[871] Prelim. Dissertation.
109. The different manner in which this all-important word was understood by philosophers is strikingly shown when they make use of the same illustration. Arnauld, if he is author of L’Art de Penser, mentions the idea of a chiliagon, or figure of 1,000 sides, as an instance of the distinction between that which we imagine, and that which we conceive or understand. Locke has employed the same instance to exemplify the difference between clear and obscure ideas. According to the former, we do not imagine a figure with 1,000 sides at all; according to the latter, we form a confused image of it. We have an idea of such a figure, it is agreed by both; but in the sense of Arnauld, it is an idea of the understanding alone; in the sense of Locke, it is an idea of sensation, framed, like other complex ideas, by putting together those we have formerly received, though we may never have seen the precise figure. That the word suggests to the mind an image of a polygon with many sides is indubitable; but it is urged by the Cartesians, that as we are wholly incapable of distinguishing the exact number, we cannot be said to have, in Locke’s sense of the word, any idea, even an indistinct one of a figure with 1,000 sides; since all we do imagine is a polygon. And it is evident that in geometry we do not reason from the properties of the image, but from those of a figure which the understanding apprehends. Locke, however, who generally preferred a popular meaning to one more metaphysically exact, thought it enough to call this a confused idea. He was not I believe, conversant with any but elementary geometry. Had he reflected upon that which in his age had made such a wonderful beginning, or even upon the fundamental principles of it, which might be found in Euclid, the theory of infinitesimal quantities, he must, one would suppose, have been more puzzled to apply his narrow definition of an idea. For what image can we form of a differential, which can pretend to represent it in any other sense than as d x represents it, by suggestion, not by resemblance?
110. The case is, however, much worse when Locke deviates, as in the third and fourth books he constantly does, from this sense that he has put on the word idea, and takes it either in the Cartesian meaning or in one still more general and popular. Thus, in the excellent chapter on the abuse of words, he insists upon the advantage of using none without clear and distinct ideas; he who does not this “only making a noise without any sense or signification.” If we combine this position with that in the second book, that we have no clear and distinct idea of a figure with 1,000 sides, it follows, with all the force of syllogism, that we should not argue about a figure of 1,000 sides at all, nor, by parity of reason, about many other things of far higher importance. It will be found, I incline to think, that the large use of the word idea for that about which we have some knowledge, without limiting it to what can be imagined, pervades the third and fourth books. Stewart has ingeniously conjectured that they were written before the second, and probably before the mind of Locke had been much turned to the psychological analysis which that contains. It is however certain that in the Treatise upon the Conduct of the Understanding, which was not published till after the Essay, he uses the word idea with full as much latitude as in the third and fourth books of the latter. We cannot, upon the whole, help admitting that the story of a lady who, after the perusal of the Essay on the Human Understanding, laid it down with a remark, that the book would be perfectly charming were it not for the frequent recurrence of one very hard word, idea, though told, possibly, in ridicule of the fair philosopher, pretty well represents the state of mind in which many at first have found themselves.
An error as to geometrical figure. 111. Locke, as I have just intimated seems to have possessed but a slight knowledge of geometry; a science which, both from the clearness of the illustrations it affords, and from its admitted efficacy in rendering the logical powers acute and cautious, may be reckoned, without excepting physiology, the most valuable of all to the metaphysician. But it did not require any geometrical knowledge, strictly so called, to avoid one material error into which he has fallen; and which I mention the rather, because even Descartes, in one place, has said something of the same kind, and I have met with it not only in Norris very distinctly and positively, but, more or less, in many or most of those who have treated of the metaphysics or abstract principles of geometry. “I doubt not,” says Locke,[872] “but it will be easily granted that the knowledge we have of mathematical truths is not only certain but real knowledge, and not the bare empty vision of vain insignificant chimeras of the brain; and yet if we well consider, we shall find, that it is only of our own ideas. The mathematician considers the truth and properties belonging to a rectangle or circle only as they are in idea in his own mind; for it is possible he never found either of them existing mathematically, that is, precisely true, in his life.... All the discourses of the mathematicians about the squaring of a circle, conic sections, or any other part of mathematics, concern not the existence of any of those figures; but their demonstrations, which depend on their ideas, are the same, whether there be any square or circle in the world or no.” And the inference he draws from this is, that moral as well as mathematical ideas being archetypes themselves, and so adequate and complete ideas, all the agreement or disagreement which he shall find in them will produce real knowledge, as well as in mathematical figures.
[872] B. iv., c. 8.
112. It is not perhaps necessary to inquire how far, upon the hypothesis of Berkeley, this notion of mathematical figures, as mere creations of the mind, could be sustained. But on the supposition of the objectivity of space, as truly existing without us, which Locke undoubtedly believed, it is certain that the passage just quoted is entirely erroneous, and that it involves a confusion between the geometrical figure itself and its delineation to the eye. A geometrical figure is a portion of space contained in boundaries determined by given relations. It exists in the infinite round about us, as the statue exists in the block.[873] No one can doubt, if he turns his mind to the subject, that every point in space is equidistant, in all directions, from certain other points. Draw a line through all these, and you have the circumference of a circle; but the circle itself and its circumference exist before the latter is delineated. The orbit of a planet is not a regular geometrical figure, because certain forces disturb it. But this disturbance means only a deviation from a line which exists really in space, and which the planet would actually describe, if there were nothing in the universe but itself and the centre of attraction. The expression therefore of Locke, “whether there be any square or circle existing in the world or no,” is highly inaccurate, the latter alternative being an absurdity. All possible figures, and that “in number numberless,” exist everywhere; nor can we evade the perplexities into which the geometry of infinities throws our imagination, by considering them as mere beings of reason, the creatures of the geometer, which I believe some are half disposed to do, nor by substituting the vague and unphilosophical notion of indefinitude for a positive objective infinity.
[873] Michael Angelo has well conveyed this idea in four lines, which I quote from Corniani.
Non ha l’ottimo artista alcun concetto,
Che un marmo solo in se non circonscriva
Col suo soverchio, e solo a quello arriva
La mano che obbedisce all’intelletto.
The geometer uses not the same obedient hand, but he equally feels and perceives the reality of that figure which the broad infinite around him comprehends con suo soverchio.
113. This distinction between ideas of mere sensation and those of intellection, between what the mind comprehends, and what it conceives without comprehending, is the point of divergence between the two sects of psychology which still exist in the world. Nothing is in the intellect which has not before been in the sense, said the Aristotelian schoolmen. Every idea has its original in the senses, repeated the disciple of Epicurus, Gassendi. Locke indeed, as Gassendi had done before him, assigned another origin to one class of ideas; but these were few in number, and in the next century two writers of considerable influence, Hartley and Condillac, attempted to resolve them all into sensation. The Cartesian school, a name rather used for brevity, as a short denomination of all who, like Cudworth, held the same tenets as to the nature of ideas, lost ground both in France and England; nor had Leibnitz who was deemed an enemy to some of our great English names, sufficient weight to restore it. In the hands of some who followed in both countries, the worst phrases of Locke were preferred to the best; whatever could be turned to the account of pyrrhonism, materialism, or atheism, made a figure in the Epicurean system of a popular philosophy. The names alluded to will suggest themselves to the reader. The German metaphysicians from the time of Kant deserve at least the credit of having successfully withstood this coarse sensualism, though they may have borrowed much that their disciples take for original, and added much that is hardly better than what they have overthrown. The opposite philosophy to that which never rises above sensible images is exposed to a danger of its own; it is one which the infirmity of the human faculties renders perpetually at hand; few there are who in reasoning on subjects where we cannot attain what Locke has called “positive comprehensive ideas” are secure from falling into mere nonsense and repugnancy. In that part of physics which is simply conversant with quantity, this danger is probably not great, but in all such inquiries as are sometimes called transcendental, it has perpetually shipwrecked the adventurous navigator.