Re: Can We Quantify over Everything?

On May 21, 12:20 am, Peter_Smith <p...@xxxxxxxxx> wrote:
> > Can We Quantify over Everything?

Sure. Just consider our /universe of discourse/ to consist of
"everything". Then "Ax" would comprise _everything_.

Well, its not as simple as *that*, or else Augustin Rayo and Gabriel
Uzquiano wouldn't have recently edited a fascinating OUP book of a
dozen essays by front-rank logicians vigorously debating the issue.

For a start, we might wonder here about the notion of a universe of
discourse: the usual textbook definition of a universe of discourse
treats it as a set -- but there are familiar problems about the idea
of a set which contains everything (e.g. all the ordinals ...).


Most probably you are referring to the book 'Absolute Generality',
whose introduction can be found at