[FOM] Richard Epstein's view

[Arnon Avron]

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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