are mortal; Socrates is a man, therefore Socrates is
mortal.' In this case, what we really know beyond reasonable doubt is
that certain men, A, B, C, were mortal, since, in fact, they have died.
If Socrates is one of these men, it is foolish to go the roundabout way
through 'all men are mortal' to arrive at the conclusion that _probably_
Socrates is mortal. If Socrates is not one of the men on whom our
induction is based, we shall still do better to argue straight from our
A, B, C, to Socrates, than to go round by the general proposition, 'all
men are mortal'. For the probability that Socrates is mortal is greater,
on our data, than the probability that all men are mortal. (This is
obvious, because if all men are mortal, so is Socrates; but if Socrates
is mortal, it does not follow that all men are mortal.) Hence we shall
reach the conclusion that Socrates is mortal with a greater approach to
certainty if we make our argument purely inductive than if we go by way
of 'all men are mortal' and then use deduction.

This illustrates the difference between general propositions known _a
priori_ such as 'two and two are four', and empirical generalizations
such as 'all men are mortal'. In regard to the former, deduction is the
right mode of argument, whereas in regard to the latter, induction is
always theoretically preferable, and warrants a greater confidence in
the truth of our conclusion, because all empirical generalizations are
more uncertain than the instances of them.

We have now seen that there are propositions known _a priori_, and that
among them are the propositions of logic and pure mathematics, as well
as the fundamental propositions of ethics. The question which must
next occupy us is this: How is it possible that there should be such
knowledge? And more particularly, how can there be knowledge of general
propositions in cases where we have not examined all the instances, and
indeed never can examine them all, because their number is infinite?
These questions, which were first brought prominently forward by
the German philosopher Kant (1724-1804), are very difficult, and
historically very important.

CHAPTER VIII. HOW _A PRIORI_ KNOWLEDGE IS POSSIBLE

Immanuel Kant is generally regarded as the greatest of the modern
philosophers. Though he lived through the Seven Years War and the
French Revolution, he never interrupted his teaching of philosophy at
Koenigsberg in East Prussia. His most distinctive contr