About existence-as-consistency

Vaughan Pratt pratt at cs.stanford.edu
Fri Jul 2 03:13:05 EDT 2021

Giovanni Sambin began by raising what sounded like a perfectly conventional
and reasonable question of history: who said what when before the time it
became well known that a first order theory was consistent iff it had a

But then he asked "is there a way to avoid assuming EaC while keeping
classical logic (and hence validity of LEM)?"

The "is" suggests that this is no longer an historical question.

Consistence of a first order theory T is well-defined, but what about

One definition would be that an interpretation of the language of T exists
if and only if it is a model of T.

With that definition, the answer to Giovanni's question would appear to be

What definition of "existence" would admit a positive answer?

Vaughan Pratt
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20210702/e9cbd104/attachment-0001.html>

More information about the FOM mailing list