[FOM] Bucknerism = Nominalism with Plural Quantification?

Harvey Friedman friedman at math.ohio-state.edu
Thu May 1 00:09:02 EDT 2003

Reply to Buckner 8:17PM 4/30/03.

I am still struggling to figure out just what position Buckner is 
taking. I will attempt to sort this out in this limited context first.

Which of the following assertions are meaningful?

1. for all integers x,y,z > 1, x^3 + y^3 not= z^3.

2. for all integers x there exists a prime p > x.

3. for all integers x, there are some primes greater than x.

4. There are some integers > 1 such that every integer > 1 is 
divisible by at least one of them.

If it can be determined just what kinds of statements involving 
integers are being admitted, then we can perhaps move towards some 
axiomatizations of some value for f.o.m.

For example, Bucker may be admitting only certain arithmetic formulas 
as meaningful. If the class is novel, then one can consider induction 
based on such formulas only, and see what we get.

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