I think I have good handle on the distinction between a concept and what a concept is a concept of. For example, my concept of Earth is one thing, and what my concept is a concept of, namely, Earth--aka the referent of the term, "Earth" is another thing. One is a mental entity, and the other is not. One's existence depends on my existence whereas the other does not.

Just as we can distinguish between 1) a concept and 2) what a concept is a concept of for concrete objects, so too ought we be able to do so for abstract objects. I'm not absolutely positive on the following note, but I think maybe the term, "abstract" is ambiguous. For example, consider the difference between my concept of class versus class. Keep in mind that the former is a concept thus a mental entity (abstract, in one sense), but the latter (what the concept is a concept of), or class, is also abstract (but in a different sense). I believe my concept of my cat was not around before me, nor do I believe that my concept of my cat will be around after i'm gone, heaven forbid, so I don't think my concepts are abstract, as we generally think of abstract entities, but my concepts are nevertheless abstract in that they are mental entities.

The way I see it is that I have a concept of the number three, and that is mind dependent (or abstract in one sense), but "three" refers not to my concept of the number three (as "my concept of the number three" refers to that) but instead refers to the number three (which is not abstract in that same sense but abstract in the other sense), as the number three is a class, and a class is a not abstract in the mind dependent sense.

Certainly the names of the substances we encounter in the world around us are referring terms. If someone wants to know where they can buy a particular substance like a cat, we can direct them to a pet store which we know has some very nice cats.
But simply because we use the names of substances to refer to an entity doesn't entail that the name of a number should be treated in the same way. Perhaps the rule for words naming abstracta are different? I think they are. That is why I suggest that if a philosopher wants a better understanding of words like "three" or "number" that they look to its use rather than begin by enquiring what sort of entity these words are referring to.

and classes are independent of the mind

I still can't wrap my head around why that is always the case. The class of animals, mammals, is independent of the mind. But what about, for instance, the class called 'classics' (good, old movies)?

The class of all pencils, the class pencil, had no particulars that belonged to the class during a time when there were no people. The class of all classics, the classics class, had no particulars that belonged to the class during a time when there were no people.

I still can't wrap my head around why that is always the case. The class of animals, mammals, is independent of the mind. But what about, for instance, the class called 'classics' (good, old movies)?

Classes may be independent of the mind, but some classifications are, of course, not natural kinds, but conventional kinds, as you point out.

And what makes you think the classes of numbers are of the natural kind? A subscription to the Quine argument?

But you're saying the class of threes did have particulars that belonged to the class during a time when there were no people?

Which are triples, which is yet another class (or group).

Number ... three ... triple ... tree1, tree2, tree3.
Class ... class ... class ... not a class, not a class, not a class.

(I think)

Why?

Because they are non-spatiotemporal. They exist, in that they have properties, but they are without location and non-temporal--not to be confused with eternal.

Our concept of the number three (and remember, our concepts are not classes) is also without location [although it's said (but only said) to be located in the mind]; however, our concepts are not non-temporal. Some form (as we learn in childhood development) at a very young age, and other concepts are formed later on.

The class of all classics, the classics class, had no particulars that belonged to the class during a time when there were no people.

And how is this different than the class of classics, which you already said:



There were no particulars which belonged to the class of numbers during a time when there were no people, either. Isn't that right? If you think there was, where is the proof of this?

You forget that a particular number is itself a class.

No classes of numbers exist without humans.

The existence of classes are human independent.

Two things.

One, we use words. We can use words to refer. But, do not confuse the fact that we use words with the other fact that words refer. I can use the word "cat" and refer to a cat, but I can also (and oddly) use the word, "cat" and refer to a dog, but no matter how I use (or misuse) the term, the term "cat" continues to refer to the class of all cats despite how well I succeed or fail in using the term. The point I'm making is to not lose sight of the fact there is a difference between our using a term to refer to something and what that word itself refers to.

Two, all words have meaning, but not all words have referents. We need to remain vigilant not to confuse the meaning of word with the referent of a word. If you're interested in understanding what a word means, then you should be interested in how words are collectively used by fluent speakers of a language, but if you're interested in knowing whether or not a term is 1) a referring term that fails to refer, 2) a referring term that succeeds in referring, or 3) a non-referring term, then you should be more interested in whether something can (and if so, does) exist (whether concrete or abstract) that instantiates the term.

I think the term "my concept of my cat" is a referring term, and I think the term, "my cat" is a referring term, and I think the term, "cat" is a referring term. The referent to the term, "my cat" is obviously concrete, but careful we should be when comparing the other two. The term, "cat" refers to the class of all cats, and classes are independent of the mind, but the referent of the term, "my concept of my cat" is mind-dependent, yet there are some that would hold that the referent to both terms are abstract, but I'm thinking to do think so is to equivocate the term, "abstract." Neither have spatial predicates, and only one has a temporal predicate.

I'm not saying that the pencil class existed during the time of dinosaurs, and the only reason I'm not saying it is because they are not within time. To say they are eternal is false. To say they are non-temporal is true.

Systems of classification are not mind-independent.

He is saying that classes are what somehow exist in a non-temporal and non-spatial way. But I agree with you: Aren't classes simply classificiations of what exist?