[FOM] Do the integers exist?

Torkel Franzen torkel at sm.luth.se
Thu May 13 12:52:30 EDT 2004

Jack Schwartz says:

 >It is an article of faith for most mathematicians that Peano's axioms
 >for arithmetic are consistent,

  No it isn't. Mathematicians in general know nothing about the formal
axioms of first order Peano arithmetic (which is what I suppose you
have in mind), nor is there any reason why they should.

 >Either of two kinds of work with integers, reasoning or computation,
 >might lead to detection of an inconsistency in Peano's axioms.

  It is of course open to anybody to look for an inconsistency in
the Peano axioms, for a natural number which does not have a unique
prime decomposition, and so on. However, such work becomes interesting
only when it yields a result.

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