action of our life we take such uniformity for granted. But he will be
obliged to admit that, whatever he may say to induce us to assent to the
principle of Nature's uniformity, his arguments will not amount to
logical proof, because every argument in some way assumes that
principle. He has come, in fact, to the limits of Logic. Just as Euclid
does not try to prove that 'two magnitudes equal to the same third are
equal to one another,' so the Logician (as such) does not attempt to
prove the uniformity of causation and the other principles of his
science.

Even when our purpose is to ascertain some general truth, the results of
systematic inquiry may have various degrees of certainty. If Logic were
confined to strict demonstration, it would cover a narrow field. The
greater part of our conclusions can only be more or less probable. It
may, indeed, be maintained, not unreasonably, that no judgments
concerning matters of fact can be more than probable. Some say that all
scientific results should be considered as giving the average of cases,
from which deviations are to be expected. Many matters can only be
treated statistically and by the methods of Probability. Our ordinary
beliefs are adopted without any methodical examination. But it is the
aim, and it is characteristic, of a rational mind to distinguish degrees
of certainty, and to hold each judgment with the degree of confidence
that it deserves, considering the evidence for and against it. It takes
a long time, and much self-discipline, to make some progress toward
rationality; for there are many causes of belief that are not good
grounds for it--have no value as evidence. Evidence consists of (1)
observation; (2) reasoning checked by observation and by logical
principles; (3) memory--often inaccurate; (4) testimony--often
untrustworthy, but indispensable, since all we learn from books or from
other men is taken on testimony; (5) the agreement of all our results.