This just in from Edward:
Proof that singular concepts (aka individual concepts) exist.
1. Common terms (‘cat’) and singular terms (‘this cat’, ‘Max’) exist.
2. These terms are meaningful, i.e. their meanings exist.
3. A concept is the meaning of a term.
4. Thus (from 1,2, 3) singular concepts, aka singular meanings, exist.
QED
This argument equivocates on 'meaning.' There are of course general and singular terms and they both have meanings if the meaning of a term is its extension, the (set of) things to which it applies. Accordingly, the meaning/extension of 'cat' is (the set of) cats, and the meaning/extension of 'Max' is Max, or his singleton. General terms also have meaning in the sense of intension. 'Cordate' and 'renate' are general terms that have the same extension but differ in intension. But the singular term 'Max,' while it has an extension, lacks an intension.
So for both (1) and (2) to be true, the meaning of a term must be its extension. But for (3) to be true, the meaning of a term must be its intension. So the argument trades on an equivocation and is for that reason invalid.
Here is a sound argument:
5. A concept is the intension of a term.
6. Singular terms lack intensions.
7. If a term lacks an intension, then there is no concept the term expresses.
Therefore
8. Singular terms do not express concepts. (From 5, 6, 7)
9. If a term does not express a concept, then there exists no concept the term expresses.
Therefore
10. There are no singular/individual concepts.
Just ask yourself: how could there be a concept of precisely Max and nothing actually or possibly different from Max? Suppose that there is a definite description that Max alone satisfies in the actual world. That description would express a concept that only one thing could bear or instantiate. But such a concept would not be singular but general since something else might have satisfied the description. For there to be an individual concept of Max, Max himself would somehow have to be a constituent of the concept. But that is impossible and for two reasons. First, concepts reside in the mind but no cat is a constituent of anything in my mind. Second, a concept is distinct from its bearer and can exist whether or not its bearer exists. But the concept MAX, if there were such a concept, would not be wholly distinct from its bearer and could not exist without its bearer.
The individual qua individual cannot be conceptualized. My conceptual grasp of an individual such as Max is always and necessarily by way of general concepts: cat, domestic cat, black cat, Tuxedo cat, black male Tuxedo cat five years old and weighing 20 lbs, cat presently in my visual field, this cat to which I am now pointing. Note that Max need not be this cat to which I am presently pointing, whence it follows that the haecceity of Max himself cannot be reached or grasped or conceptualized in the concept this cat to which I am presently pointing.
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