It is said that one of the distinguishing features of humans from other animals, is the capacity for abstract thought. But what is the definition of "abstract"? I know it when I see it, but I would like a definition of it. Also, have any philosophers talked about this?
The SEP article on the topic lists seven positive demarcations, and caps the list off with a variety of negative opinions. To quote sec. 3.8 in full:
We come finally to proposals that reject the abstract/concrete distinction. We can consider three cases. First, there are the nominalists who both reject abstract entities and reject the distinction as illegitimate. They focus on arguing against the formulations of the distinction proposed in the literature. A second group of eliminativists reject real objects of any kind, thereby dismissing the distinction as irrelevant; these are the ontological nihilists. A final group of eliminativists agree that there are prototypical cases of concrete objects and abstract objects, but conclude that a rigorous philosophical distinction can’t be made clearly enough to have any explanatory power (see Sider 2013, 287). This recalls Lewis’ pessimism (1986a, 81–86) about the possibility of establishing a distinction that is sufficiently clear to be theoretically interesting.
But this still leaves us with the more fine-grained set of questions regarding the preceding seven positive options. For example, if we started out by defining abstract objects as causally inert, then even if we jettisoned our use of the abstract/concrete distinction, we can still ask if there are causally inert objects. Or if something were beforehand said to be abstract when it is "outside of spacetime," we can always keep asking about whether anything is not spatiotemporal. If we have given objects and we have an intellectual function for them that we heretofore referred to as "abstraction," we can drop the word "abstraction" for the time being and just ask about the outputs of the function, such as they are. And so on and on.
Now Edward Zalta is both (A) perhaps the premier user of the distinction and (B) one of those heading up the entire Stanford Encyclopedia of Philosophy, so if one wishes to use the distinction, one could not go so wrong for deferring to him to some extent. For he has a relatively independent notion of properties-as-exemplified (AKA instantiated; c.f. the phrase "subsumption of particulars under generalities") vs. properties-as-encoded, which distinction can be defended independently, then. But so abstracting(!) over the notion of properties to the question of properties-vs.-tropes, with tropes supposed to be abstract particulars, we can make a little bit of terminological headway by rephrasing "abstract particular" as "particular that encodes a property," i.e. there is no absolute reason to suppose that no particular encodes any property. We have, to be sure, collapsed tropes to properties, then, or conflated the two terms, but since no one in the known world has a universally compelling answer to all such questions of conceptual analysis, we can make do for now by wondering if the exemplifying/encoding distinction on the one hand, combined with the particular/general distinction on the other, is useful as a response to Lewisian pessimism (as mentioned in the quote at the outset of this answer).