"And fire, on the other hand, on the approach of cold, must either give way to it or be destroyed; nor can it ever endure, having admitted cold, to continue to be what it was, fire and cold.... Such I assert to be the case with the number 3 and many other numbers. Shall we not insist that the number 3 shall perish first ... before it would endure while it was yet 3 to become even?... What then? what do we now call that which does not admit the idea of the even?"
"And that which does not admit the just, nor the graceful?"
"The one, ungraceful, and the other, unjust."
"Be it so. But by what name do we call that which does not admit death?"
"Does the soul, then, not admit death?" (Socrates has already suggested that whatever the soul occupies it brings life to.)
Socrates' argument drawn from the number 3 brings before us a great host of these older absurdities of scientific thought, embracing many grave conclusions drawn from fanciful considerations of number, everywhere occurring. For briefest example: Aristotle in his book "On the Heavens" proves that the world is perfect by the following complete argument: "The bodies of which the world is composed ... have three dimensions; now 3 is the most perfect number ... for of 1 we do not speak as a number; of 2 we say _both_; but 3 is the first number of which we say _all_; moreover, it has a beginning, a middle and an end." You may instructively compare with this the marvelous matters which the school of Pythagoras educed out of _their_ perfect number which was 4, or the _tetractys_; and Plato's number of the _Republic_ which commentators to this day have not settled.
These illustrations seem sufficient to show a mental attitude towards facts which is certainly like that one has towards a far-off country which one does not expect to visit. The illustration I have used is curiously borne out by a passage in Lactantius, writing so far down as the fourth century, in which we have a picture of mediæval relations towards nature and of customary discussions.
"To search," says he, "for the causes of natural things; to inquire whether the sun be as large as he seems, whether the moon is convex or concave, whether the stars are fixed in the sky or float freely in the air; of what size and what material are the heavens; whether they be at rest or in motion; what is the magnitude of the earth; on what foundations it is suspended and balanced;--to dispute and conjecture on such matters is just as if we chose to discuss what we think of a city in a remote country of which we never heard but the name."