Witt

It's my opinion that:

x=x is an axiom, a belief, of modern logic.

We presume that any proper name can be a value of x.
For example; John Smith = John Smith, 2=2, Mars=Mars, etc.

But, Vulcan=Vulcan is false, where Vulcan is the planet (hypothesized by astronomers) in our solar system that is needed to explain via Newtonian physics, the unusual orbit of Mercury.

Proper names, such as Vulcan, that do not refer are a part of our language.

The axiom x=x does not include non-referring proper names as values of x.

We implicitly presume, in logic, that all proper names refer to existent objects.
Proper names from fiction or science or math, that do not refer, are not values of our variables at all.

Quine: "to be is to be a value of a variable"
"no entity without identity"

Objects described by contradictory predicates do not exist either, and are not values of x in x=x.

Descriptions are values of our variables only if they do exist, only if they do refer.

Examples:
(the present king of France)=(the present king of France) is false.
(that which is not equal to itself)=(that which is not equal to itself) is false.
(the whole number between 2 and 3)=(the whole number between 2 and 3) is false.

Where 'E!' is the existence predicate:
E!x <-> x=x. That is, x exists if and only if it is self identical.
(for all x, named or described)

Things that do not exist are not self identical, they have no primary truths at all.
We talk about them via secondary truths, we can say what they are not.
Things that do not exist, are not meaningless, i.e. it makes sense to say,
the existent present king of France does not exist.

Another reason why the axiom x=x should be rejected is that, necessarily(x=x), follows.
That is, there are no contingent identities and there are no contingent existences.

E!x <-> Ey(x=y)...x exists, if and only if, there is some existent object that x is.

The axiom (x=x) is OK for logical/mathematical objects but it fails for empirical objects.
That is, it works in mathematical logic but it fails in philosophical logic, imo.

It is necessarily true that (George Bush)=(George Bush), is false.
It is necessarily true that (George Bush)exists, is false.

George Bush exists, is true.
Necessarily George Bush exists, is false.

I have a problem with the conclusion that, necessarily everything exists, do you?

Is a revision of 'Identity theory' in order, I think so.

Witt

Darth Dane

Very interesting read


I have a problem with the conclusion that, necessarily everything exists, do you?

No.



DD - Life Spliff

yguy

OK, how about this:

It is possible to assign a unique name to every extant object in the universe.

Let x = an object whose unique name is x.

Then, x=x.

In that case, (-1)^(1/2), or i, is not equal to i. Correct?

Keith Russell

You're trying to say that the name of a thing is equal to the thing itself, and that--when the name refers only to a concept, but not also to an actual existent--the Law of Identity is thus invalidated.

Not so. Not at all.

The name is equal to the name, the concept is equal to the concept, and the thing is equal to the thing.

K

AdamWho

Isn't a little funny that you deny A=A by using language? If A!=A then maybe your post is a shakespear sonnet, a three toed sloth or the IPU!

Witt

Witt:
I have a problem with the conclusion that, necessarily everything exists, do you?

Darth: No.

If necessity includes, at all times, then..

When x names a physical object:
Necessarily(x exists), is false...since there was a time at which x did not refer.

Vulcan exists, is false.
Necessarily(Vulcan exists), is contradictory.

Darth exists, is true. (At this time)
Necessarily(Darth exists), is a contradiction.

Abstract objects are dependent on the existence of minds.

When x is an abstract object:
Necessarily(x exists) is false...since there were times at which minds do not exist.

Necessarily(3 exists), has no sense if there are no minds to understand it.

What is your understanding of 'necessity'?

Witt

Dominus Paradoxum

By God, you've discovered the difference between sense and reference.

Nope. It only follows that numerical identity can't be contingent (Kripke's thesis). But there can be other kinds of identity.

Nonsense. No necessitarian would think that. They would argue that if x came into existence at time t1 then previously to t1 x necessarily did not exist, and that after t1, it did. The necessity, of course, would be conditional, not absolute. And anyway, it's a moot point, since 'existence' is not a first-order predicate there can be no such thing as necessary existence.

That's a nice unsupported assertion for you.


You should check out these links:

http://plato.stanford.edu/entries/existence/

http://plato.stanford.edu/entries/identity-relative/

Witt

Witt:
Descriptions are values of our variables only if they do exist, only if they do refer.

Examples:
(the present king of France)=(the present king of France) is false.
(that which is not equal to itself)=(that which is not equal to itself) is false.
(the whole number between 2 and 3)=(the whole number between 2 and 3) is false.
--------------------------------------------------------------------------------

In that case, (-1)^(1/2), or i, is not equal to i. Correct?

Yes, if we read (-1)^(1/2), as the square root of (-1).
Within complex numbers, the square root of x does not exist, because there are 2 different solutions.

The positive square root of (-1) does exist and is equal to +i, and +i=+i is true.

Witt

Witt

Another reason why the axiom x=x should be rejected is that, necessarily(x=x), follows.
That is, there are no contingent identities and there are no contingent existences.
--------------------------------------------------------------------------------


Dominus Paradoxum:
Nope. It only follows that numerical identity can't be contingent. But there can be other kinds of identity.

What is numerical identity?
What other kinds of identity are there?

I see only one '='.

x=y, defined, (all F)(Fx <-> Fy).

quote:
--------------------------------------------------------------------------------
When x names a physical object:
Necessarily(x exists), is false...since there was a time at which x did not refer.
--------------------------------------------------------------------------------


Dominus:
Nonsense. No necessitarian would think that. They would argue that if x came into existence at time t1 then previously to t1 x necessarily did not exist, and that after t1, it did. The necessity, of course, would be conditional, not absolute. And anyway, it's a moot point, since 'existence' is not a first-order predicate there can be no such thing as necessary existence.

I agree that necessity is not absolute.

Exists(x) defined Ey(x=y), is a first-order predicate.
As is, Exists(x) defined x=x.


Thanks for the links.

Witt

yguy

You appear to be directly contradicting yourself. At first you agree with me that, according to your premise, i does not equal i, but then you say the "positive" square root of -1 exists, wherefore i=i.

What am I missing?