Re: Is "existence" a predicate?

On Apr 16, 8:21 am, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:
On Tue, 15 Apr 2008 07:04:11 -0700 (PDT), holden_o...@xxxxxxxx wrote:
On Apr 15, 7:34 am, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:
On Mon, 14 Apr 2008 10:04:31 -0700 (PDT), holden_o...@xxxxxxxx wrote:
On Apr 14, 9:36 am, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:
On Mon, 14 Apr 2008 01:47:21 -0700 (PDT), sanchopanch...@xxxxxx wrote:
Hello,

I have read somewhere that "existence" wouldn't be a predicate in the
way e.g. "having a leg" is a predicate. Does anyone have a good and
actual reference on that or liks me to tell why?

A predicate is supposed to divide the universe into two classes,
the things that satisfy the predicate and the things that don't.
Existence doesn't do this, because _everything_ exists!

Yes, everything exists. If you want to claim otherwise you
have to prove the existence of something that does not exist,
and that's going to be hard.

The way language is used it often sounds like it's talking about
things that do not exist, but that's just a problem with the way
language is used.

Thanks,
S.

David C. Ullrich

I don't agree.

We know that.

If we allow 'things' to include described objects as well as existent
objects,
then there are non-existent things, For example the described object,
the present king of France,
does not exist.

Yes, if we allow the meaning of the word "things" to include things
which are not things then things change. There is no such thing
as the present king of France. _calling_ it "the described object"
does not change the fact that there is no such thing.

The description 'the present king of France' does exist, but it does
not have a referent.
It has sense but no reference.

Of course the description exists! That has no bearing on the
question of whether everything exists - the description does
in fact exist.

I didn't say that the description didn't exist. And I didn't
say that the description does not "have sense". What
I said was that there's no such thing as the present
king of France. There isn't. So it's not a counterexample
to my assertion that everything exists.

What you mean to say, imo, is that there is no existent object
described as 'the present king of France'.
And we all agree within the context of First Order Predicate Logic.
If we only allow existent objects as values of our variables,
then it is not a surprise that we can conclude that all values of our
variables must exist.

That everything exists, can only be asserted within the context of
FOPL.

There are other logics in which this is not the case.

All of truth is relative to the system that decides it.

Is the Russell class a thing for you?
Is the universal set a thing for you?
Surely the answers are dependent on which system of decision you are
using.






Saying that the present king of France does not exist is of course
exactly an example of what I meant when I said that the way
we use language sometimes seems to contradict the fact that
everything exists. The sentence really means that for every x,
x is not the present king of France.

Yes, ~Ex(x = (the present king of France)) is true,

as is ~((the
present king of France)=(the present king of France)).

There is no primary predicate (property) that is true of the present
king of France.

ie. ~EF(F(the present king of France)) means that it does not exist.

This has always seemed like one of the stranger of your assertions.
If we are going to talk about the present king of France, why do
we not say that he satisfies the predicate "is the king of a country"?

Because it is clearly false.
(the present king of France) is a king, is false.
(the present king of France) is present, is false.
(the present king of France) is a Frenchman, is false.
(the present king of France) has existence, is false.
(the present king of France) has non-existence, is false.

There is no property that (the present king of France) has.

Proof:
F(the present king of France) <-> Ey(Ax(x=y <-> x is a present king of
France) & Fy)
F(the present king of France) <-> Ey(Ax(x=y <-> (x is a present king
of France & there is no present king of France) & Fy)
(x is a present king of France & there is no present king of France),
is a contradiction.
F(the present king of France) <-> Ey(Ax(x=y <-> contradiction) & Fy).
But, Ax(x=y <-> contradiction) <-> ~Ex(x=y).
But, Ex(x=y) is a theorem.
therefore,
F(the present king of France) <-> contradiction.
ie. ~(F(the present king of France)), for all F.

~EF(F(the present king of France), is a theorem.
There is no property that the present king of France has. ie. it does
not exist.

~(Fx) <-> (~F)x, iff, x exists.

ie. ~(F(the present king of France)) <-> (~F)(the present king of
France), is false.

(the present king of France) has existence. or (the present king of
France) has non-existence. ..is a contradiction.
(the present king of France) has existence. or ~((the present king of
France) has existence). ..is a tautology.

David C. Ullrich- Hide quoted text -

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