FOM: the blind spot about theory-completeness and categoricity
csilver at sophia.smith.edu
Wed Dec 17 06:07:57 EST 1997
On Tue, 16 Dec 1997, Neil Tennant wrote:
> The blind spot in question was the failure to realize that one would
> not be able simultaneously to maximize deductive power (to achieve
> theory-completeness) and expressive/descriptive power (to achieve
> categoricity). Let us call this the Ineffability Theorem.
> All one needs is the two *concepts* (1) completeness of a system of
> finitary proof, and (2) categoricity of a set of sentences---and the
> Ineffability Theorem follows easily. One does NOT need either a strong
> completeness theorem or the compactness theorem. (For the technical
> confirmation I am endebted to Harvey Friedman and Steve Simpson.)
Would you please state the Ineffability Theorem explicitly?
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