'space' (extension) and 'time' (succession) feelings, and purged of the
subjective variations of these experiences. Nevertheless, geometry
forms the handiest system for applying to experience and calculating
shapes and motions. But, ideally, other systems might be used. The
'metageometries' have constructed other ideal 'spaces' out of postulates
differing from Euclid's, though when applied to real space their greater
complexity destroys their value. The postulatory character of the
arithmetical unit is quite as clear; for, in application, we always have
to _agree_ as to what is to count as 'one'; if we agree to count apples,
and count the two halves of an apple as each equalling one, we are said
to be 'wrong,' though, if we were dividing the apple among two
applicants, it would be quite right to treat each half as 'one' share.
Again, though one penny added to another makes two, one drop of water
added to another makes one, or a dozen, according as it is dropped.
Common sense, therefore, admits that we may reckon variously, and that
arithmetic does not _apply_ to _all_ things.

Again, it is impossible to concede any meaning even to the central 'law
of thought' itself--the Law of Identity ('A is A')--except as a
postulate. Outside of Formal Logic and lunatic asylums no one wishes to
assert that 'A is A.' All significant assertion takes the form 'A is B.'
But A and B are _different_, and, indeed, no two 'A's' are ever _quite_
the same. Hence, when we assert either the 'identity' of 'A' in two
contexts, or that of 'A' and 'B,' in 'A is B,' we are clearly _ignoring
differences which really exist--i.e._, we postulate that in spite of
these differences A and B will for our purposes behave as if they were
one ('identical'). And we should realize that this postulate is of our
making, and involves a risk. It may be that experience refuses to
confirm it, and convicts us instead of a 'mistaken identity.' In short,
_every identity we reason from is made by our postulating an irrelevance