the way we must think than with any fact of
the outer world. We noted in the preceding chapter the three principles
commonly called 'laws of thought'. The view which led to their being so
named is a natural one, but there are strong reasons for thinking
that it is erroneous. Let us take as an illustration the law of
contradiction. This is commonly stated in the form 'Nothing can both be
and not be', which is intended to express the fact that nothing can at
once have and not have a given quality. Thus, for example, if a tree
is a beech it cannot also be not a beech; if my table is rectangular it
cannot also be not rectangular, and so on.

Now what makes it natural to call this principle a law of _thought_
is that it is by thought rather than by outward observation that we
persuade ourselves of its necessary truth. When we have seen that a tree
is a beech, we do not need to look again in order to ascertain whether
it is also not a beech; thought alone makes us know that this is
impossible. But the conclusion that the law of contradiction is a law
of _thought_ is nevertheless erroneous. What we believe, when we believe
the law of contradiction, is not that the mind is so made that it must
believe the law of contradiction. _This_ belief is a subsequent result
of psychological reflection, which presupposes the belief in the law of
contradiction. The belief in the law of contradiction is a belief about
things, not only about thoughts. It is not, e.g., the belief that if we
_think_ a certain tree is a beech, we cannot at the same time _think_
that it is not a beech; it is the belief that if the tree _is_ a
beech, it cannot at the same time _be_ not a beech. Thus the law of
contradiction is about things, and not merely about thoughts; and
although belief in the law of contradiction is a thought, the law of
contradiction itself is not a thought, but a fact concerning the things
in the world. If this, which we believe when we believe the law of
contradiction, were not true of the things in the world, the fact
that we were compelled to _think_ it true would not save the law of
contradiction from being false; and this shows that the law is not a law
of _thought_.

A similar argument applies to any other _a priori_ judgement. When we
judge that two and two are four, we are not making a judgement about our
thoughts, but about all actual or possible couples. The fact that our
minds are so constituted as to believe that two and two a