[FOM] Logic/syntax versus arithmetic

Timothy Y. Chow tchow at math.princeton.edu
Wed Feb 26 21:02:43 EST 2020

Sam Sanders wrote:

> <begin>
> Note:  As Church thought likely, the "finitistic nominalism" of Quine 
> and Goodman has been useless for linguistics, both theoretical and 
> computational. The following excerpt from Church's 1951 article, The 
> need for abstract entities, is an early proposal for a formal semantics 
> of natural language. In 1967, Church moved from Princeton to UCLA, where 
> Rudolf Carnap, Richard Montague, Hans Kamp, Barbara Partee, and others 
> were actively debating and developing formal semantics for NLs.
> </end>
> In light of the above, what do contemporary nominalist approaches have 
> to offer, beyond "development for their own sake", that Quine and 
> Goodman's approach lacked?

While I have my own objections to nominalism, I'm not too impressed by 
criticisms that nominalism is useless.  The charge of uselessness can be, 
and has been, leveled at f.o.m. generally, by (to use a favorite phrase of 
Harvey Friedman's) "core mathematicians."  Mathematics in general, not 
just f.o.m., is frequently criticized for being useless.  The author of 
the biblical book of Ecclesiastes seems to invite the reader to 
contemplate the possibility that all of life is useless.

Now, if someone claims that X is useful for something, and it's not clear 
that this is true, then it's perfectly legitimate to question whether X is 
really useful.  But that doesn't seem to be what nominalists are claiming 
for nominalism.


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