Re: quantifiers and existence

[jorge@PHYAST.PITT.EDU]

djer:
> I think what pc means here is that something of the form:
>
> E(x)[A(x)broda(x)]. has a scope that asserts the second x exists.

I don't think pc would accept that as a well formed expression. You can't
quantify the same variable twice. (You can use the same variable in two
independent expressions, but that's a different story.)

> pc has said that "re broda" means the standard  Russell expression
> which I take to be:
>
> ExEy[(x\=y & Az(z=x v z=y)) & broda(x) & broda(y)].

This is not quite right. {re broda} is an argument, it is not a claim.
Russell's expression corresponds to a full bridi. It would apply to
{reda broda}.

But you are still missing something there.  Az(z=x v z=y) should be replaced
by Az(broda(z) -> (z=x v z=y)). Otherwise, you are claiming that there are
only two things in the universe.

> What does it mean now to say "lo re broda"?

{lo re broda} is not constructed from {re broda}. Remember that {re broda}
is only a shorthand for {re lo ro broda}. (Or maybe it is something else,
as pc proposes, but in any case it is not the inside part of {lo re broda}.

In {lo re broda}, the "re broda" part cannot stand alone.

> lo by itself claims existence
> for the broda it modifies.

No, the article only says that we are talking about individuals. The existence
comes from its default quantifier. {lo broda} stands for {su'o lo ro broda},
but you can override the default by giving another explicit quantifier.

{lo re broda} means {su'o lo re broda} = "at least one of the two broda
that there are in all". It claims nothing by itself because it is a sumti,
not a bridi.

> lo is also a determiner.

"Determiner" is very ambiguous, but the key difference between {lo}
and {le} is that {lo} is indeterminate or nonspecific and {le} is
determinate or specific. {lo} does not tell you _which_ broda you
are talking about. {le} does.

> Now what does "pa lo re broda" mean?

"Exactly one of the two broda that there are in all."

> In exploring this we find that the
> lo has yet another function. It separates the pa and re from merging
> into one number, pare, or 12. But there is no difference between
>
> "pa ti lo ci broda"  and
> "pa ti ci broda".

Both of those expressions are two sumti: {pa ti} and {lo ci broda}
or {ci broda} respectively.

{pa ti} means "one of these". The second part is a separate sumti.

Jorge