[FOM] Yablo, Mirimanoff, and Negative Types

[Roger Bishop Jones]

On Tuesday 17 September 2002  2:14 pm, A.P. Hazen wrote:

>    If I'm right, Yablo has given us the proof of a theorem in the
> metatheory of negative type theory: it's language can't express
> well-foundedness.

And hence cannot have the "standard semantics"
for a higher order logic, i.e. some of the power sets must be
incomplete.

So though the theory is consistent when formulated as
a many-sorted first order theory, it is semantically inconsistent
(i.e. has no models) when formulated as a type theory
with "standard semantics".

Roger Jones