[hist-analytic] Quine's Holism

Rogério Passos Severo rpsevero at gmail.com
Fri Feb 6 14:03:52 EST 2009

Dear Roger,

Geometry is traditionally sorted as branch of mathematics. In the eighteenth
and nineteenth centuries, the axioms of Euclidean geometry were thought to
be true of physical space. Nowadays physicists say space is non-Euclidean.
General relativity is now thought to better explain observations than
Newtonian physics. So here we have an instance of changes in physics coming
along hand-in-hand with changes in mathematics. This is exactly what Quine's
holism says: the sentences of a theory are not accepted/rejected one by one,
but as "a corporate body".

Here's another example: Descartes and others argued that negative numbers
were absurd. They thought the idea made no sense at all. And indeed, for a
long time math had no negative numbers. But then people began to use them
"instrumentally", so to speak. People began to try them out, and see what
they could do with them. Later it became clear that math with negative
numbers was much more useful (for science) than without them. And so
negative numbers were incorporated. This was a significant change in
mathematics brought about by empirical considerations (what you could do
with them in the empirical sciences).

But I see your point: inside mathematics there is a justification system in
place which is more or less impervious to what goes on outside (in the
natural sciences). This is ok by Quine. He acknowledges that in several
places. His point was a more general and abstract one: no sentences are
justified in isolation, and mathematics as a whole is not justified
independently of the rest of science. Changes in the other disciplines may
have effects on mathematics.

Best wishes,
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