o have as much evidence
as any belief can need. But among the propositions which one man finds
indubitable there will be some that another man finds it quite possible
to doubt. It used to seem self-evident that there could not be men at
the Antipodes, because they would fall off, or at best grow giddy from
standing on their heads. But New Zealanders find the falsehood of this
proposition self-evident. Therefore, if self-evidence is a guarantee of
truth, our ancestors must have been mistaken in thinking their beliefs
about the Antipodes self-evident. Meinong meets this difficulty by
saying that some beliefs are falsely thought to be self-evident, but in
the case of others it is self-evident that they are self-evident, and
these are wholly reliable. Even this, however, does not remove the
practical risk of error, since we may mistakenly believe it self-evident
that a certain belief is self-evident. To remove all risk of error, we
shall need an endless series of more and more complicated self-evident
beliefs, which cannot possibly be realized in practice. It would seem,
therefore, that self-evidence is useless as a practical criterion for
insuring truth.

The same result follows from examining instances. If we take the four
instances mentioned at the beginning of this discussion, we shall
find that three of them are logical, while the fourth is a judgment of
perception. The proposition that two and two are four follows by purely
logical deduction from definitions: that means that its truth results,
not from the properties of objects, but from the meanings of symbols.
Now symbols, in mathematics, mean what we choose; thus the feeling of
self-evidence, in this case, seems explicable by the fact that the whole
matter is within our control. I do not wish to assert that this is
the whole truth about mathematical propositions, for the question is
complicated, and I do not know what the whole truth is. But I do wish to
suggest that the feeling of self-evidence in mathematical propositions
has to do with the fact that they are concerned with the meanings of
symbols, not with properties of the world such as external observation
might reveal.

Similar considerations apply to the impossibility of a thing being in
two places at once, or of two things being in one place at the same
time. These impossibilities result logically, if I am not mistaken, from
the definitions of one thing and one place. That is to say, they are not
laws of