(3) Statistics do indeed show that, of a given people under given circumstances, one in so many misdirects a letter, or commits a murder, or can read three languages ; and that the ratios remain very nearly constant from decade to decade unless the environment changes. But this is precisely what would happen if human actions were the resultants of environment and of a factor of spontaneity which, like a throw of honest dice, was absolutely unpredictable. We should get, just as we now do get, agreements where the basis of estimation is large, and discrepancies where it is small; indeed, if the argument from statistics were worth anything, then we could prove in like manner that the throws of dice are governed by discoverable laws and not by chance, — which is practically untrue.
So with character: if it be the joint product of environment, heredity, and volition, then in the long run it may seem to result mainly or wholly from environment and heredity, for the reason that volition (unless guided by principles whose development is, itself, largely due to environment, etc.)] is like dice throwing, now this way and now that, so that its net result varies nearly as the square root of the number of cases that have come up, while the result of a steady pull from heredity or environment varies as the number of cases.
(4) To examine the facts of consciousness belongs more to the philosopher than to the mathematician. My own consciousness, however, appears on the whole to testify neither to complete determinism nor to complete freedom; and I suspect that its evidence is really in close accord with the theory sketched out above.
It would seem then that the analogies of physical and mathematical science are not unfriendly to that old faith in freedom to which the conscience and common sense of the race have substantially held; and if we cannot now hold to it in the old simple way, this is mainly because the world as known to us is so much larger and more complex than as known to our fathers. We cannot do or become at once just what we would: the ego can act effectively only through, or as part of, an intricate mechanism, and perhaps much that it seems to initiate is mere ideo-
