It seems that you are confusing abstractness with being a universal. Some may defend that universals are abstract (but not all do: some people defend that universals are wholly present in their instances, and are therefore concrete), but I don't think anyone defends that every abstract object is a universal. Numbers, sets, and mathematical objects in general are abstract, but they are not universals. Consider the number 2. It is abstract, but it has no instances, so it is not a universal.

The problem of characterizing abstract objects is very difficult. If you want some pointers, I strongly recommend reading Sam Cowling's Abstract Entities. Most people define abstract entities as entities which are not located in space-time. However, this raises the problem of how to characterize types. Consider, for instance, the letter "a". It is a type which can be tokened in many ways (by ink, by pixels, etc.). It clearly has no spatial location (in contrast to its tokens), but what about a temporal location? It seems intuitive to say that it was created at some point in time, and that perhaps it could cease to exist (if every token of it, including the tokens that are encoded in our memories, considered as physical states of the brain, were to be destroyed). On the other hand, types seems to be abstract, since we do not seem capable of interacting with them in the same way we interact with concrete objects.

One way to amend this would be to require only that abstract objects not be located in space, but allow them to be located in time. But now, suppose substance dualism is true and the mind is not physical. It would follow that the mind is not in space (though it is in time), and therefore that it is abstract. But this seems counter-intuitive. Of course, most people think that substance dualism is not true, but the point is conceptual. So we would like to avoid this, if possible. It is not entirely clear how to fix the definition, though (for some---to my mind, ad hoc---suggestions, cf. Bob Hale's Abstract Objects).

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We can have an abstract idea of a circle. If we look at 10 circles we might find what is simmilar in all of them. This must be the universal. Abstraction gives us the universal.
You seem to say that I am wrong. Why?

Aquinas wrote this "This is what we mean by abstracting the universal from the particular,..."
https://www.newadvent.org/summa/1085.htm#article1

What am I missunderstanding?

What is some good definitions of abstraction? Some people seem to use the term to refer to something that is ambiguous or not defined. An example of what people sometimes say is: love is such an abstract concept. — musicpianoaccordion

Consider the differences between the phenomena of love and mathematical truth's.

A mathematical truth that describes how gravity works, or how a structural beam is sized correctly, is indeed an abstract entity that describes something. That something may or may not be relative to an object (metaphysical).

Love, on the other hand, would be considered a metaphysical abstract not necessarily because it's ambiguous or not well defined, but because it's a phenomenon that can't really be properly articulated in a concrete way. It's existence is mysterious, sometimes ineffable, subjective/objective, and at times illogical.

It seems one feature of abstract existence that appears to be the same relates to the subject-object/metaphyscial relationship.

Again, from the fact that some (perhaps all) universals, like "circleness" (the universal), are abstract, it does not follow that every abstract entity is a universal. Consider a particular circle, say the one described by the equation $x^2 + y^2 - 1=0$ in the Cartesian plane. This is obviously an abstract entity. But it is not a universal (what would be its instances?). Similarly for particular numbers, say the number 2.

Consider the number 2. It is abstract, but it has no instances, so it is not a universal. — Nagase

Is not any pair of objects an instance of the number 2?


In any case, etymologically “abstract” means “pulled apart”, so I think the OP example of breaking down and analyzing a car, or of removing unnecessary details, etc, is on the right track. “Catness” is whatever features all individual cats have, pulled apart from the features that differ between individuals. “2” is whatever is in common between all pairs of objects, pulled apart from the unnecessary details that differ between them. Etc.

One way of looking at the term abstraction is this: you take away all the unnecessary details. Then you will find the universal. — musicpianoaccordion

That seems to be the original meaning of the term "to abstract"; probably an analogy with the act of removing the flesh from the bones of an animal. Over time, the physical skeleton came to metaphorically represent some metaphysical essence (Soul??), or logical structure of the thing or concept being abstracted.

If you truly remove all irrelevant details, you will find that which is common to many real objects. For example, anatomists have discovered that there are commonalities of bone structure in almost all vertebrate animals. The hand of a human contains bones that map onto the flippers of a dolphin. From this evidence, they reason that there is something universal underlying all vertebrate structures.

From that basic contemporary knowledge, we can infer that the "essence" of those skeletons was encoded as abstract information (rules for organization) and stored in genetic material that reproduces itself over millions of years. But, if you abstract even further back, you could say that the potential or mathematical "logic" of bone structure was encoded in the hypothetical original Singularity, and stored in the space-time energy that emerged in the Big Bang.

But if you are really into the notion of reductive reasoning, and continue the cutting-away process of abstraction --- in search of what's universal to our physical universe --- you will face the question of what is more essential, more abstract, than the Singularity. In other words, what came "before" the Bang? Some people call that pre-BB abstraction "multiverse", while others call it "God". But what are the essential qualities or properties of that de-fleshed logical structure?

Unfortunately, the essence of the M'verse can be abstracted further back, exhaustively, into the black hole of Infinity. Which is why some prefer to stop that endless regression of abstraction at a hypothetical "black box", that can be assumed to be the ultimate logical order and structure (necessity) of everything in the world. :nerd:

I don't personally think there is any property that is common to every two pair of objects (except in a gerrymandered way), but let us leave this to the side. What about the circle defined by $x^2 + y^2 -1 =0$ on the Cartesian plane? What are its instances?

All actual circles, obviously. None of which are perfectly identical to that ideal circle, but the thing they have in common with each other that makes them al circles is their similarity to that ideal circle.

I don't understand. Consider two actual (in contrast to potential?) circles on the Cartesian plane, say, one described by $x^2+y^2 - 1=0$ and the other described by $x^2 + y^2 -2=0$. Are they instances of each other?