[FOM] Fictionalism About Mathematics

[Colin McLarty]

On Sat, Mar 10, 2012 at 7:13 PM, Kevin Scharp <scharp.1 at osu.edu> wrote:

> The results of a recent poll of philosophers on prominent philosophical
> issues is here: http://philpapers.org/surveys/results.pl
> The second question is on abstract objects, and "Platonism" is the most
> popular answer with 39.3%.

Of course platonism here stands for many variant approaches, not
closely tied to anything Plato wrote.

There are a lot of alternatives and they are not always carefully distinguished

Probably the most popular alternatives in philosophy of math are
various nominalisms, saying statements of conventional mathematics are
not true at face value, but (all, or many) can be re-interpreted as
truths.  For example they may be interpreted as not true but merely
possible.

A close rival might be various versions of formalism, which say
statements of conventional mathematics are not meant to be true, they
are meant to be symbol strings derivable from suitable symbol strings
called axioms.

Formalism and nominalism are often hybridized, using some techniques from each.

Fictionalism says the statements of conventional mathematics are not
true, any more that statements in novels are true.  But statements in
a (good) novel have to make sense within the framework of the novel.
Mathematics faces quite different constraints than novels do,
obviously, and statements of mathematics work in that framework rather
than being true.

Contextualism says different contexts always have their own standard
of truth.  In a day-to-day context space has three dimensions -- in
quantum gravity that needs re-thinking.  So a mathematical context
makes true statements about, say, the continuum, which are not true in
a physical context.

All these are respectable in philosophy, though each also has
impassioned detractors both in philosophy and among mathematicians.

colin