[FOM] Richard Epstein's view
hdeutsch at ilstu.edu
Sat Mar 17 00:49:02 EDT 2012
The most famous opponent of it was Frege in the
On Mar 16, 2012, at 9:39 AM, Timothy Y. Chow wrote:
> Buried in the now-defunct thread about fictionalism, Richard Epstein
>> 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
>> 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?
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