The rival doctrine, sometimes called the Berkeleyan, contains no such difficulties, and it makes evident that the difficulties discussed above arise simply out of a confusion of samenesses, and are gratuitous. Its discussion demands that I call to mind a few distinctions already made.
One must bear in mind, in the first place, that a line immediately known, existing in consciousness, is the same with an "external" line corresponding to it, not in sense first, but in sense seventh. That is, they are two lines, not one, and in the interests of clearness they should be considered separately.
One should remember, in the second place, that a line in consciousness at one moment is not, in the strictest sense, the same with a line in consciousness at another moment. One may stand for the other and thus be the same with it in sense fifth; or the two may be regarded as both belonging to the one series of experiences, which, taken together, represent to us "an object," in which case they are the same in sense third. A thing the same with another thing in either of these senses is not necessarily much like it. It must only be able to serve as its representative.
Now I see a line about an inch long on the paper before me. It is a certain distance from my eyes. I shall concern myself for the present only with the line immediately perceived, which means for me so much sensation. If I move this line (which remains the same in sense third), nearer to me or farther away, I do not perceive the identical thing that I did before. My quantity of sensation is increased or diminished. If I keep the line at the same distance and change none of the conditions, the quantity of sensation remains presumably the same. The question arises, Is this line as actually experienced at this moment infinitely divisible or not? I can certainly conceive of it as divisible to some extent, for I see part out of part, and I can think of these parts as separated. But if this line were divided, the division would soon result in parts which could be seen, but which could not be seen to consist of part out of part. Were these apparently non-extended parts (they would remain the same in sense third), approached to the eyes, they, too, would be seen to consist of part out of part, but then I should simply have substituted for the apparently non-extended a representative which was extended. This would not prove that what was before in consciousness was extended and could be divided. Consciousness certainly seems to testify that any particular line in consciousness is composed of a limited number of indivisible parts, and when one adds to this reflection the consideration that a point moving over a given line does not appear to have an endless task before it, but soon arrives at the final term, one is irresistibly impelled to the conclusion that the parts of the line are not infinite, but that the division results in the indivisible, the simple element of sensation, which, joined with other such elements, makes an extended object, but which taken alone is not extended at all. The whole difficulty lies in keeping to the line and the parts with which one started. It is so easy to pass from sameness in sense first to sameness in sense third or sense fifth; it is so natural to bring an object which is, as we say, imperfectly seen, closer to the eye and thus substitute for what was seen before a new experience connected with it in the order of nature, confident that any system of relations derived from the latter may safely be carried over to all possible experiences connected with the former; one does this so instinctively that a man may very readily suppose that he is still busied about the apparently non-extended element with which he started, when he is in reality dividing and sub-dividing its representative, which is evidently extended. But the question is not whether, when one has divided a line until the parts cannot be seen to consist of parts, one may substitute for these parts what evidently does consist of parts, and go on dividing that. The question is, whether an apparently non-extended element of a line in consciousness is divisible or not. Any argument from the possibility of dividing its substitutes evidently has nothing to do with this point.
It is plain that this doctrine, which makes any particular finite line in consciousness to consist of a limited number of simple parts, is not open to the objection that it necessitates the absurdity of exhausting an endless series. Moving along such a line, Achilles could overtake the tortoise, for the successively diminishing distances between them do not constitute an endless series. The descending series results after a limited number of terms in the simple, and the series is broken, for the simple does not consist of parts. In this there is at least no contradiction. It remains to see what other objections may lie against it.
It may be argued, first, as it often is argued, that it is impossible to conceive of any part of a line as not itself extended and having parts. It may be admitted that the small parts arrived at do not seem to have part out of part; that these sub-parts are not observed in them, but still it is said that one who thinks about them cannot but think of them as really having such parts. I ask one who puts forward this objection to look into his own mind and see whether he does not mean by "thinking about them," bringing them in imagination nearer to the eye, or by some means substituting for them what can be seen to have part out of part. That one can do this no one would think of denying, but, as I have said, this does not prove the original parts to be extended.
It may be objected again that extension can never be built up out of the non-extended—that if one element of a given kind has, taken alone, no extension at all, two or more such elements together cannot have any extension either. I answer that a straight line has no angularity at all, and yet two straight lines may obviously make an angle; that one man is not in the least a crowd, but that one hundred men may be; that no single tree is a forest, but that many trees together do make a forest; that a uniform expanse of color is in no sense a variegated surface, but that several such together do make a variegated surface. It may be that extension is simply the name we give to several simple sense-elements of a particular kind taken together. One cannot say off-hand that it is not.
Should one object, finally, that, if a given line in consciousness be composed of a limited number of indivisible elements of sensation, consciousness ought to distinguish these single elements and testify as to their number; I answer that what is in consciousness is not necessarily in a clear analytical consciousness, nor well distinguished from other elements. For example, I am at present conscious of a stream of sensations which I connect with the hand that holds my pen. The single elements in this complex I cannot distinguish from each other, nor can I give their number. It does not follow that I am to assume the number to be infinite. Much less should I be impelled to make this assumption, if it necessitated my accepting as true what I see to be flatly contradictory, as in the case under discussion. It was because of this vagueness and lack of discrimination in the testimony of consciousness that I said, some distance back, that consciousness seems to testify that any finite line in it is composed of simple parts. If the testimony were quite clear, the matter would be settled at once. As it is not quite clear, the matter has to be settled on a deductive basis. The most reasonable solution appears to be the Berkeleyan.
So much for the line immediately perceived, the line in consciousness. What shall we say to one who is willing to admit that this line is not infinitely divisible, but is composed of simple sense-elements; and yet who maintains that there exists an "external" line corresponding to it, which is not immediately perceived, and is infinitely divisible? We may begin by suggesting to him that an "external" point moving over this "external" line must perform the wholly impossible feat to which Clifford condemns a point moving over a line; and we may farther suggest that, if the "external" world be an intelligible world at all, a contradiction may be as much out of place in it as anywhere else. And if the existence of this world be problematic, a thing not self-evident, it seems quite reasonable to demand very good proof indeed of the existence, of that which contains in its very conception such excellent reasons for believing in its non-existence. This proof, the student of the history of speculation will testify, has not as yet been forthcoming.
Sec. 37. With this I close my analysis of samenesses, and of confusions which have resulted in needless embarrassments and gratuitous difficulties. More instances of the latter could be given, of course. The reader will be able to furnish, I presume, many like them. Those which I have given seem to me quite sufficient to prove the need of much greater care and exactitude than one commonly finds in metaphysical reasonings. Loose reasoning is bad reasoning, and leads to bad results. Its one virtue is that it does not require much mental application on the part of either author or reader. On the other hand, the attempt to be cautious and exact, to distinguish between things easily confounded, and to keep strictly to the thing in dispute through a long discussion, these things are wearisome to all concerned. Although I am quite conscious of this fact, I have tried to do these things: with what result, my fellow-analysts must judge. I feel reasonably sure that I have succeeded in being wearisome, and for this I make due apology.