Page:On an Evolutionist Theory of Axioms.djvu/21

14 instance, generation after generation of a particular race had never seen swans which were not white. Countless generations living in certain parts of the earth have never seen water in a solid form.

Thus from the very manner of its formation our belief that the arc must be greater than its chord is compatible with the existence of arcs which are not greater than their chords. There are ways enough in which our limitation to one kind of arc may have come about. For instance, naturalists expect to find new forms of flora and fauna in regions which are being explored for the first time. How do we know—not to speak of what may be found in other planets and stars—that the polar regions have not an abundance of that other kind of arc and chord? And was it not as important scientifically that the naturalists in the Challenger should have dredged the deep seas for them as for those objects in which they were immediately interested?

Or again, allowing, what could not be known if the theory we are examining were true, that all the arcs in the world now are greater than their chords, how can the evolutionist know that in early geological periods there were even any arcs at all which were greater than their chords } For aught he can say the arcs not greater than their chords may have been contemporary with the 'dragons of the prime' and have perished with them. Why should he expect us to allow arbitrary assumptions here, which are allowed in no other empirical science?

It is quite remarkable to find the evolutionist confidently making such statements as the following, without even asking himself how he could be entitled to them.

'Space-relations have been the same not only for all ancestral men, all ancestral primates, all ancestral orders of mammalia, but for all simpler orders of creatures.'

But there is another and more serious form of the difficulty.