I was recently reading the Wikipedia entry on "nominalism" and found it fairly direct and understandable. Here is the opening:
In metaphysics, nominalism is a philosophical view which denies the existence of universals and abstract objects, but affirms the existence of general or abstract terms and predicates. 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.
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. 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, bananas).
Nominalism is primarily a position on the problem of universals, which dates back at least to Plato, and is opposed to realist philosophies, such as Platonic realism, which assert that universals do exist over and above particulars. However, the name "nominalism" emerged from debates in medieval philosophy with Roscellinus. The term 'nominalism' stems from the Latin nomen, "name". John Stuart Mill summarised nominalism in the apothegm "there is nothing general except names".
This is a subject we've touched on in several earlier Lucretius Today podcasts, but not explored too deeply there or in the forum that I can recall. The article does not mention Epicurus or take a position on how Epicurean philosophy may relate to nominalism, and I think that would be worth exploring. We quite often see discussions of The Problem of Universals (link to the same article), and we can be sure that Epicurus rejected Plato's views of ideal forms, and probably Aristotle's views of "essences" as well. But does that mean that Epicurus held, in John Stuart Mill's terms, that "there is nothing general except names?"
I think there are several passages that would bear on this including the following from Lucretius Book One (Bailey translation). I should note that this is a passage where I think the translation of eventum as "accidents" would be much better as "events," but that's another argument. Here , the issue is the question of eternal properties vs. transient qualities, and how those can be viewed through the analogy of the Trojan War:
 But now, to weave again at the web, which is the task of my discourse, all nature then, as it is of itself, is built of these two things: for there are bodies and the void, in which they are placed and where they move hither and thither. For that body exists is declared by the feeling which all share alike; and unless faith in this feeling be firmly grounded at once and prevail, there will be naught to which we can make appeal about things hidden, so as to prove aught by the reasoning of the mind. And next, were there not room and empty space, which we call void, nowhere could bodies be placed, nor could they wander at all hither and thither in any direction; and this I have above shown to you but a little while before.
 Besides these there is nothing which you could say is parted from all body and sundered from void, which could be discovered, as it were a third nature in the list. For whatever shall exist, must needs be something in itself; and if it suffer touch, however small and light, it will increase the count of body by a bulk great or maybe small, if it exists at all, and be added to its sum. But if it is not to be touched, inasmuch as it cannot on any side check anything from wandering through it and passing on its way, in truth it will be that which we call empty void. Or again, whatsoever exists by itself, will either do something or suffer itself while other things act upon it, or it will be such that things may exist and go on in it. But nothing can do or suffer without body, nor afford room again, unless it be void and empty space. And so besides void and bodies no third nature by itself can be left in the list of things, which might either at any time fall within the purview of our senses, or be grasped by any one through reasoning of the mind.
 For all things that have a name, you will find either properties linked to these two things or you will see them to be their accidents. That is a property which in no case can be sundered or separated without the fatal disunion of the thing, as is weight to rocks, heat to fire, moisture to water, touch to all bodies, intangibility to the void. On the other hand, slavery, poverty, riches, liberty, war, concord, and other things by whose coming and going the nature of things abides untouched, these we are used, as is natural, to call accidents. Even so time exists not by itself, but from actual things comes a feeling, what was brought to a close in time past, then what is present now, and further what is going to be hereafter. And it must be avowed that no man feels time by itself apart from the motion or quiet rest of things.
 Then again, when men say that ‘the rape of Tyndarus’s daughter’, or ‘the vanquishing of the Trojan tribes in war’ are things, beware that they do not perchance constrain us to avow that these things exist in themselves, just because the past ages have carried off beyond recall those races of men, of whom, in truth, these were the accidents. For firstly, we might well say that whatsoever has happened is an accident in one case of the countries, in another even of the regions of space. Or again, if there had been no substance of things nor place and space, in which all things are carried on, never would the flame of love have been fired by the beauty of Tyndaris, nor swelling deep in the Phrygian heart of Alexander have kindled the burning battles of savage war, nor unknown of the Trojans would the timber horse have set Pergama aflame at dead of night, when the sons of the Greeks issued from its womb. So that you may see clearly that all events from first to last do not exist, and are not by themselves like body, nor can they be spoken of in the same way as the being of the void, but rather so that you might justly call them the accidents of body and place, in which they are carried on, one and all.
There is also the question of whether it is possible to "know" something, and what that would mean. We have several passages on that:
Diogenes Laertius 121: "...he will give definite teaching and not profess doubt...."
Diogenes of Oinoanda: Fragment 5 - Now Aristotle and those who hold the same Peripatetic views as Aristotle say that nothing is scientifically knowable, because things are continually in flux and, on account of the rapidity of the flux, evade our apprehension. We on the other hand acknowledge their flux, but not its being so rapid that the nature of each thing [is] at no time apprehensible by sense-perception. And indeed [in no way would the upholders of] the view under discussion have been able to say (and this is just what they do [maintain] that [at one time] this is [white] and this black, while [at another time] neither this is [white nor] that black, [if] they had not had [previous] knowledge of the nature of both white and black.
This post is going to end up being mostly to pose the question, because this is a very deep subject that I don't think has an easy answer. So for now I will post this and come back when I have time or others add to the thread.