MS 842 (1908) - A Neglected Argument - Early Drafts

G134

but also the ends of the lead-pencil line into immediate contact.) Having done so, and the ribbon ends being already pasted together, please to take a differently colored pencil and between your line and the right hand edge of the ribbon mark another line and continue it until it returns into itself with[out] crossing your first line. The second line will have twice the length of the ribbon. Now the surface of your half twisted ribbon-ring has in the direction of its length the same shape that the projective geometers conceive a plane to have in every direction. Your first line along the middle is like their straight line on the plane. The other line

G135

is like a hyperbola so placed that the straight line lies half way between its two branches. The hyperbola is all in one piece because in the projective plane there is but one point at an infinite distance along any straight line. So that if the straight line is a vertical line and the hyperbola cuts the celestial sphere at any distance, say 1°, to the north of the zenith, this is the same point as the point of the celestial-sphere 1° south of the nadir. The result is that the hyperbola passes along the whole length of the vertical line twice before returning into itself, and will cut the north and south vertical plane into two parts, just as your second line on the ribbon separates its middle part from the edges, though your

G126

of nature, and indeed all experiential laws were results of evolution, being developed out of utterly causeless determinations of single events under a tendency to habit-taking conjoined with a survival of the fittest, their fitness consisting in their growth not essentially tending to produce characters that would necessarily remove any objects that conformed to them from the sphere of experience; the tendency to habit-forming itself growing under this very influence. Since putting forward that theory, I have in the intervening years, been led to make a slight though fundamental modification of it; no longer supposing that it was from single fortuitous events that law[s] have developed; since that could not account for the origin of time itself, but from the fortuitous embodiments of characters and forms of relationship. It is plain that if this hypothesis were true, it would account for the existence of laws in nature. It remains to test this hypothesis by deducing experiential consequences from it and comparing these virtual predictions with the facts

G127

Of such consequences, three occur to me. In the first place, although, as a general rule, it is impossible to make sure that a given concept is absolutely simple; but I have found as I believe a demonstration that one is so; and further I have found strong reason to think that, whether there are any indecomposable concepts or not, that every concept not of that nature has one or more absolutely true analyses, and not merely analyses that seem so to human faculties. Since this accords with the general opinion, I will not give an

G128

that there are any concepts that are, in their own nature simple. I find, as a result of observation, that those concepts which we take to be simplest are those which we think the most easily and naturally. That, I believe to be a sound induction, even if it be not a mere consequence of our unconsciously assuming the most facile conceptions to be the most simple. If there be any absolutely simple concepts, their applicability in experience, must be a priori independent of one another, since any experiential connection between two concepts that had no common ingredient would constitute a law of experience, whether it were universal or only statistical. It would, therefore, follow that,