our most precise writers, of these obviously inconsistent metaphors, does not justify us in concluding, that none of them has any connection with the true theory of the phenomena which he conceives them to explain; and that they deserve the attention of the metaphysician, merely as familiar illustrations of the mighty influence exerted over our most abstracted thoughts, by language and by early associations.*

Nor must it be forgotten, that, even in pure Mathematics, our technical language is borrowed from the physical properties and affections of matter; a proposition, of which it is unnecessary to mention any other proofs, than the terms employed to express the most elementary notions of geometry; such terms, for example, as point, line, surface, solid, angle, tangent, intersection, circumference; not to insist on such phrases as, involutes and evolutes, osculating circle, and various others of a similar description. The use made of this sort of figurative language in arithmetic is an instance, perhaps, still more directly to our present purpose; as when we speak of the squares, cubes, and fractions of numbers; to which may be added, as a remarkable instance of the same thing, the application of the word fluxion to quantity considered in general.

Notwithstanding these considerations, I do not know of any person, possessing the slightest claim to the name of philosopher, who has yet ventured to infer, from the metaphorical origin of our mathematical language, that it is impossible for us to annex to such words as point, line, or solid, any clear or

See Note (Q.)

precise notions, distinct from those which they literally express; or, that all our conclusions, founded on abstractions from the combinations presented by our external senses, must necessarily be vain and illusory. It is possible, indeed, that some may be disposed to make a distinction between having a notion or idea of an object, and being able to treat it as a subject of reasoning ;-between having a notion, for example, of length without breadth, and reasoning concerning the one dimension without any reference to the other. To this distinction, trifling as it is in reality, I have no material objection to state on the present occasion, as I should be completely satisfied, if it were as scrupulously attended to in the philosophy of Mind, as it uniformly is in the demonstrations of the mathematician ;-the sensible images presented to the fancy by the metaphorical words employed to denote the internal phenomena, being considered as analogous to the extension of points, and the breadth of lines, in a geometrical diagram; and thre same abstraction from the literal import of our words being steadily maintained, in all our reasonings on the former science, which is indispensably necessary to enable us to arrive at any useful conclusions in the latter.

Of Mr Tooke's opinion on the nature of general reasoning, we are not, as yet, fully informed; nor has he even explained himself concerning the logical principles of mathematical science. He has, indeed, given us to understand, that he conceived the whole of his second volume to be levelled at the imaginary power of abstraction; and towards the

close of it, he expresses himself, in pretty confident terms, as having completely accomplished his object: "You have now instances of my doctrine, in, I suppose, about a thousand words. Their number

may be easily increased. But I trust these are "sufficient to discard that imagined operation of the "mind which has been called abstraction; and to that what we call by that name is merely "one of the contrivances of language for the purpose of more speedy communication." *

66

66

prove,

In what manner Mr Tooke connects this very copious induction, with the inference he deduces from it, I must confess myself unable to comprehend. For my own part, I can perceive no logical connection whatsoever between his premises and his conclusion; nor do his numerous examples appear to me to establish any one general truth, but the influence of fancy and of casual association on the structure of speech. Not that I consider this as a conclusion of little moment; for of the reciprocal influence of speech on our speculative judgments, I am fully aware; and, perhaps, if I wished for an illustration of the fact, I should be tempted to refer to the train of thought which has given birth to the second volume of the Diversions of Purley, as the most remarkable example of it that has yet occurred in literary history." Credunt homines," says Bacon, "rationem suam verbis imperare, sed fit etiam, "ut verba vim suam super rationem retorqueant. With respect to abstraction, I think it probable

Tooke, Vol. II. p. 396.

Essay V. that Mr Tooke has fallen into an error very prevalent among later writers,―that of supposing Berkeley's argument against abstract general ideas to have proved a great deal more than it does.

That Berkeley has shewn, in the most satisfactory manner, the incorrectness of Locke's language upon this subject, and that he has thrown a clear and strong light on the nature of general reasoning, is now, I believe, admitted by all who are acquainted with his writings. But does it follow from Berkeley's argument, that abstraction is an imaginary faculty of the mind, or that our general conclusions are less certain than former logicians had conceived? No one, undoubtedly, can, for a moment, admit such suppositions, who understands what the word abstraction means, and who has studied the first book of Euclid's Elements.

On these, and some other collateral points, it is to be hoped that Mr Tooke will communicate his peculiar views more unreservedly, in the farther prosecution of his design:-in looking forward to which, I trust I shall be pardoned, if I express a wish (which I am sure I feel in common with many of his admirers) that he would condescend to adopt the usual style of didactic writing, without availing himself of a form of composition which eludes the most obvious and the most insuperable difficulties, by means of a personal sarcasm, or of a political epigram.

Strongly impressed with the prevalence of errors, similar to those which have misled Mr Tooke to so unprecedented a degree, a philosophical grammarian,

of the first eminence, long ago recommended the total proscription of figurative terms from all abstract discussions. * To this proposal D'Alembert objects, that it would require the creation of a new language, unintelligible to all the world :-for which reason, he advises philosophers to adhere to the common modes of speaking; guarding themselves, as much as possible, against the false judgments which they may have a tendency to occasion. † To me it appears, that the execution of the design would be found, by any person who should attempt it, to be wholly impracticable, at least in the present state of metaphysical science. If the new nomenclature were coined out of merely arbitrary sounds, it would be altogether ludicrous; if analogous, in its formation, to that lately introduced into chemistry, it

Du Marsais. Article Abstraction in the Encyclopédie. "Un Grammairien Philosophe voudroit, que dans les mati"ères metaphysiques et didactiques, on évitât le plus qu'il est possible, les expressions figurées ; qu'on ne dit pas qu'une idée en renferme une autre, qu'on unit ou qu'on separe des idées, "et ainsi du reste. Il est certain que lorsqu'on se propose de "rendre sensibles des idées purement intellectuelles, idées sou"vent imparfaites, obscures, fugitives, et pour ainsi dire, a demi"ecloses, on n'eprouve que trop combien les termes, dont on est "forcé de se servir, sont insuffisans pour rendre ces idées, et sou"vent propres à en donner des fausses; rien ne seroit donc plus "raisonnable que de bannir des discussions métaphysiques les "expressions figurées, autant qu'il seroit possible. Mais pour "pouvoir les en bannir entièrement, il faudroit créer une langue exprès, dont les termes ne seroient entendu de personne; le "plus court est de se servir de la langue commune, en se tenant sur ses gardes pour n'en pas abuser dans ses jugemens."-Melanges, Tome V. p. 30.