Causation serves as a good example. Experience as it first comes to us
is a mere flood of happenings, with no distinction between causal and
casual sequences. Clearly our whole ability to control our life, or even
to continue it, demands that we should _predict_ what happens, and guide
our actions accordingly. We therefore postulate a right to _dissect_
the flux, to fit together selected series without reference to the
rest. Thus, a systematic network of natural 'laws' is slowly knit
together, and chaos visibly transforms itself into scientific order. The
postulation of 'causes' is verified by its success. Moreover, it is to
be noted that to this postulate there is no alternative. A belief that
all events are casual would be scientifically worthless. So is a
doctrine (still popular among philosophers) 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.
Public-domain text, read in full here on John Shaqi.
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