y to recollection of the experiences of the soul in its disembodied
state in the world of Ideas.

The reasons assigned by Plato for believing in this doctrine may be
reduced to two. Firstly, knowledge of the Ideas cannot be derived from
the senses, because the Idea is never pure in its sensuous
manifestation, but always mixed. The one beauty, for example, is only
found in experience mixed with the ugly. The second reason is more
striking. And, if the doctrine of recollection is itself fantastic,
this, the chief reason upon which Plato bases it, is interesting and
important. He pointed out that mathematical knowledge seems to be
innate in the mind. It is neither imparted to us by instruction, nor
is it gained from experience. Plato, in fact, came within an ace of
discovering what, in modern times, is called the distinction between
necessary and contingent knowledge, a distinction which was made by
Kant the basis of most far-reaching developments in philosophy. The
character of necessity attaches to rational knowledge, but not to
sensuous. To explain this distinction, we may take as our example of
rational knowledge such a proposition as that two {214} and two make
four. This does not mean merely that, as a matter of fact, every two
objects and every other two objects, with which we have tried the
experiment, make four. It is not merely a fact, it is a necessity. It
is not merely that two and two do make four, but that they must make
four. It is inconceivable that they should not. We have not got to go
and see whether, in each new case, they do so. We know beforehand that
they will, because they must. It is quite otherwise with such a
proposition as, "gold is yellow." There is no necessity about it. It
is merely a fact. For all anybody can see to the contrary it might
just as well be blue. There is nothing inconceivable about its being
blue, as there is about two and two making five. Of course, that gold
is yellow is no doubt a mechanical necessity, that is, it is
determined by causes, and in that sense could not be otherwise. But it
is not a logical necessity. It is not a logical contradiction to
imagine blue gold, as it would be to imagine two and two making five.
Any other proposition in mathematics possesses the same necessity.
That the angles at the base of an isosceles triangle are equal is a
necessary proposition. It could not be otherwise without
contradiction. Its opposite is unthinkable. But that Socrates is
st