I referenced this article above, "Nagarjuna and the limits of thought." Therein they discuss an issue similar to Thakchoe in this post and following. The below sounds like a contradiction to our formal logic. But per previous posts they use paraconsistent logic, or vision-logic in my interpretation. Or as they call it in the article, the "transconsistent" (18). They note that Nag goes beyond the 'limit of expressibility' paradox akin to Wittgenstein, Derrida and Heidegger (and similar to Thakchoe in this series of posts) but adds the 'ontological paradox.' From the section "The ultimate truth is that there is no ultimate truth":
"The centerpiece of his Madhyamaka or 'middle way' philosophy is the thesis that everything is empty. This thesis has a profound consequence. Ultimate truths are those about ultimate reality. But since everything is empty, there is no ultimate reality. There are, therefore, no ultimate truths. We can get at the same conclusion another way. To express anything in language is to express truth that depends on language, and so this cannot be an expression of the way things are ultimately. All truths, then, are merely conventional. [...] The views that one must relinquish are views about the ultimate nature of reality. And there is no such thing as the ultimate nature of reality. That is what it is for all phenomena to be empty. [...] There are, therefore, ultimate truths. Indeed, that there is no ultimate reality is itself a truth about ultimate reality and is therefore an ultimate truth!" (10-11)
"If Nagarjuna is correct in his critique of essence, and if it thus turns out that all things lack fundamental natures, it turns out that they all have the same nature, that is, emptiness, and hence both have and lack that very nature. This is a direct consequence of the purely negative character of the property of emptiness, a property Nagarjuna first fully characterizes, and the centrality of which to philosophy he first demonstrates. Most dramatically, Nagarjuna demonstrates that the emptiness of emptiness permits the 'collapse' of the distinction between the two truths, revealing the empty to be simply the everyday, and so saves his ontology from a simple-minded dualism. Nagarjuna demonstrates that the profound-limit contradiction he discovers sits harmlessly at the heart of all things. In traversing the limits of the conventional world, there is a twist, like that in a Mobius strip, and we find ourselves to have returned to it, now fully aware of the contradiction on which it rests" (19).
From this post:
In this post I discussed Graham Priest's article on Buddhist logic, which argues around Aristotle's excluded middle. The latter is prerequisite to the claim of performative contradiction, whereas Priest's Buddhist logic doesn't accept that premise. Priest's logic is what he calls paraconsistent, and I of course twist and fold it even further to show how their is an ultimate truth, but not in the metaphysical sense.
PS: accepting the excluded middle is a hallmark of formal operations with its bivalent either/or, and in that sense is 'metaphysical.' Postformal dialectics of the kind Priest discusses goes 'postmetaphysical' in that sense, while still making metaphysical (ontological) claims as to the nature of reality. I've also weaved this into Lakoff's work on embodied realism in various threads (especially real/false reason), another story, but 'on topic' to this thread.
You'll have to read the linked Priest article on Buddhist logic. It's only a contradiction to formal logic that accepts the excluded middle. Recall in Wilber's intro to the fourth turning the 4-fold Buddhist logic: something is, is not, is both, is neither. And used it to justify nonconceptual direct experience as the answer. Priest does a far better job on explaining this. Interestingly, and more than just a pun, it's no accident that Madhyamaka is called the 'middle' way.* It's between conceptual and nonconceptual, absolute and relative etc. in how it mediates these same/differences. Like Desilet and Derrida, not coincidentally.
Or that Lakoff's image schema are in the 'middle' of classical hierarchies, thereby changing the naive set theory and false reason upon which mathematical models of hierarchical complexity are founded. The latter have the same metaphysical notions of you're either in or out of a category, hence the hierarchy has a lowest concrete particular and a highest generalization that are bivalent and disconnected (or 'transcended and included'). Image schema are the middle foundation for both, another form of embodied middle way not caught in formal performative contradictions. Lakoff & Johnson do an excellent job in Philosophy of the Flesh on how this (formal) false reasoning was the foundation for much of western philosophy and metaphysics. (Eastern too, but they didn't address that.) It's so ingrained in us from the start that we cannot even see it.
*The Prasangika Madhyamaka is broadly defined by two camps: Tsongkhapa and Gorampa. See The Two Truths Debate by Thakchoe in the Batchelor thread. This debate is pivotal to the connection between metaphysical (false) and postmetaphysical (real) reasoning.