Περὶ τοῡ μὴ ὄντος ἢ Περὶ φύσεως ["On nonbeing, or, On nature"]. Opinions diverge regarding the content and aim of this text. Some believe that presented here is merely an example of the most overdone dialectics and sophistry; others find positive and serious deliberations, to be sure not without a strong influence from the art of formal argumentation. Aristotle wrote Πρὸς τὰ Γοργίου ["Against the views of Gorgias"], and we can assume Aristotle would not do battle against a mere babbler.
The content of the text in three theses: 1. There is nothing. 2. But if there were something, it would be unknowable. 3. If there were something and it were knowable, then the knowledge of this being would be incommunicable and could not be expressed or interpreted.
The Being of beings, the knowability of Being, and the communicability of what is known are denied.
Regarding 1: Being. εὶ γἀρ ἔστι-"if Is." There is nothing. a) What is not is not. b) Beings are not either: aa) eternal, or bb) produced by becoming, or cc) both at once. c) Beings must either be one or many; but they can be neither. d) Likewise, both the one and the many cannot be at the same time.
Regarding 2: What is thought of would have to be; nonbeings could not be thought of.
Regarding 3: Every sign is different from what is signified. Words are something other than colors. The ear doe snot hear colors. How is the same intended thing supposed to be in two different "subjects"?
My shortcut understanding of the Sophists is that they are clever. MH's work probably has been accused of cleverness to the detriment of clear thinking, but MH's probing of nothingness (contrary to Sartre's or Gorgias') is insightful.
I do appreciate Gorgias' comment "Words are something other than colors."
Socrates calls the sophists Rhetoricians--or flatterers-- rather than philosophers, or scientists. Doesn't Aristotle suggest the Heraclitean macho men were sort of sophists (or at least they were disparaged, somewhere).
There's probably more to it--and subtleties to each school which most mortals will never get (the stoics also quite interesting--they were doing propositional logic, early on, a bit different than Aristotle's categories). Cicero also ranks the Stoics above the Plato-Aristotle school, did he not. Sextus Empiricus also quite...trippy, like Hume of 300 AD or something. But...IMHE there is something not entirely satisfactory about returning to the greeks. Knowing something about them, yes (and the beautiful language....there Ezra Pound might agree with MH)--but insisting that all answers are still to be found in Plato , et al...nyet
I agree that we won't find all the answers by looking for them in the ancient Greeks. At the same time, many of today's controversies are just revisiting ground they covered, so its helpful to know the tradition, if only to see what's genuinely new.
The ancients' debate on Being/Non-being does not seem fundamentally different than the battles between the logical positivists and Heidegger and Hegelian tradition in general. Is Nothing just...denial, "not" or something in the world? Continental philosophers seem to follow Heraclitus in regarding "nothing" or nothingness as something in the world--in ways that may metaphorical rather than logical, as absence or...destruction, perhaps (decay...entropy?) . But there's not really a quantitative contradiction ala Aristotle.
Hegelian dialectic may have a certain plausibility (say in regard to historical process) but good luck using it in any precise fashion. As a..post hoc model, perhaps--as science, nyet. But...Hegelians insist otherwise (and most Heideggers are neo-hegelians, usually)
However the buddhist conceptions are...psychological. That's not to say all buddhism is psychology (some of it quite otherworldy and mystical, obviously) but usually "nothing" meant something like realizing the illusion of self or permanence. Bewildering, like most eastern religion. Some early Budd.--the greatest hits of the Dhammapada-- seems rather profound. Gautama, assuming he existed, was probably a great counselor and sage (tho still has...hindu like meditations on birth-death and becoming--the dukkhas). Schopenhauer thought so. But a lot of "Confucius says" material as well. You see that now, in like the starbucks "zen"--.
Been a long time since I read some of MH's deliberations on the nothing that nothings. Even then, I was over my head.
I seem to recall that he has four kinds of das Nichts, but I cannot elaborate. Instead, I think of his nothing as mutually implicated with beyng, along the lines of his exposition of identity and difference.
That is, beyng implies nothing and vice versa. MH's beyng is not Plato's Being or Aquinas'. Nor is it the logical positivists entity or whatever their equivalent might be.
My guess is that beyng is only available to us as an item of possibly impossible knowledge. My personal distortion of it is to refer to it with non-MH folks as "the whole of things." We have no perspective from which identify that. We can only think and talk about it. Will it show itself to us? Maybe. Maybe not.
Anxiety reveals Nothing...within the ground of Dasein, or something (right?)--. yet at times MH's Nothing ...seems to be Dasein. That is quite different than Hegel, where contradictions are...perceivable (allegedly), as phenomena, present in World-History, so to speak (greeks vs persians...etc). There's a subjectivity to MH which one doesn't find in the Hegelian programme, such as it is, IMHE. Perhaps Heidegger's just too enigmatic for us stupid Americanische.
But you are correct that Heid. does not say Nothing/Nicht is merely denial, or megation (~A). It seems to have a slightly theological implication (he at times echoes Kierkegaard as well). Nothing as...the Devil? Or maybe just one of His henchmen. Beelzebub then.
Regardless, Heidegger did modify the Hegelian programme substantially (and...ergo, Marxism as well). He internalizes in a sense (which seems common to existentialism)-- introspection (..anxiety--) was verboten, initially to german idealism, IMHE. The Idea...manifests Itself, mo or less.
Perhaps that subjectivity was one reason the euro-left hated him (WSWS gang still does), at least until a few of the Frankfurt sorts read QCT--their ...ideology was being jacked.
I don't claim mastery, however read Was ist Metaphysik? back in the day. His comments on the business of science are still a bit interesting--foreshadowing..QCT perhaps. when he applies his schema, via Techne, I start to get him, maybe. But the ...interior/psychology not really).