sated, staw, cram, stuff, farse, reoruit.

        Emptying, evacuate, vacant, Vacuity, rid, void, exhaust, Chasm, clear, lanke, lave, draw dry.

  • Motion of bodies, chiefly fluids; according to the more general name: or that which is involuntary, and besides intention. Edition: current; Page: [153]
    • 8.

      Pouring, Effusion, Infusion, gush, guggling, yewer, Tunnel.

      Spilling, shedding, run out, seeth over.

“III. Operations belonging to Agriculture, do concern either

• The Ground, or Land: in respect of,
  • Loosening it; either by single persons; or by the help of drawing Beasts.
    • 1.

      Digging, delve, break up, spit, spade.

      Plowing, tilling, breaking up, coulter, share.

  • Breaking the clods, and smoothing the surface.
    • 2.

      Harrowing.

      Rolling.

  • Helping or directing the fertility of the Ground, by adding some new matter, or removing the impediments of noxious Plants.
    • 3.

      Manuring, cultivate, dunging, marling, soiling, Tilth, culture. Weeding,

• The Grane or Seed, chiefly of Herbs; in respect of
  • Putting it into the ground, or taking it off from the ground upon its maturity.
    • 4.

      Sowing, seminate.

      Reaping, mowing, Crop, Harvest, Sithe, Sickle, stubble, swarth.

  • Separating of it from the straw or lesser husks;
    • 5.

      Threshing, Flail.

      Winnowing, Fan, Ventilation.

• The Propagation of Trees or Shrubs, chiefly by
  • Putting the Root of the Plant in the ground; to which may be adjoined, the putting of Grain segregately into the ground, which is sometimes used for pulse.
    • 6.

      Planting, implant.

      Setting.

  • Joyning a part of one plant to another, either to the top of the body, or some branch being cut, or to the sides of the body.
    • 7.

      Grafting, ingraft, Imp.

      Inocolating.

  • Cutting off superfluous Branches; to which may be adjoyned, the cutting down of the whole.
    • 8.

      Pruning, dressing, cutting, coping.

      Felling, grubb, Wood-fall.

“IV. By Fabrile Operations, (Smith, Carpenter, Mason, &c.) are meant all such kinds of works as do primarily concern our Houses or Utensils, whether for necessity or ornament: to which may be adjoyned, those operations which concern the making of earthen ware, styled, Figulatory, Potter. These are distinguishable into such as denote

• Dissolution of Continuity; either by
  • Separating of some thin parts from the surface of a body by rubbing with an edge; or breaking the body itself into minute parts by percussion with some obtuse body.
    • 1.

      Shaving, scraping, raze, razour.

      Contusion, bruising, pounding, stamping, braying, morter, pestle.

  • Dividing from a body some small part; either by affriction upon a stone, or with an iron instrument.
    • 2.

      Grinding, attrition, Grist, Quern, Mill.

      Filing, Raspe.

  • Dividing the parts of a body, by cutting it, either in roundish caveties, or in oblong scissures.
    • 3.

      Boring, perforate, foraminate, pierce, Bodkin, Dril, Awle, Gimlet, Wimble, Trepann, Awgre.

      Sawing, Saw, whipsaw, &c.

  • Uniting, either of metalline or other bodies, by some third body adhering.
    • 4.

      Sodering, Cement, luting.

      Gluing, cementing, glutinous, conglutinate.

  • Shaping of bodies into particular figures; either by Hammering or Melting.
    • 5.

      Forging.

      Casting, melt, founding, fusile, molde.

  • Cutting, either a solid and bulky, or a flat figure.
    • 6.

      Carving, Sculpture.

      Graving, engrave, etching.

  • Compressing of a soft body; or circumagitating either a soft, or hard body.
    • 7.

      Kneading, moulding, plastic.

      Turning, Lathe.

• Adorning the surface of the body; either by variety of colours, or adding an external lustre to it. Edition: current; Page: [154]
  • 8.

    Painting, limn, draw, enamel, fucus, pensil.

    Varnishing, size.

V. Sartorian Operations do concern either the

• Preparations of stuffs; by
  • Making several vegetable or animal substances into Thread.
    • 1.

      Twisting, tortion, wreath, writhing, twine, winding.

      Spinning, Spinster, Rock, Distaff.

  • Joyning such Threads together into Cloth.
    • 2.

      Weaving, Texture, Contexture, Loom, Web, braid, woven, Hurdle, Shuttle, Wicker, Matt.

      Knitting.

  • Thickening and colouring such cloth.
    • 3.

      Fulling, milling, Fuller.

      Dying, stain, Tincture, tinge, ingrain.

• Making of Stuffs into Vests; either by
  • Uniting necessary, and cutting off unnecessary parts.
    • 4.

      Sowing, Stitch, Seam-ster, Suture, Welt, needle, dearn, quilt, draw cloth, rip.

      Clipping, Scissors, shear, shorn, cut.

  • Placing together the parts in greater or lesser plicatures.
    • 5.

      Folding, wrap, lap, plait, clinching, clutching, doubling, envelop.

      Curling, crisping, frizling, furling.

• Preserving of such stuffs or vests clean; common likewise to other things.
  • By the help of water or liquor; either when
    • Things are put into, and agitated in the water; to which may be opposed the putting upon them other bodies of a more gross consistence; styled,
      • 6.

        Washing, scouring, Lotion, rince, Laver, Laundress, gurgling.

        Smearing, daubing, anoint, ointment, Unction, greaze, chrism; and many with [be] as bespaul, spit, spue, sprinkle.

    • Water is imbibed and communicated to the thing; to which may be adjoined, for its affinity, the putting of things into liquor in order to the communicating of some new quality to such liquor.
      • 7.

        Soaking, steeping, embrewing, macerating, watering Land, &c., bathing, imbibe, sinke, sop, brewis, embrew.

        Infusion, watering Fish, &c., macerate, Decoction, impregnate.

  • By external Motion of or upon them, more or less violent.
    • 8.

      Rubbing, scrape, Friction, Frication, scrub, chafe, Attrition, frit, gall, scowr, taw, grate.

      Wiping, stroke, terse, handkerchief, towel, knapkin.

  • By Instruments to separate those minuter bodies which adhere to the superficies.
    • 9.

      Brushing, sweeping, Beesom, Whisk, Brush, Broom, Maukin.

      Combing, carding, currying.

“VI. By Chymical Operations are meant such kind of works as tend to the changing of bodies, with respect to the position and figure of their minuter parts. By this, amongst other ends, medicaments are usually prepared; for which reason those kind of operations styled Pharmaceutical, belonging to the apothecary, may be hereunto annexed.

The operations belonging to this head, do concern the changing and preparing of bodies; either by

• Instruments, for the reduction of them into minute parts; by compression and affriction betwixt two hard bodies; or by separating the parts so reduced, through a porous plain.
  • 1.

    Grinding.

    Sifting, bolting, Sieve, siercing, ranging.

• Liquors; either
  • Changing the consistence of bodies; by reducing them into a more liquid, or a more dry consistence.
    • 2.

      Dissolution, melt, liquifie, dissolve, thaw, fusil, flux, run about.

      Coagulation, congealing, Clod, Curd, Gelly, Clottered Gore, Concretion, grumous.

  • Dividing hard bodies into minute parts; by an acid liquor, through which such parts are dispersed; or sinking down of such parts to the bottom, by the mixture of some other liquor.
    • 3.

      Corrosion, eating, fretting, gnawing, caustic.

      Precipitation, settling.

  • Separating of these parts from the liquor; by passing them through a porous body; either downward, or both upward and downward.
    • 4.

      Straining, Percolation, squeeze, colender.

      Filtration, filtre.

• Heat, applicable chiefly either toEdition: current; Page: [155]
• Liquid bodies; which being kept for some considerable time in a gentle heat, upon this usually follows, either the
  • Loosening the inward parts of such bodies, so as by agitation they work one upon another; styled,
    • 5.

      Digestion.

      Fermentation, work, fret, Leven, Yeast, Barm, Rennet.

  • Separating of the finer parts, by raising them up in the form of a liquor; or, the farther separating of the more spirituous from the watery parts of this liquor.
    • 6.

      Distillation, still, Limbeck, cohobation.

      Rectifying.

• Hard and solid bodies; either by
  • Driving away the more watery and volatil parts and leaving the more solid; or, raising the volatil parts in the form of a salt.
    • 7.

      Charring, churk, Tinder.

      Subliming, sublimation.

  • Burning away the combustible parts of a body; or turning the parts remaining after such burning into a liquor.
    • 8.

      Calcination.

      Lixiviation, deliquiate, Lye, Buck.”

I.

Principles, with correspondent Exercises, applying specially or exclusively to Geometry.

• 1. Geometrical-Relation—Verbally-Expressing, or Purely-Verbal-Expression-Maximizing, or Diagram-Occasionally-Discarding Principle.
• 2. Practical-Use-Indication-Maximizing, or Practical-Application-Maximizing Principle.
• 3. Genealogical-Table-Employing, or Synoptic-Filiation-Indicating Principle.
• 4. Special Visible Sign-Employment-Maximizing, or Verbal-Expression-Occasionally-Discarding Principle.

II.

5. Key-Presenting, or Contrivance-Indicating Principle.*

Among the five above-mentioned principles, of the four that apply to Geometry, between the first and the fourth an intimate relation will, at first glance, be seen to have place, they being in fact the converse of each other. But, of the fourth, neither the use, nor consequently the nature, can be fully explained till that of the third, to which it is subservient, has been brought to view. In the character of exercises or modes of learning, the utility of them, has, in both instances, received, though in respect of the number of the learners, as yet but on a narrow scale, the attestation of experience.

I.: Geometrical-Relation-Verbally-Expressing, or Purely-Verbal-Expression-Maximizing, or Diagram-Occasionally-Discarding Principle.

Of this principle, the great use is, to serve as a test, and, by that means, an instrument of, and security for, intellection.—See above, Exercise No. 9, Princip. No. 24. (pp. 44, 51.)

Mode of Performing this Exercise.

Without the aid of any diagram, and, consequently, without the use of any of those signs, such as the letters of the alphabet, which, as often as for bringing to mind the figure in question, a diagram or delineation of it is employed, are necessary for designating and distinguishing from each other the parts of the figure, a proposition (in the geometrical sense of the word) and, consequently, the figure which is the subject of it, is expressed in words alone; which words will, of course, be such, that every proposition (using the word proposition in the logical and grammatical Edition: current; Page: [156] sense) which they serve to constitute, will be what is called a general proposition, having for its subject not merely an individual object, but a class, genus, or sort, of objects.

Without the aid of any diagram, any such description, can it then be given in such manner as to be intelligible? From his own experience,—from experiments made at his suggestion, in the instance of three persons, at two widely distant points of time,—the writer of these pages is enabled to answer in the affirmative. In the instance of two of them, the experiment began with Euclid’s Elements, and went no farther than the first six books. In the instance of the other person, it began with one of the most copious, and, at that time, best approved institutional works on Conic Sections,* and was continued, if he misrecollects not, to the very end. In both instances the papers in which the descriptions in question are contained, are in his possession, though at this moment not accessible. In all three instances the learners were of a self-directing age. What was done, was done purely for the satisfaction as well as instruction of the operators themselves, and not in the way of exercise for the satisfaction of a teacher; for, except the learners themselves, in no one of the three instances was there any teacher in the case. In the case of the Conic Sections, though he himself neither did at that time read, nor since then has ever read, so much as a page of what was written, yet, so it was, that the whole of it was written in his presence: and well does he remember the tokens of self-satisfaction, as well as promptitude and velocity, with which the performance of the self-imposed task, continued as it was during a course of some months, was accompanied,—symptoms which, for such a length of time, nothing but the full sense of continual success could assuredly have produced.

But, without a perfect conception, or, at any rate, without the supposed consciousness of such perfect conception, a task of this kind and of this length never could have been performed. From first to last no diagram having been employed, consequently, no reference to any actually drawn diagram made, it is only by words—by words of a purely general nature, that the several relations borne by the several parts of the figures in question to each other, that the ideas in question, could have been expressed. But, in this way, the ideas in question having actually been expressed, how much superior, in the character of an intellectual test, this species of exercise cannot but have been, in comparison with any other, will, it is hoped, without entering into any diagrammatical exemplifications, be found sufficiently intelligible.

For this purpose a particular mode of designation, applicable to the several parts of a geometrical figure, required to be devised, and was devised and settled accordingly. For example, in order that such words of designation as right, left, top, bottom, and the like, might be capable of being employed, it was necessary that, of the figure of which a description was to be given, the position should be determined. But, once for all, care was taken to declare and record, that it was merely for the purpose of description and exemplification that, so far as concerned position, this declaration was made; and that, in whatsoever position the figure were placed, the species it belonged to and the properties it possessed would be the same.

I. Enunciation or enunciative part,—enunciative, viz. of the proposition to be demonstrated.†

II. Demonstration or demonstrative part. In every portion of discourse, to the whole of which the term proposition—a proposition—is customarily applied by geometricians, these two parts at least will be found. To these will in most instances be found added what may be termed the direction—directive part, or preparatively directive part, viz. the part by which direction is given for the operation to be performed, and for necessary additions to be made to the originally exhibited or conceived figure, for the purpose of preparing the ground for the demonstration.

In Euclid’s Elements without exception, and for a considerable extent, if not for the most part, in other books, in the higher branches of geometry, in giving expression to the enunciation as above, the mode of purely verbal designation here proposed for all the above-mentioned parts is actually employed. But, so far as this practice is pursued, the propositions (taking the word proposition in the logical sense) are all general; the ideas conveyed by them are all general ideas; and in this original state it is, and without need of extension, that, in so far as they have place in the mind, they lie there ready to be applied, upon occasion, to all such individual figures as are respectively comprehended within their import.

But now, instead of being thus general, suppose the mode of designating them such, as to confine the application of them to the individual Edition: current; Page: [157] figure, exhibited by the diagram that accompanies them. For example, instead of saying, a square having for its side the longest boundary of a right angled triangle is exactly equal to both the squares taken together, which have for their sides respectively the two other boundaries of the same triangle, suppose the proposition worded thus—in the triangle in question (describing it by letters,) the square having for its side such boundary (describing it again by letters,) is exactly equal to both the squares taken together, which have for their sides respectively the two other boundary lines, (describing them also by letters.)

By such a mode of expression or designation, if it be supposed that no other more general mode is ever added or substituted to it, what general ideas—what practically applicable instruction would be conveyed? Answer;—Surely not any. For rendering the proposition susceptible of conveying any such instruction, what would be the course necessary to be pursued? Answer;—To substitute to this diagrammatical and individualizing mode of expression or designation, the purely verbal, and thence general, mode of expression or designation here in the first place brought to view. Here, then, before any real acquisition in the way of science can be made, there is an additional operation that must be performed,—an additional operation requiring much greater exertion of mind to perform it, as well as a much greater strength and maturity of mind to be able to perform it, than the original one.

This general mode of expression or designation, which, to the purpose of useful and practically applicable intellection, will, in the case of the enunciation, as above explained, be acknowledged to be, at least to a very considerable extent, absolutely necessary, will, it is hoped, in the case of the other two parts of the proposition, be acknowledged to be at least useful; useful, viz. on the supposition of its being practicable: and that it is practicable hath, as above, been already proved by repeated experience, without any contrary experience to oppose to it.

Diagram occasionally discarding principle: by the word occasionally, thus inserted in the composition of this, one of the names to be employed for the designation of this principle, intimation is given, that upon the diagrammatical, i. e. the ordinary mode of designation, no permanent exclusion is proposed to be put: that it is in aid, and not in lieu, of that ordinary mode, that the one proposed—the purely verbal mode—is proposed to be employed. So far is any such constant exclusion of the diagrammatical mode from being intended, that by the principle mentioned in the fourth place, this diagrammatical mode is to some purposes, by means of a set of adapted signs, proposed to be employed by itself: by itself, and thereby to the occasional and temporary exclusion of the verbal mode.

That, under the burthen imposed by the labour of forming, by means of a description given in the purely verbal mode, a conception of the figure meant to be presented to the mind, considerable relief will very frequently be afforded by a glance at the figure, cannot admit of doubt. For facilitating conception, in the first instance, the verbal mode and the diagrammatical mode will thus be employed in conjunction in conjunction, and so far, perhaps, with not very unequal advantage.

In comparison with the diagrammatical mode, no mean advantages will, it is believed, be found attendant on the purely verbal mode.

1. One is—the giving to the general ideas, the presence of which in the mind is, in every instance, necessary to intellection, a sort of perpetual and uniform fixation, by means of a determinate set of words,—thoroughly considered, apposite, and thereby, sooner or later, perfectly adequate words,—instead of leaving these general ideas to be, on each individual occasion, in a hasty, and, therefore, frequently in an inadequate manner, caught up in the way of abstraction: caught up without words for the fixation of them; and therefore, in case of error, without possibility of correction, there being no permanent or determinate object to which correction can apply.

2. The other advantage is—the saving that will frequently be made of the expense of time and labour, necessarily attached to the making out the several parts of the figure, by means of the letters employed in the designation; and, moreover, of the perplexity, and, as it were, mental stammering, with which the operation of ringing the changes upon these letters is, especially in unpractised minds, so apt to be attended. Sometimes, it is true, it may happen that, in addition to the general glance taken of the figure, recurrence to these letters may, for the purpose of forming a conception of this or that part of it, be found necessary. But at other times it may happen that no such recurrence will be found necessary: the need of it having been effectually superseded by the purely verbal description, by means of the general words contained in it.

A question here presents itself, as one which, by any learner in geometry, might not unaptly be put to the author of any institutional work, by means of which he was occupied in teaching himself. The directions and reasonings, the only use of which is to convey so many general ideas, why is it that for giving expression to them you have not (while in the case of the enunciation made of the proposition to be demonstrated you actually have) employed the correspondent general words? These general words, did you know where or how to find them? Then, why is it that you have not found them and produced them? With all its load of unavoidable and immoveable difficulty, is not the task heavy enough for us? Must this additional, this moveable difficulty, be left pressing on us? These same general Edition: current; Page: [158] and only adequate words, is it then that you have not been able to find them? You, to whom, by so many years of study, and so often continually repeated applications to practice, the subject has been rendered so perfectly familiar,—with what degree of consistency can you entertain any such expectation as that we, to all of whom the subject is perfectly new, and many of whom are, in various degrees, dull or inattentive, or both, should be able to accomplish at the moment, and at every moment, a work, which our master has not been able to perform in so many years?*

Thus much will not, it is believed, be found open to dispute. The only idea which, in any case, is conveyed by the individual figure in question, as delineated in the diagram in question,—the individual figure, of which the parts are designated by the letters of reference,—is an individual one. But, except in as far as by abstraction from these individual ideas, general or specific ideas are formed, from no number of such individual diagrams, can any general ideas, applicable to any practical purpose, be deduced. This process of generalization, the learner in question, is he competent to the performance of it? If he is, then proportioned and equal to the number of these acts of generalization that he is competent to, and performs accordingly, is the stock of mathematical science which he actually lays up, at any rate, for the time. But, in any given instance, suppose a general idea thus formed, and for the moment laid up, note well the great disadvantage under which the operation is performed. No precise form of general words has the learner before him, by which this idea of his stands expressed, and by which, were he provided with it, the idea might, as it were, be anchored in his mind. If the occasion of making application of it recur with a certain degree of frequency, he will, notwithstanding the want of apt words for the expression of it, retain it in a state fit for use. But let it, for a certain length of time, be unemployed, the words which should have held it fast being wanting, the consequence is, it drops out of his mind, and as well might it never have been lodged there.

Whatsoever form of words is necessary and sufficient to the giving expression to the general idea, which the individual diagram with the letters which all along apply to it, are intended to convey,—now, suppose it, as in the case of Euclid’s proposition as above-mentioned, ready provided, and extended not only to the propositions, but also to the demonstrations, and the directions by which the preparatory additions to the figure are described. Things being in this state, the idea from the very first presents itself to his mind, in all its generality: in the only garb and condition in which it is capable of being applied to use. If then so it is, that, from the proposition in question, demonstrations, as above included, he has succeeded in deducing any idea at all, that idea is a general one, an idea fit for use, it is not a mere individual idea, having for its necessary support the individual figure. In that case, employing the general words in question, or others that are equivalent to them, he will, in addressing himself either to a teacher for the purpose of proving, or to a learner for the purpose of communicating, his proficiency, find himself, on the occasion of any line, for instance, which, for the purpose of the demonstration, requires to be drawn, in a condition able to describe it by words designative of the relation which, when drawn, it will bear to the other parts of the figure: he will not say, draw A B, or draw A C, leaving it for the party addressed to make discovery of the place which the line, when drawn, will occupy; a discovery which, otherwise than by seeing the diagram, and thereupon copying that part of the diagram, he will, for want of the general words in question, find it impossible to make.

True it is, that without actually having given, either by word of month, or in writing, any such purely verbal description of it, to have framed and entertained a clear, correct, and complete conception of the proposition in question, be it what it may, is altogether possible; if it were not, scarcely perhaps would so much as a single person be found by whom, in relation to any such proposition, any such conception had ever been entertained. But not the less true is it, that by one who, upon being required, were to find himself ultimately unable to give, in relation to it, that sort of purely verbal description, no such clear, correct, and complete conception of it could really be entertained.

Of the propositions themselves (considered as distinct from the demonstrations and the introductory steps, as above) by Euclid a description of the sort in question—a purely verbal description—has, as in every instance, been actually given. But, when he comes to the introductory steps, (preparatory additions,) then it is, that, as if to save the trouble of finding for his conceptions an adequate assistance of general expressions, having given his diagram, it is to the component parts of that individual diagram, as indicated by the letters of the alphabet, that he refers us. Draw the line A B, or draw B C, says the direction that he gives us. But on what account was it that he required us to draw this line? Plainly on this account, and no other, viz. on account of a certain relation which the line so drawn would, when drawn, be found to bear to the other parts of the figure; it is only in virtue of some such relation that the lines, when drawn, can be applicable to the purpose. But, by the letters A B, or B C, is this relation in any degree expressed? Not it, indeed. That same instructive, that same intellection-proving, Edition: current; Page: [159] and, at the same time, intellection-conveying mode of expression which he uniformly applied to his propositions,—i. e. the mere grammatical sentence, enunciative, in each instance, of the geometrical relation, the existence of which is thereby undertaken to be demonstrated—how happened it that he did not continue the application of it to his demonstrations, and the directions given for the preparatory steps? Had the question been put to him; for despatch, would probably have been his answer. But, for want of knowing very well how, would not improbably have been the more correct answer; and, at any rate, what should be not only a correct answer, but, moreover, an addition to such effect as would have been necessary to the forming a complete one. For the composition of a book of instruction upon that plan, the human mind had not, in his time, made sufficient advance. The mathematician is one sort of person; the logician is another. It is by generalization that all inventions are accomplished; most discoveries made. But generalization by wholesale, generalization upon an all-comprehensive scale, is the work of the logician: it is, by the same process, performed upon a comparatively small scale,—performed, as it were, by driblets,—that the particular discoveries in Mechanical Philosophy, in Chemical Philosophy, and even in Mathematics, have been made. But it is one thing to make progress in a certain track; another thing to be able to give a description, a clear, and correct, and complete, and easily apprehensible, description of the progress so made in that same track.

Thus it is, that in this as in so many other parts of the field of science, infancy, under the preposterous name of antiquity,—infancy continues to set the law to maturity; inexperience to experience.

In regard to this gap in the mass of requisite instruction, ask for the reason of its existence; if, by the word reason, be meant a productive cause, having its root in the essential nature of the subject, no such reason will be found. But if, by the word reason, be meant a cause having its root in the nature of the human mind, there is nothing in it but what, in every part of the field of thought and action, lies constantly under our eyes.

Authority and habit.—In these two words, in as far as sinister interest is out of the question, may be seen the cause of all deficiencies in the system of instruction which (time for the operation not having been wanting) continue unsupplied. Authority,—the authority of great names: habit,—the habit of continuing to travel without reflection, in the track in which, with or without reflection, men have begun, or continued to travel already.

In the use of general terms for giving expression to the correspondent general relations between the correspondent sorts of figures and parts of figures, Euclid, the father of Geometry, went not beyond the collection of words expressive of the purely enunciative part of the discourse called a proposition; for the demonstrative part and the preparatory part he left it to the learner to deduce the general ideas from the individual objects, presented by the individual diagram, in company with the words, of which, by the reference made to it, the import was in like manner individualized. Can there be any need of doing, or so much as use in doing, that which, in the eyes of the father of the science, was not fit, or at least not necessary, to be done?

The papers in question, in and by which application was, so long ago made, of the purely-verbal-expression-maximizing principle to a large portion of Euclid’s Elements, not being immediately accessible, an exemplification of it applied to the first proposition of these Elements, has, by the writer of these pages, been hastily formed for the purpose, and will be found in the Appendix.* To save recurrence to books, along with it is given a reprint of the same proposition as exhibited in the customary form in Mr Professor Playfair’s Elements of that science.

Whether in any, and if in any, in what degree, the conception of the subject is facilitated by the mode here proposed, is a question, to the answering of which, an understanding matured, and in other respects not ill furnished, but by which little or no attention has happened to have been bestowed upon this branch of science, will be in a particular degree well adapted.

Mode of making the experiment, to try the utility of the proposed mode, so far as concerns facility of conception.

1. Try whether the purely verbal mode of designation is intelligible without a diagram. For this purpose, the diagram, as given without the letters of reference, and the diagram, as given with the letters of reference, should both be covered.

2. If it be not perfectly or readily intelligible without a diagram, uncover that diagram which has not any letter of reference.

3. If it be not perfectly or readily intelligible even then, uncover now the diagram which has the letters of reference.

As to the giving facilities to conception, by this advantage, should it in any way be found included among the effects of the proposed mode, not only in the instance of each scholar would the labour be alleviated, and expenditure of time diminished, but in a greater degree than antecedently to experience would perhaps be expected, the number of the scholars Edition: current; Page: [160] reaping from this part of the instruction substantial benefit would be increased.

Even in the grammar school, under the old and still subsisting mode, large according to an eminent and most amply experienced master,* is the proportion of scholars by whom, at the end of a long series of years, no efficient learning is obtained. Larger, again, by far, among those by whom, after years spent in the endeavour, on one part, to infuse learning in this shape, on the other to imbibe it, [is the proportion by whom,] no efficient stock of it is obtained.

Under the name of the Ass’s Bridge, the 5th proposition, in the very first book of Euclid, is the known stumbling-block, the ne plus ultra to many a labouring mind.† Why? Because, to the purpose of clear conception, to the purpose of efficient instruction, the method traced out by Euclid, and followed blindfold for so many ages, is lamentably incompetent. In the Chrestomathic School, it may be presumed with some confidence, there will be no Ass’s Bridge.

The Ass’s Bridge having thus presented itself to view, the temptation of exhibiting this additional test of the utility of the purely verbal-expression-maximizing principle was too strong to be resisted. To the labour of giving expression in this mode to Euclid’s first proposition, has, accordingly, been added in the Appendix, the corresponding-like labour applied to the 5th proposition, called the Ass’s Bridge.‡

To what length in the field of mathematics this substitution of ordinary and unabbreviated language, to scientific and abbreviated, is in the nature of the case capable of being carried with advantage, can scarcely be determined antecedently to experiment. What is certain is, that in the details, in the actual performance of algebraical operations, i. e. on any other occasion, or for any other purpose than that of explanation, practised in the way of instruction, it cannot be carried over the whole. For in as far as pursued in detail, the system of abbreviation is essentially necessary to the performance of the operations themselves, when taken in the aggregate. But for this assistance, a long life might be consumed before more than a small part of those which have actually been performed, could be perused and understood, after their being respectively invented, not to speak of the labour expended in the course of the invention.

But while the uses of ordinary language were confined to the giving expression to principles, i. e. to propositions of so general and extensive a nature, as that by each of them large bundles of details, bundles more or less large and copious [might be embraced,] whether a degree of progress, considerable enough to be productive of sensible advantage, might not thus be made, is a matter to which experiment may be looked to for a determinate answer; and in the meantime the conjectures, in anticipative views taken of the subject by the learned, for a provisional one.

In proportion as in the character of principles, a number of these propositions, all expressed in ordinary language, are brought to view,—and laid before the reader all of them in one view,—such point of conformity and disconformity will, it may be expected, be found to have place among them, as will enable the mind to bind a number of them together into bundles, capable of being each of them designated by a term of more extensive import, these bundles into still smaller bundles, and so on: at each step of this abstractive process, the number of the bundles thus diminishing, and the extent of each thus receiving increase. To what length the nature of the case would suffer this process to be carried on, the greatest adept would scarcely venture to predict. But, that the further it were carried on, the more clear and complete would be the view thus rendered obtainable, will hardly be regarded as matter of dispute.

That, for this purpose, changes would require to be made in the stock of expression afforded by ordinary language, seems scarcely to admit of doubt: some terms might require to be added, others substituted, to that part of the ordinary language which is applicable to the purpose. But it is in the way of definition that the whole of this business might be despatched. In these definitions, in as far as the word had been already employed in different senses, the object and effect of the operation would be to fix the import: in as far as it was new, to give to it, for the first time, an import applicable to the subject. In all these cases, in the first instance, the defined word alone would be the word which would be foreign to the stock of the ordinary language: to the ordinary language would belong all the words employed in the explanation of it. True it is that, when once a word in itself new, and thence foreign to the ordinary language, had thus received its explanation, viz. in ordinary language, it then, without inconvenience, might be employed, and of necessity would be employed, in the explanations given of other such new words.

But in comparison with the perplexity produced by the introduction of an extensive system of new characters, the utmost perplexity that would be produced by the introduction of new words, supposing them to be, in a moderate degree, expressive, and at the same time elucidated, by explanations expressed in ordinary language, would be inconsiderable indeed, especially if the number of them was so insignificant as to admit of their being, in the form of a synoptic table, spread under the eye all together at one time.