Witt

Witt:
Things are descriptions of: physical objects, classes of physical objects, classes of classes..etc.

John:
Yes, but also "things" are physical objects etc.

All objects can be described: e.g. the description (the x: x=y) is equal to y.
Also, (an x: x=y) is equal to y.

(the x: x=y)=y is a theorem for all objects y.
(an x: x=y)=y is also a theorem for all objects y.

John:
Things can be used to describe other things, but if there are only descriptions one sinks into idealism. IMO our minds employ categories to concoct complex descriptions and outside the mind these categories are meaningless.

Agreed, Russell's Types are a good example of this.
Various logics utilize different presumptions.

When we see a forest of trees we can still see the individual leaves and the individual trees...each of which is percieved in the same way. Our mental organizing, our logic, categorizes things into types etc.

We can interpret predicates as the collection of those objects which have that predicate.
We can also interpret objects as the collection of predicates that apply to it.
All collections are mental things. They make thinking easier.

That is to say: the leaf, the class of leaves, the tree, the class of trees, the class of the classes of leaves, etc., are all essentially the same kind of object.
Interpretation makes the difference.

Witt:
Some predicates are non-typical in the sense that they apply to different levels of objects. For example Existence and Identity are universal predicates in that they apply to all levels of objects.

John:
I disagree. There are no universal predicates.

Why not?

John:
First, we can define non-existent objects (both physically non-existent and mental non-existent).

We can only describe them. That a described objects does not exist does not make any claim about non-existent objects.

John:
Second, identity is a necessary fiction of the mind, referencing the concept that points in spacetime are unique.

I disagree with your definition of identity.
There is no referencing 'the concept that points in spacetime are unique' when 2+2=4, is there?
Even if we agree that mind is dependent on time through brain, we still can't find the coordinates of space for any mind, can we?

What spacetime reference do you have for the number 2 ?

Your definition seems to apply to physical objects only.

John: Identity is true for all mental objects, though, otherwise the means of perceiving them as separate mental objects would not exist!

?

What spacetime reference do you have for mental objects?

Witt:
x=x or E!x, has sense for: physical objects, classes of physical objects, classes of classes of physical objects..etc. and when x is a proposition or a predicate or a description of any of the above.

John:
Hmmmmmm. But there is no such thing as a universal proposition

Again, why not?

John: ..therefore the truth of x=x only has sense as an assumption.

Not so, imo, we can define identity in terms that are prior to identity.
Its meaning is explained within language.

Witt:
Russell denied the existence of all unstratified predicates, including ~(x e x), to avoid his paradox.
But, if x is the class of teaspoons, then ~(x e x), is true.

John:
Depends what you mean by both x's. A description of a teaspoon is not its class. Similarly, the class "teaspoon" is not a description of "class teaspoon".

Witt:
For example, Carnap's simple language A (Intro to Symbolic Logic, 1962), where he identifies all predicates with their extension..ie. with their class.

John:
Carnap didn't go far enough, the language notation must unambiguously show that all identities are unique -

Uniqueness is a condition of our ontological commitments.

"Identity of object I express by identity of sign, and not by using a sign for identity. Difference of objects I express by difference of signs."
And,
"Roughly speaking, to say of 'two' things that they are identical is nonsense, and to say of 'one' thing that it is identical to itself is to say nothing at all" Wittgenstein, Tractatus, page105.

I would rather say that: a=a is tautolouous and a=b is contradictory, for all b's different from a.
Identity is surely needed to express equalities among different descriptions of objects.

John: identifying a predicate with only its class assumes class membership a priori.

Yes, by naive intuitition: y is a member of class determined by the predicate F, iff, y satisfies the predicate F...is valid.

i.e. (y e {x: Fx}) <-> Fy, for all predicates F and all y's.

See: Quine, Set Theory and Its Logic (1980), page16.
"2.1 y e {x:Fx} for Fy."

But, my D1. and 1b. z e {x:Fx} <-> (EyAx(x e y <-> Fx) & Fz), prove that Quine is wrong!

Witt

Big Spoon

As term's finished I'm giving my mathematical brain a bit of a holiday, but I'm certainly glad it's been resolved!

Witt

As term's finished I'm giving my mathematical brain a bit of a holiday, but I'm certainly glad it's been resolved!

In virtue of sarcasm, your certainty is suspect.
Why would anyone care about your term's end?

John Page

Yes, but my point (I think) is that "y" is not the object, it is yet another description.
Agreed.
Are you saying Object is equivalent to Predicate?
Please see previous post but essentially a predicate is a mental entity and mental entities are not universal, intersubjective at best.
Perhaps you missed my point - the term "non-existent object" does refer to something, what we are debating is its form.
Then to what does the term "identity" refer if it is not a fiction of the mind?
Please think of a reference as a set of coordinates to an instance of a thing. When I have the idea of "two pigs" the concept of twoness is associated with the concept of piginess to create the instance of the idea "two pigs".

My definitions apply to both physical and mental objects. Mental objects exist in the physical substrate of the mind/brain. The spatial coordinates for mind (sum of an individual's ideas?) coincide with the spatial coordinates for their nervous system (brain++).
Our ideas change over time, they are dynamic things.
The classification is a mental act and it is only due to the mental act that we have the notion E!x. x=x in the mind. It has sense for all mental objects.
Well, that's what we're trying to do. I argue you have to describe an identity as a mental concept that must exist a priori in order for us to discuss it. Maybe I don't understand what you mean by "prior".
Not necessarily. Example "They have the same idea" is a reasonable statement that violates uniqueness.
Trust Witty to say nothing at all!
...but as Witty points out, to say that two things are identical is nonsense. a=a is saying there are two things that for sake of argument we will say have the same properties. Apart from being a little bit different that is. Not that it really matters .

Seriously, it is exactly upon this point that we need a system of logic that properly recognizes and accomodates this issue of identity and abstraction that ultimately dives rise to the mental condition of Russell's Antinomy.
This is making my head hurt! I think what it comes down to is that <-> defines a union of x and y using the function F. But this means x and y are different and F results in (or is) the assumption of equality.

I really can't work out what the "& Fz" is doing other than asserting that a sub-class may exist. I admit I'm guessing but my intuition is that functions nesting x,y and z are dependent on "orderly" or strictly heirarchical categories. Dogs are animals and cats are animals but there is no function that a dog is a cat except on Nickelodeon (i.e. another conceptual level).

Cheers, john