[FOM] Fictionalism About Mathematics
Richard Heck
rgheck at brown.edu
Mon Mar 12 17:24:22 EDT 2012
On Mar 11, 2012, at 10:37 AM, Alan Weir wrote:
> Of course that raises lots of philosophical questions: it's correct
> but untrue? It's true in some 'light sense' but not in any weightier
> one? If correctness = 'true in the story' as in Harry'sgloss, that
> can't mean, 'has been published and will never be challenged' for we
> have good reason to believe false 'theorems' will have been published
> and remain undetected, and anyway most mathematical theses will be
> such that neither they nor their negations will ever be concretely
> inscribed. Does it mean 'is provable from axioms which constitute 'the
> story''? Then we seem to be moving towards formalism.
On 03/12/2012 02:58 AM, Harry Deutsch wrote:
>
> This comment is the essential point. If mathematics is a fictional
> story, what (who) determines what is true in the story? In fiction
> the author is the absolute authority, but that does not, of course,
> seem true of mathematics.
>
Which is to say that fictionalism, in at least some of its forms, is
close kin of formalism of the most extreme variety. Avoidance of this
kinship usually involves making some kind of strong tie to the
applications of mathematics, as Field tried to do in /Science Without
Numbers/. But that rather limits the scope of the view and so *does*
bring it into conflict with "accepted mathematical practice", a point of
which John Burgess, e.g., is fond.
Richard
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