Re: Name the thesis: "Formal sentences capture informal ones"

From: Torkel Franzen (torkel_at_sm.luth.se)
Date: 01/30/05 

Date: 30 Jan 2005 06:09:34 +0100

tchow@lsa.umich.edu writes:

> O.K., let me try another version.
>
> (*) Intension-preserving formalization of informal mathematical
> statements is always possible.
> Maybe this should be thought of not as a thesis but as a "thesis schema"?
> Instances of the schema would be things like:
>
> (+) Con("PA") is an intension-preserving formalization of "PA is
> consistent."

  (+) is not on the face of it an instance of (*), since it states not
only that an itension-preserving formalization of "PA is consistent"
is possible, but that a particular arithmetical formula is such a
formalization. What is required of an intension-preserving
formalization? In formalizing Con(PA) or the fundamental theorem of
arithmetic in PA, we need to represent finite sequences of numbers
as numbers. This can be done in many ways, but are they
intension-preserving?

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