anding is not a necessary truth. He might just as well be sitting.

Since a mathematical proposition is necessarily true, its truth is
known without verification by experience. Having proved the
proposition about the isosceles triangle, we do not go about measuring
the angles of triangular objects to make sure there is no exception.
We know it without any experience at all. And if we {215} were
sufficiently clever, we might even evolve mathematical knowledge out
of the resources of our own minds, without its being told us by any
teacher. That Caesar was stabbed by Brutus is a fact which no amount
of cleverness could ever reveal to me. This information I can only get
by being told it. But that the base angles of an isosceles triangle
are equal I could discover by merely thinking about it. The
proposition about Brutus is not a necessary proposition. It might be
otherwise. And therefore I must be told whether it is true or not. But
the proposition about the isosceles triangle is necessary, and
therefore I can see that it must be true without being told.

Now Plato did not clearly make this distinction between necessary and
non-necessary knowledge. But what he did perceive was that
mathematical knowledge can be known without either experience or
instruction. Kant afterwards gave a less fantastic explanation of
these facts. But Plato concluded that such knowledge must be already
present in the mind at birth. It must be recollected from a previous
existence. It might be answered that, though this kind of knowledge is
not gained from the experience of the senses, it may be gained from
teaching. It may be imparted by another mind. We have to teach
children mathematics, which we should not have to do if it were
already in their minds. But Plato's answer is that when the teacher
explains a geometrical theorem to the child, directly the child
understands what is meant, he assents. He sees it for himself. But if
the teacher explains that Lisbon is on the Tagus, the child cannot see
that this is true for himself. He must either believe the word {216}
of the teacher, or he must go and see. In this case, therefore, the
knowledge is really imparted from one mind to another. The teacher
transfers to the child knowledge which the child does not possess. But
the mathematical theorem is already present in the child's mind, and
the process of teaching merely consists in making him see what he
already potentially knows. He has only to look