657. The
propositions of mathematics might be said to be fossilized. – The proposition
“I am called …” is not. But it too is regarded as incontrovertible by those who, like myself, have overwhelming
evidence for it. And this is not out of thoughtlessness. For, the evidence’s
being overwhelming consists precisely in the fact that we do not need to give way before any contrary
evidence. And so we have a buttress similar to the one that makes the
propositions incontrovertible.
the
propositions of mathematics –
are
really just syntactical games –
and yes –
as it stands at this point time –
these
games have a stable form –
a stable
use
short of
the development of a new mathematics –
we can
expect that stability to maintain –
however
there is no necessity here –
the
matter is contingent –
a
question of circumstance –
effectively
intellectual circumstance –
and that
can change
you may not need –
to give way before contrary evidence –
or consider a different theory –
or different account –
but the fact remains –
different views are possible –
and for that reason no proposition –
is incontrovertible
and in any case what you need –
can and does change –
it’s hardly a certainty
