If something is a product of the mind, then it's temporal, and if it's temporal, then it's not an abstract object, and if it's not an abstract object, it's a concrete object.

Abstract objects are not in space or time. Abstract concepts (which are concepts of abstract objects) are, like all other concepts, in time (and maybe, soace-depending on your ontology of concepts).

Well, things which do not exist do not have properties. But imaginary characters can have properties. So, at the least, it seems we are stating the concept of X imaginary character exists. Isn't that so?

To say that X is fictional is not like saying that X is circular. X is fictional does not mean that something is X and X is fictional. But X is circular does mean, Something is X and X is circular.

So you think that Santa is fat, but that is because you do not distinguish between Santa and the fictional character Santa. Let us assume for a moment that you just happen to be mistaken in your belief that Santa does not exist. All of a sudden, you no longer want to call Santa a fictional character and thus are then willing to concede that the term, "Santa" successfully refers, but what then (I ask) are we to say of the fictional character Santa that we hear about all the time?

Imaginary characters do not have properties.

But how do you know when you've found an abstract object, as opposed to a product of the mind? What method do you use to distinguish? Which properties must a seek?

They don't? Then how do I know that Rudolph has a red nose?

Rudloph doesn't have a red nose, for Rudolph does not exist, so how could it? What is depicted as having a red nose is the fictional character Rudolph.

Awe. For example, the number three. How do we know it's an abstract object and not a product of the mind. Well, I know because I know that the number three is a class and that classes are abstract objects.

Well, things which do not exist do not have properties. But imaginary characters can have properties. So, at the least, it seems we are stating the concept of X imaginary character exists. Isn't that so?

If they have properties at all, they have imaginary properties, not real properties. The question is whether imaginary characters have real properties. How could nothing be red except, of course, if it is not the case that anything is red?

I edited my comment. What I am saying is that my concept of Rudolph, the fictional character, has a red nose.

This is because my concept exists. And that is the point. When someone says they are assigning properties to an imaginary character,

I find no reason to believe there is a class, as opposed to just a concept, of the number three.

But can't concepts have properties? Aren't we in agreement concepts exist?

I have spoken about imaginary properties before, but I think their existence is debatable. That is why I refrained from speaking about them here. I don't know.

Interestingly enough, "Santa" is a referring term, but it is a referring term that fails to refer. The term, "fictional character Santa" is a referring term as well, but unlike the term, "Santa", it successfully refers, but it doesn't refer to Santa, as it refers instead to the fictional character Santa. Notice how it will continue to do so even if you are mistaken about Santa's existence.

Interestingly enough, "Santa" is a referring term, but it is a referring term that fails to refer. The term, "fictional character Santa" is a referring term as well, but unlike the term, "Santa", it successfully refers, but it doesn't refer to Santa, as it refers instead to the fictional character Santa. Notice how it will continue to do so even if you are mistaken about Santa's existence.

Of course concepts have properties. But, what has that to do with it? We are talking about Mickey Mouse, not the concept of Mickey Mouse. Yes, the only properties imaginary objects could have are imaginary properties, which is why imaginary objects are so problematic.

Of course concepts have properties. But, what has that to do with it? We are talking about Mickey Mouse, not the concept of Mickey Mouse. Yes, the only properties imaginary objects could have are imaginary properties, which is why imaginary objects are so problematic.

What about numbers? Do you think there is a class of all numbers and that the number three belongs to that class?

the only properties imaginary objects could have are imaginary properties, which is why imaginary objects are so problematic.

That is under your theory of reference. I"m more interested in how words are used.
And as I said earlier, your theory of reference doesn't match standard usage. Perhaps language should work according to your theory but it doesn't.

When you write "class", I find myself thinking we're not talking about the same thing. I do not seem to have the same understanding of "class" as you do. You seem to think of classes as these independent entities, and I do not know anything about that.

Some people (on this forum) say, that unicorns exist, but "only as concepts". I often correct them, and point out that what they actually mean is that unicorns do not exist, only the unicorn-concept exists. And sometimes they deny that "translation". Should they say that maybe language should work according to my theory, but it doesn't? And insist that what they are saying is that unicorns exist only as concepts (with the implication that unicorn exist)?

Wittgenstein wrote that his aim was to teach people how to pass from disguised nonsense to patent nonsense.