The question which Kant put at the beginning of his
philosophy, namely 'How is pure mathematics possible?'
is an interesting and difficult one, to which every
philosophy which is not purely sceptical must find some answer.
The answer of the pure empiricists, that our mathematical
knowledge is derived by induction from particular instances,
we have already seen to be inadequate, for two reasons:
first, that the validity of the inductive principle itself
cannot be proved by induction;  secondly, that the general
propositions of mathematics, such as 'two and two always
make four', can obviously be known with certainty by
consideration of a single instance, and gain nothing by
enumeration of other cases in which they have been found
to be true.  Thus our knowledge of the general propositions
of mathematics (and the same applies to logic) must be
accounted for otherwise than our (merely probable) knowledge
of empirical generalizations such as 'all men are mortal'.

   From "The Problems of Philosophy" by Bertrand Russell, chapter 8.