Re: Is "existence" a predicate?

On Fri, 18 Apr 2008 04:14:10 -0700 (PDT), holden_owen@xxxxxxxx wrote:

On Apr 17, 7:40 am, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:
On Wed, 16 Apr 2008 10:17:26 -0700 (PDT), holden_o...@xxxxxxxx wrote:
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.

There is nothing other than an "existent object" that _can_ be
the value of a variable. The present King of France cannot
be the value of a variable, because there is no such thing as
the present king of France.

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.

No. First, the answers depend on what axioms of set theory I'm using,
which has nothing to do with whether everything exists or not.

{x:x=x} is the set of everything, does it exist or not.

The details below simply show that yes, whether there is a
universal set depends on what axioms of set theory I'm using,
exactly as I said. None of it says anything about whether
or not everything exists.

In particular, if we're talking about ZF, then formally
we _cannot_ say "{x:x=x} does not exist". The construction
{x:x=x} is simply not allowed. We can say that there does
not exist a set S which has as elements all the x such that
x = x (and when we put it that way it no longer appears
that we're ascribing non-existence to something).

If you are using ZFC then there is no set of everything.
If you are using Quine's New Foundations or his Mathematical Logic,
then V the universal set does exist.

If you are using ZFC or NF, the Russell class does not exist, but
within NBG, Von Neuman claims that the Russell class does exist but it
is a proper class and not a set.


And more to the point, if I'm using standard set theory, where
one might say "the universal set does not exist", that is once
again not an actual example of a non-existent thing, it just
looks that way because of the language.

It seems odd to me to say, everything exists and the set of everything
does not exist.

Of course it seems odd to say that. Are you deaf or what? The
_reason_ such odd things are said is because of quirks with
the way English works. English usage has very little to do with
logical consistency. Sentences of the form "[whatever] does not
exist" do not _really_ mean that [whatever] is a thing which
does not exist. In each case the real meaning of the sentence
is "there does not exist something which satisfies [the
apparent definition of whatever]". As in "the set of everything
does not exist" being explicated as "there does not exist a
set which contains everything".


I'm curious about something. You seem to be talking about
the "theory of descriptions". In the standard theory of description,
if there is such a thing, do people actually claim that they're
talking about things that do not exist?

Yes, I do include Russell's theory of desriptions, don't you?
No, people do not claim that non-referring described objects exist.

Or does that theory
just give a sensible explication of what's really going on with
natural-language idioms that _appear_ to be talking about
things that do not exist?

I've always had the impression that you've been basing your
ideas on Russel's theory of descriptions. And I've always been
unhappy that Russel would say such silly things. Happily,

Nobody is claiming that non-referring objects exist within classical
logic.
Non-referring descriptions are not values of any variable in FOPL.

I just tried to look it up - at

http://en.wikipedia.org/wiki/Theory_of_descriptions

I find the quote

"Thus, what Russell wants to avoid is admitting mysterious
non-existent entities into his ontology. "

This comes as a great relief to me, in re how I think of Russel.

Nowhere on that page do I see anything that seems to hint
at allowing things that do not exist to be values of variables;
the description of the theory and of criticisms of it all look
like ways to explicate the meaning _without_ such things.
in a discussion of "the present king of France is bald".

It is interesting to note that Russell claimed that the predicate of
existence only
applies to descriptions and not to immediately given objects.

Is it? I guess it's "interesting" that he often avoided nonsense, yes.

That is, E!a has no meaning, but E!(the x:x=a) does have meaning.
This claim is difficult because of *14.2 page 189 of Principia, (the
x:x=a)=a.
Surely (the x:x=a) =a -> E!(x:x=a) <-> E!a.

Is "surely" a valid deduction rule in the formal system of PM?

David Ullrich exists, makes sense to me.

I think Russell is wrong about the existence of given objects, do you?

giggle.

See:
http://quod.lib.umich.edu/cgi/t/text/pageviewer-idx?c=umhistmath&cc=umhistmath&idno=aat3201.0001.001&frm=frameset&view=pdf&seq=201








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.

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David C. Ullrich
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