Scrambles

Exists is a meaningless predicate. [edit: at least when used as a predicate]

When you described Vulcan, you were describing a predicate...

Vulcan(x) <---> Planet(x) & Newton(x)

where Newton(x) means that x accounts for observations under Newtonian mechanics.

[Edited out a bit about numerical identity cos I didn't read the thread].



Scrambles

Dominus Paradoxum

Witt-

Suppose I have a formless ball of clay, and I make it into a statue. Now the ball of clay is not *numerically* identical to the statue, because it existed before the statue did. Thus, current analytic philosophers would say that the ball of clay is 'contingently identical' to the statue. I would say that the statue is one out of many possible 'arrangements' or 'form'(s) of the clay. And, no existence is not a first-order predicate. You should read the articles I provided, they discuss all the relevant issues.

Witt

Scrambles:
Exists is a meaningless predicate. [edit: at least when used as a predicate]

When you described Vulcan, you were describing a predicate...

Vulcan(x) <---> Planet(x) & Newton(x)

where Newton(x) means that x accounts for observations under Newtonian mechanics.
----------------------------

Why do you believe 'x exists' is meaningless?

The proper name 'Vulcan' was given to the described planet, which happens to not exist, within modern physics.

Witt

Witt

Originally posted by Witt
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.
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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?
-------------------------

You are missing the point that (the square root) is not a unique function within complex numbers.
(the positive square root) is a unique funtion.

(the square root of (-1))=(the square root of (-1)), is false in C.

Because there is more than one root.

(the positive square root of (-1))=(the positive square root of (-1)), is true in C.

Because there is one and only one such root.

There is an endless number of different numbers whose square is (-1)...see: commutitive hypercomplex numbers.

Witt

Scrambles

x exists is only meaningful when applied to a description. When you say "Vulcan exists". What you really mean is

(E x) (Vulcan(x)).

Where Vulcan(x) means that x has the properties required for something to be called Vulcan. It is just bad syntax to say "Vulcan exists". When you have a description of something, then you have a predicate. "x exists" is meaningless absent a description of x. On the other hand a predicate like "x is yellow" is not meaningless absent a description of x. The description is always there somewhere when we say "x exists". So that we are actually saying

(E x)(Description(x))


Scrambles

P.S. I guess Exists(Vulcan) is valid, but Exists is then a second order predicate.

AdamWho

yguy
The real contridiction is that Witt is assuming A=A for the words he is using but dening it in other contexts. I think the correct respose to A!=A is

aevim;eia;eamkepr9kr9pniw4; ptka5t]NP576]/5me6\u'

since if A!=A then we cannot even assume language.

Scrambles

On denoting - Bertrand Russell

In the case of 'Vulcan', and the statement
'Vulcan = Vulcan': 'Vulcan' would be taken as a denoting phrase being the same as 'the 10th planet in the solar system, necessary to account for observations under newtonian mechanics'. Denoting phrases do not have significance on their own account. The statement 'Vulcan = Vulcan' becomes,

'It is not always false of x that x is the 10th planet in the solar system necessary to account for observations under newtonian mechanics and that x is identical with x and that "if y is the 10th planet etc. then y is identical with x" is always true of y'

This statement would be false, but not because x = x is false. It would be false because there is no Vulcan, so the first part fails. When all statements are interpreted in the way Russell defines, identity is not applied to non-existent individuals. non-existent individuals have infact been eliminated.



Scrambles

Witt

Scrambles:
In the case of 'Vulcan', and the statement
'Vulcan = Vulcan': 'Vulcan' would be taken as a denoting phrase being the same as 'the 10th planet in the solar system, necessary to account for observations under newtonian mechanics'. Denoting phrases do not have significance on their own account. The statement 'Vulcan = Vulcan' becomes,

'It is not always false of x that x is the 10th planet in the solar system necessary to account for observations under newtonian mechanics and that x is identical with x and that "if y is the 10th planet etc. then y is identical with x" is always true of y'

For Russell:
(the x:Vx)=(the x:Vx) <-> Ex(Vx & Ay(Vx -> x=y) & x=x)
(the x:Vx)=(the x:Vx) <-> Ex(Ay(x=y <-> Vx) & x=x)

Scrambles: This statement would be false, but not because x = x is false. It would be false because there is no Vulcan,

Yes, for Russell: If Vx is contradictory then ~E!(the x:Vx).

Russell: G(the x:Fx) defined Ey(Ax(x=y <-> Fx) & Gy)

Frege: G(the x:Fx) defined Ey(Ax(x=y <-> Fx) & Gy) v (~Ey(Ax(x=y <-> Fx) & G{}).

~EyAx(x=y <-> Fx) -> (the x:Fx)={}.
See: Quine, Set Theory and its Logic, (1980), page 57.

For Frege, Vulcan =Vulcan is true.
And, Vulcan={} is true.

Witt

John Page

From Witt's OP But all words and other components of language are adjectives.

See paragrahph 3 in this link

I think this approach is consistent with the "denote" approach taken in this thread and others.

Cheers, John

Primal

This post is somewhat of a non squitur based on a sort of straw man.

When one says A=A one does not mean literally the "A" symbol written equals the other "A" symbol beside it. If that were the case Aristotle's system would have never even gotten off the ground.

That's like saying 2 plus 2 equals 4 is invalid because the symbols "2" and "2" do not look like 4.

The formula is not a purely empirical one, but a conceptual/logical one.

What the forumula illustrates is that an object is equal to itself in the rather crude symbols that we are limited to. Like I said, the statement is conceptual, not empirical, its just that symbols are limited to the empirical.

Thus like we all understand that 2 plus 2 equals 4 as a nonempirical truth, we can recognize A=A as a conceptual one, not meaning one symbol equals another but that an object equals itself.


As for your examples, that's the fallacy of equivocation i.e. same symbol with two different meanings.

Kind of like saying "Which way were we supposed to go...left?"

And answering "right". You can mean two different things.

Thus stating that "Vulcan" does not equal Vulcan has two problems as a counter-example.

First the thing is not equaling itself, but supposedly something else. Second, the meaning changes, and this is not allowed as that is equivocation.