Good explanation, very clearly written. I’m going to take issue with it, but as we’re talking metaphysics it is going to be challenging to articulate my objection. I will start here:
I will take issue with the expression that universals are ‘mental abstractions’. That is close to two kinds of view of universals, conceptualism and psychologism. Conceptualism is the theory that universals—general concepts like “beauty” or “humanity”—are only real within the mind as mental constructs, rather than independently so. Psychologism is a more modern term but similar in meaning, in that it too wishes to depict universals (numbers, logical laws, etc) as products of the mind, not as recognised by the mind. And there’s a difference.
On the other hand, I definitely heed the warning about reification and agree that in no way are universals objects. In classical literature, they are spoken of as abstract objects or intelligible objects, but I don’t believe they are objects in any sense but the metaphorical. I would say they are nearer to acts. When we grasp a number or mathematical relationship, the word ‘grasp’ is more than figurative - the mind holds the idea correctly. It’s an activity in that sense.
It is often said that universals are predicates which inhere in a substance (in the proper use of substance) but I’m also wary of describing them in wholly linguistic terms. Of course it is true that much of analytic philosophy wishes to analyse everything whatsoever in linguistic terms, but I don’t believe this truly comes to terms with the kind of reality they possess.
This is why I say that I believe that abstract ‘objects’ can be described as real, but not necessarily as existent. To say that, for example, the number 7 exists, is to reify the concept as object, when it is the grasping of specific quantity. And while the number 7 is in no way dependent on your or my mind, it can nevertheless only be grasped by a mind. That is what is meant by an ‘intelligible object’, bearing in mind the caveat about the use of that term in this context.
This is conveyed in Eric Perl: Thinking Being, Introduction to Metaphysics in the Classical Tradition:
Forms…are radically distinct, and in that sense ‘apart,’ in that they are not themselves sensible things. With our eyes we can see large things, but not largeness itself; healthy things, but not health itself. The latter, in each case, is an idea, an intelligible content, something to be apprehended by thought rather than sense, a ‘look’ not for the eyes but for the mind. This is precisely the point Plato is making when he characterizes forms as the reality of all things. “Have you ever seen any of these with your eyes?—In no way … Or by any other sense, through the body, have you grasped them? I am speaking about all things such as largeness, health, strength, and, in one word, the reality (ouisia) of all other things, what each thing is” (Phd. 65d4–e1). Is there such a thing as health? Of course there is. Can you see it? Of course not. This does not mean that the forms are occult entities floating ‘somewhere else’ in ‘another world,’ a ‘Platonic heaven.’ It simply says that the intelligible identities which are the reality, the whatness, of things are not themselves physical things to be perceived by the senses, but must be grasped by reason (p 28).
This, of course, is the original form of metaphysics, before it was even taken up by Aristotle. But I still think it conveys the point about the kinds of reals that universals are. They’re not things, but they’re also not just thoughts. They are that to which thought itself must conform.
Well, whatever the I is, it is not an object. It is that to whom or which experience occurs. But you can never grasp the identity of the subject for the very simple reason that ‘the eye cannot see itself, the hand cannot grasp itself’ (a maxim that is conveyed in the Indian philosophical scriptures, The Upaniṣads.)
Speaking of which there was a famous Indian guru, died 1960, who’s entire teaching was based on the question ‘Who am I?’ It was the central self-inquiry method taught by Ramana Maharshi to realize the true Self (Ātman) by tracing the “I-thought” to its source.
Here, I’m not wanting to evangalise or advertise Ramana’s teaching, but only to point out the central role of the question ‘Who am I?’ in his Advaita (non-dual) philosophy. Advaita seeks to impart to the seeker his/her ‘true identity’ as Ātman rather than as the transient personality or ego with which s/he usually identifies [more info].