[FOM] Richard Epstein's view
Arnon Avron
aa at tau.ac.il
Sat Mar 17 13:09:37 EDT 2012
I would like to repeat an argument already made here in the past
(like almost any other argument..) concerning views of this sort, no matter
what "ism" is attached to them: Even people like Epstein
should accept as meaningful and absolute propositions
of the sort: "The formal sentence A is/isn't a theorem of
the formal system T". I do not see how a view of mathematics (or
science in general) that denies this can be coherent, and in what
possible sense can the truth of such a proposition be "only true or
false in application". And of course, once one understands this,
s/he sees the meaningfulness and absoluteness of
at least quantifiers-free arithmetics.
Arnon Avron
On Fri, Mar 16, 2012 at 10:39:37AM -0400, Timothy Y. Chow wrote:
> Buried in the now-defunct thread about fictionalism, Richard Epstein
> wrote:
>
> >In my recent book *Reasoning in Science and Mathematics* (available from
> >the Advanced Reasoning Forum) I present a view of mathematics as a
> >science like physics or biology, proceeding by abstraction from
> >experience, except that in mathematics all inferences within the system
> >are meant to be valid rather than valid or strong. In that view of
> >science, a law of science is not true or false but only true or false in
> >application. Similarly, a claim such as 1 + 1 = 2 is not true or false,
> >but only true or false in application. It fails, for example, in the
> >case of one drop of water plus one drop of water = 2 drops of water, so
> >that such an application falls outside the scope of the theory of
> >arithmetic.
> >
> >On this view numbers are not real but are abstractions from counting and
> >measuring, just as lines in Euclidean geometry are not real but only
> >abstractions from our experience of drawing or sighting lines. The
> >theory is applicable in a particular case if what we ignore in
> >abstracting does not matter there.
>
> This sounds like a version of nominalism. On this view, I think,
> mathematical nouns are akin to pronouns. So we can recognize the truth of
>
> You refer to me as "you" and refer to yourself as "me"
>
> while at the same time denying that asking whether "you" exists makes any
> sense except insofar as it asks about the existence of some particular
> *instantiation* of "you."
>
> This view must be very old, but as I think about it now, I don't recall it
> being discussed explicitly very often. Can someone name some famous
> proponents of it?
>
> Tim
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