scribe a geometrical judgement, e. g. that two straight lines cannot
enclose a space, as a mental law, because we are bound to think it
true. Then we may state the presupposition by saying that objects,
e. g. individual pairs of straight lines, must conform to such a mental
law. But the explicit recognition of this presupposition and the
conscious assertion of it in no way assist the solution of particular
geometrical problems. The presupposition is really a condition of
geometrical thinking at all. Without it there is no geometrical
thinking, and the recognition of it places us in no better position
for the study of geometrical problems. Similarly, if we wish to think
out the nature of God, freedom, and immortality, we are not assisted
by assuming that these objects must conform to the laws of our
thinking. We must presuppose this conformity if we are to think at
all, and consciousness of the presupposition puts us in no better
position. What is needed is an insight similar to that which we have
in geometry, i. e. an insight into the necessity of the relations
under consideration such as would enable us to see, for example, that
being a man, as such, involves living for ever.

Kant has been led into the mistake by a momentary change in the
meaning given to 'metaphysics'. For the moment he is thinking of
metaphysics, not as the inquiry concerned with God, freedom, and
immortality, but as the inquiry which has to deal with the problem as
to how we can know _a priori_. This problem is assisted, at any rate
prima facie, by the assumption that things must conform to the mind.
And this assumption can be said to be suggested by mathematics,
inasmuch as the mathematician presupposes that particular objects must
correspond to the general rules discovered by the mind. From this
point of view Kant's only mistake, if the parallelism is to be
maintained, is that he takes for an assumption which enables the
mathematician to advance a metaphysical presupposition of the advance,
on which the mathematician never reflects, and awareness of which
would in no way assist his mathematics.

In the second place the 'Copernican' revolution is not strictly the
revolution which Kant supposes it to be. He speaks as though his aim
is precisely to reverse the ordinary view of the relation of the mind
to objects. Instead of the mind being conceived as having to conform
to objects, objects are to be conceived as having to conform to the
mind. But i