How To Place Epicurus In Relation To "Nominalism"?

As a reminder, here is the issue as Wikipedia states it:

In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels.^[1][2] There are at least two main versions of nominalism. One version denies the existence of universals – things that can be instantiated or exemplified by many particular things (e.g., strength, humanity). The other version specifically denies the existence of abstract objects – objects that do not exist in space and time.^[3]

William of Ockham

Most nominalists have held that only physical particulars in space and time are real, and that universals exist only post res, that is, subsequent to particular things.^[4] However, some versions of nominalism hold that some particulars are abstract entities (e.g., numbers), while others are concrete entities – entities that do exist in space and time (e.g., pillars, snakes, and bananas).

Nominalism is primarily a position on the problem of universals. It is opposed to realist philosophies, such as Platonic realism, which assert that universals do exist over and above particulars, and to the hylomorphic substance theory of Aristotle, which asserts that universals are immanently real within them. However, the name "nominalism" emerged from debates in medieval philosophy with Roscellinus.

Further:

The problem of universals

Nominalism arose in reaction to the problem of universals, specifically accounting for the fact that some things are of the same type. For example, Fluffy and Kitzler are both cats, or, the fact that certain properties are repeatable, such as: the grass, the shirt, and Kermit the Frog are green. One wants to know by virtue of what are Fluffy and Kitzler both cats, and what makes the grass, the shirt, and Kermit green.

The Platonist answer is that all the green things are green in virtue of the existence of a universal: a single abstract thing that, in this case, is a part of all the green things. With respect to the color of the grass, the shirt and Kermit, one of their parts is identical. In this respect, the three parts are literally one. Greenness is repeatable because there is one thing that manifests itself wherever there are green things.

Nominalism denies the existence of universals. The motivation for this flows from several concerns, the first one being where they might exist. Plato famously held, on one interpretation, that there is a realm of abstract forms or universals apart from the physical world (see theory of the forms). Particular physical objects merely exemplify or instantiate the universal. But this raises the question: Where is this universal realm? One possibility is that it is outside space and time. A view sympathetic with this possibility holds that, precisely because some form is immanent in several physical objects, it must also transcend each of those physical objects; in this way, the forms are "transcendent" only insofar as they are "immanent" in many physical objects. In other words, immanence implies transcendence; they are not opposed to one another. (Nor, in this view, would there be a separate "world" or "realm" of forms that is distinct from the physical world, thus shirking much of the worry about where to locate a "universal realm".) However, naturalists assert that nothing is outside of space and time. Some Neoplatonists, such as the pagan philosopher Plotinus and the Christian philosopher Augustine, imply (anticipating conceptualism) that universals are contained within the mind of God. To complicate things, what is the nature of the instantiation or exemplification relation?

Yes to me the consideration of mathematical symbolism helps make the issues involved in debating nominalism and reductionism clear.

Two things plus two things equals four things, because we define it that way. But what is a "thing"? In the end the usefulness of such symbolic equations becomes a matter of identifying what "thing" means. You can reduce everything over and over into a series of definitions as you try to assign meaning to your symbols, but in the end you have to remember that definition games can be circular and be a fool's errand, and the only way to prevent that is to tie things ultimately to observations of the facts observed by senses, anticipations, and feelings.

Surely there are practical "rules" or "conventions" about how to define things, based on experience, that will generally work to make the process more accurate. But in the end the definition game had better tie back to observations from the senses (or anticipations or feelings) or else the entire game collapses into circular abstractions.

It appears to me that Epicurus was waving major red flags about definition games, and he would have done the same with implying that all knowledge is a matter of definitions in the mind that are infinitely malleable. I would see the same issue with "rules of construction" such as we apply in the law, or as we deal with in deciding what is good logic vs what is a logical fallacy. Ultimately justice is not a matter of robotically following rules, nor is identifying truth a matter of definitions.

You have to eventually come to conclusions in order to survive, and it's fair to work as hard as you can to describe the best process of reasoning so that you can reproduce that process over and over.

But the cardinal and overriding rule seems likely to be that in the end rules cannot be considered to override the facts of the sensations ,anticipations, and feelings in ultimately analyzing any situation.

And the temptation to try to develop "rules" to be considered universal and infallible seems to be at least as great a hazard as the temptation to deny the usefulness of any and all rules. Epicurus certainly had his own rules of thought, such as PD23 and PD24, but they were always couched in terms of the ultimate rule being that the sensations, anticipations, and feelings are the ultimate abiter. In any situation of conflict between pure rules vs pure evidence (from the sensations, anticipations, and feelings, not including "rules of symbolic logic,") the ultimate arbiter of what we should acknowledge to be true is not the result of rules, but the result of facts established by the sensations, anticipations, and feelings.

Wow! I have never seen them before - but it does touch on the issue!