losophers) that the only true 'cause'
is the total universe at one moment, the only true 'effect,' the whole
of reality at the next. For that is merely to reinstate the given chaos
science tried to analyse, and to forbid us to make selections from it.
It would make prediction wholly vain, and entangle truth in a totality
of things which is unique at every instant, and never can recur.

The principles of mathematics are as clearly postulates. In Euclidean
geometry we assume definitions of 'points,' 'lines,' 'surfaces,' etc.,
which are never found in nature, but form the most convenient
abstractions for measuring things. Both 'space' and 'time,' as defined
for mathematical purposes, are ideal constructions drawn from empirical
'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