[FOM] Richard Epstein's view

[Harry Deutsch]

The most famous opponent of it was Frege in the 
Grundlanden
On Mar 16, 2012, at 9:39 AM, 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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