[FOM] Richard Epstein's view
Timothy Y. Chow
tchow at alum.mit.edu
Fri Mar 16 10:39:37 EDT 2012
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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