FOM: Silly questions (Reply to Tennant and Silver on arithmetic v. geometry)

Charles Silver csilver at
Sun Oct 11 19:23:50 EDT 1998

Vladimir Sazonov:
> > > But there is nothing here (except possibly of my
> > > education) what forces me to think that the structure I am working
> > > with is mysteriously unique one, even up to isomorphism, because
> > > I even do not know WHAT DOES IT MEAN *any* "isomorphism" and *any*
> > > structure in this general context.

	Take these second-order axioms:

1) (Ax)Sx <> 0
2) (Ax)(Ay)(Sx = Sy --> x = y)
3) (AX)(X0 & (Ay)(Xy -> XSy) --> (Ay)Xy)

	What is wrong with the proof that any structure satisfying these
axioms must be isomorphic to <N,0,S>, the standard structure?  Or is it
that you accept this proof, but want to raise the question: Just what *is*
this standard structure?  Or are you asking just what is it to *be* a
structure in the first place?  Or,...?

Charlie Silver

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