Re: Can We Quantify over Everything?

On 20 May 2007 12:15:12 -0700, LauLuna <laureanoluna@xxxxxxxx>
wrote:


Can We Quantify over Everything?

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


The aboutness paradox seems to show that no proposition can quantify
over itself.

Hmmm...

Hypothesis: "No proposition can quantify over itself."

Counterexample: Consider the "proposition":

(*) All propositions are either true or false.

Regardless of the question if (*) is true or false, obviously (*)
talks about ALL propositions and hence about (*) too. No?


This supports the claim that no proposition can quantify over
itself.

Well, the counterexample above seem to disprove the claim that no
proposition can quantify over itself. No?


If no proposition can quantify over itself, then no proposition can
quantify over everything.

Right. Though the antecedence of this if-then-statement seems to be
false. (See comment above.)


(7) for each proposition p there is something which p does not
quantify over

The counterexample given above (and similar examples) seem to
disprove this statement. For example:

(**) All propositions are propositions.

Obviously (**) is a true statement or "proposition". And since
it is a "proposition" it talks about itself too: If (**) is a
proposition it is a proposition.


F.

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