Well, I don't believe ideas are abstractions, although an idea may be an idea of an abstraction. My idea of democracy is an idea of an abstraction. But my idea of an elephant is an idea of a concrete object, not an abstraction. I think we need to distinguish between what an idea is, and of what it is an idea. A particular idea, like my idea of democracy is of an abstraction, but it is not itself an abstraction. If I tell someone that I have a good idea, let's go to the movies, I am not referring to an abstraction, nor is the idea an idea of an abstraction.
As I have been saying, the word, "exist" is univocal, although, of course, different kinds of things exist.

So you agree that abstractions do not actually exist?

No, I did not say that. I think that numbers (like the number three) are abstractions, but I think that the number three exists. It has a number of properties. It is odd, it is prime, and so on.

No, I did not say that. I think that numbers (like the number three) are abstractions, but I think that the number three exists. It has a number of properties. It is odd, it is prime, and so on.

But it doesn't have physical properties and that's my problem. I understand that the number three has abstract properties, but it has no physical ones. Now the question comes to this: if a thing doesn't have physical properties, can it still be considered to be a part of reality? If you're a realist like me, and you believe that reality is independent of human perception, then how can abstractions be a part of reality outside of their representation of reality?

Plato was a realist who believed that there were abstract objects. He thought that abstract objects were part of reality. I don't think you are a realist, but a materialist, and that is different. Plato was a realist, but not a materialist. I believe that numbers are part of reality (that they exist). They are abstract objects. Don't you think that the number three exists?

Kennethamy: Unicorns do not exist.
Opponent: Yes they do.
K: No, they have no properties.
O: Yes they do - they have one horn, they are depicted, they appear in stories....
K: Those are not real properties.
O: Why not? I know there are no physical unicorns, but nor are there any physical ideas, and you accept that ideas have real properties.
K: Ideas are different from unicorns, because ideas exist and unicorns do not.
O: Yes they do....

Some say that Platonic realism should really be called Platonic idealism. I'm a realist in the sense that I hold that reality is independent of an observer. I'm just not a realist as it pertains to abstract concepts in themselves.

Unicorns don't exist because there is not something with the properties of unicorns (an animal with the body of a horse with a single horn in the middle of its forehead, magical powers, or anything else one would associate with unicorns.)

A depiction of you is not you, nor is a depiction of a unicorn a unicorn. I would argue that a depiction is not even a property, but a depiction can certainly illustrate a property as well as illustrate something with the properties associated with something that doesn't exist . . . such as a unicorn.

In that sense, one could accurately say that a picture of a unicorn exists, but not the unicorn pictured. If I were to draw (make a depiction) of a unicorn, I would have to have the idea of a unicorn in mind. Therefore, I would say my idea of a unicorn exists, or I would be drawing a blank, so to speak.

This is how it would seem to me, at any rate. But I'm okay with the idea that I may be wrong.

Plato held that Ideas (Forms) are mind-independent. And the Forms are abstract entities. Therefore he was a realist about abstract entities. You seem not to be a realist about abstract ideas because you think that whatever exists is material, and abstract ideas are not material. You are a materialist.

No one is infallible, so anyone might be wrong. But whether someone may be wrong would depend on the evidence pro and con.

E!x =df EF(Fx).

(x exists), means, there is a property that x has.

Fx -> EG(Gx). x has property F implies x exists.

This definition applies to empirical objects and to abstract objects.

(1>0) -> (1 exists).

My car is blue, implies, my car exists.


~E!x <-> ~EF(Fx).

Things described by contradictory predications do not exist.

(the x:(Fx & ~Fx)) exists, is contradictory.
(an x:(Fx & ~Fx)) exists, is also contradictory.

Within first order predicate logic with identity...

(x exists) =df Ey(x=y).

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

(the x:Fx) exists <-> Ey((the x:Fx)=y).
(an x:Fx) exists <-> Ey((an x:Fx)=y).

Ken:
"And, of course, x does not exist means, nothing has such a property. (Not, x has no properties). "

I don't agree.

~(x exists) <-> ~EF(Fx).
If there is no primary property that x has, then, ~(x exists).

What does this mean? 'Nothing has such a property.

Ax(x=x <-> Ey(x=y)).

Depends on what it is being denied exists. Unicorns do not exist = Nothing has the properties of being equine, and having a horn on top its forehead. Quine suggests that in a pinch we can just say, "nothing unicornizes".

Do you mean that something can have secondary properties and not exist? How? Color is supposed to be a secondary quality. Can something be red and not exist?

It is not the case that the present king of France is bald, is true.
and The present king of France does not exist.

Primary predication implies existence while secondary predication does not.

I agree with the first, but it is not inconsistent with what I said.

Why does secondary predication not imply existence? Perhaps, though, you had better tell me what you mean by "primary and secondary predication"?

The distinction is from,

On Denoting, Russell..

A secondary occurrence of a denoting phrase may be defined as one in which the phrase occurs in a proposition p which is a mere constituent of the proposition we are considering, and the substitution for the denoting phrase is to be effected in p, and not in the whole proposition concerned. The ambiguity as between primary and secondary occurrences is hard to avoid in language; but it does no harm if we are on our guard against it. In symbolic logic it is of course easily avoided.

The distinction of primary and secondary occurrences also enables us to deal with the question whether the present King of France is bald or not bald, and general with the logical status of denoting phrases that denote nothing. If `C' is a denoting phrase, say `the term having the property F', then[INDENT]`C has property phi' means `one and only one term has the property F, and that one has the property phi'. [/INDENT]If now the property F belongs to no terms, or to several, it follows that `C has property phi' is false for all values of phi. Thus `the present King of France is not bald' is false if it means [INDENT]`There is an entity which is now King of France and is not bald', [/INDENT]but is true if it means [INDENT]`It is false that there is an entity which is now King of France and is bald'. [/INDENT]That is, `the King of France is not bald' is false if the occurrence of `the King of France' is primary, and true if it is secondary. Thus all propositions in which `the King of France' has a primary occurrence are false: the denials of such propositions are true, but in them `the King of France' has a secondary occurrence. Thus we escape the conclusion that the King of France has a wig.

Just adding some some fuel to the discussion.....


Main Entry:
Pronunciation: \ig-ˈzist\
Function: intransitive verb
Etymology: Latin exsistere to come into being, exist, from ex- + sistere to stand, stop; akin to Latin stare to stand - more at stand
Date: circa 1568
1 a : to have real being whether material or spiritual <did unicorns exist> <the largest galaxy known to exist> b : to have being in a specified place or with respect to understood limitations or conditions <strange ideas existed in his mind>
2 : to continue to be <racism still exists in society>
3 a : to have life or the functions of vitality <we cannot exist without oxygen> b : to live at an inferior level or under adverse circumstances <the hungry existing from day to day>