FOM: the blind spot about theory-completeness and categoricity

Charles Silver csilver at
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.

[Stuff deleted]

> 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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