122. But before I come more particularly to discuss this matter, I find it proper to consider extension in abstract: for of this there is much talk, and I am apt to think that when men speak of extension as being an idea common to two senses, it is with a secret supposition that we can single out extension from all other tangible and visible qualities, and form thereof an abstract idea, which idea they will have common both to sight and touch. We are therefore to understand by extension in abstract an idea of extension, for instance, a line or surface entirely stripped of all other sensible qualities and circumstances that might determine it to any particular existence; it is neither black nor white, nor red, nor hath it any colour at all, or any tangible quality whatsoever and consequently it is of no finite determinate magnitude: for that which bounds or distinguishes one extension from another is some quality or circumstance wherein they disagree.
123. Now I do not find that I can perceive, imagine, or any wise frame in my mind such an abstract idea as is here spoken of. A line or surface which is neither black, nor white, nor blue, nor yellow, etc., nor long, nor short, nor rough, nor smooth, nor square, nor round, etc., is perfectly incomprehensible. This I am sure of as to myself: how far the faculties of other men may reach they best can tell.
124. It is commonly said that the object of geometry is abstract extension:
but geometry contemplates figures: now, figure is the termination of magnitude:
but we have shewn that extension in abstract hath no finite determinate magnitude. Whence it clearly follows that it can have no figure, and consequently is not the object of geometry. It is indeed a tenet as well of the modern as of the ancient philosophers that all general truths are concerning universal abstract ideas; without which, we are told, there could be no science, no demonstration of any general proposition in geometry. But it were no hard matter, did I think it necessary to my present purpose, to shew that propositions and demonstrations in geometry might be universal, though they who make them never think of abstract general ideas of triangles or circles.
125. After reiterated endeavours to apprehend the general idea a triangle, I have found it altogether incomprehensible. And surely if anyone were able to introduce that idea into my mind, it must be the author of the Essay concerning Human Understanding ; he who has so far distinguished himself from the generality of writers by the clearness- and significancy of what he says. Let us therefore see how this celebrated author describes the general or abstract idea of a triangle. 'It must be (says he) neither oblique nor rectangular, neither equilateral, equicrural, nor scalenum;but all and none of these at once. In effect, it is somewhat imperfect that cannot exist; an idea, wherein some parts of several different and inconsistent ideas are put together' Essay on Hum. Understand. B .
iv. C. 7. S.9· This is the idea which he thinks needful for the enlargement of knowledge, which is the subject of mathematical demonstration, and without which we could never come to know any general proposition concerning triangles. That author acknowledges it doth 'require some pains and skill to form this general idea of a triangle.' ibid. But had he called to mind what he says in another place, to wit, 'That ideas of mixed modes wherein any inconsistent ideas are put together cannot so much as exist in the mind, i.e. be conceived.' vid. B. iii. C. 10. S. 33. ibid. I say, had this occurred to his thoughts, it is not improbable he would have owned it above all the pains and skill he was master of to form the above-mentioned idea of a triangle, which is made up of manifest, staring contradictions. That a man who laid so great a stress on clear and determinate ideas should nevertheless talk at this rate seems very surprising. But the wonder will lessen if it be considered that the source whence this opinion flows is the prolific womb which has brought forth innumerable errors and difficulties in all parts of philosophy and in all the sciences: but this matter, taken in its full extent, were a subject too comprehensive to be insisted on in this place. And so much for extension in abstract.
126. Some, perhaps, may think pure space, vacuum, or trine dimension to be equally the object of sight and touch: but though we have a very great propension to think the ideas of outness and space to be the immediate object of sight, yet, if I mistake not, in the foregoing parts of this essay that hath been clearly demonstated to be a mere delusion, arising from the quick and sudden suggestion of fancy, which so closely connects the idea of distance with those of sight, that we are apt to think it is itself a proper and immediate object of that sense till reason corrects the mistake.
127. It having been shewn that there are no abstract ideas of figure, and that it is impossible for us by any precision of thought to frame an idea of extension separate from all other visible and tangible qualities which shall be common both to sight and touch: the question now remaining is, whether the particular extensions, figures, and motions perceived by sight be of the same kind with the particular extensions, figures, and motions perceived by touch? In answer to which I shall venture to lay down the following proposition: The extension, figures, and motions perceived by sight are specifically distinct from the ideas of touch called by the same names, nor is there any such thing as one idea or kind of idea common to both senses. This proposition may without much difficulty be collected from what hath been said in several places of this essay.
But because it seems so remote from, and contrary to, the received notions and settled opinion of mankind, I shall attempt to demonstrate it more particularly and at large by the following arguments.
