In contemporary Buddhist Studies (which refers to the mostly Western, semi-global academic study of Buddhism, and not the indigenous systems of actually existing Buddhadharma) the Madhyamaka is often rendered as a form of philosophical anti-foundationalism, which is opposed to totalizing, metaphysical forms of thought based on self-sufficient first principles or self-grounding foundations which pretend to, at least in principle, provide the means to gain an understanding of reality from an absolute, transcendental standpoint.
It could be said that, similar to its Western counterparts, Madhyamaka anti-foundationalism consists of a negative ontology that asserts the lack of any self-subsisting foundation to any thing and a critical epistemology that renders knowledge and truth as functions of social practice and not as indexes of something ultimately real. From this view, it can be said that the Madhyamaka is suspicious of any claim to ultimate foundations or objective truths in order to ground the validity of a given proposition, in the manner of an axiomatic principle. It makes global assertions (all phenomena are empty without remainder) at the same time that it delimits the pervasion or applicability of these assertions to their local situations (phenomena exist only by way of conventional designation). As well as anti-foundational, the Madhyamaka can be said to be anti-metaphysical: well-suited for the derivation of truths valued only in terms of their pragmatic utility or functional efficacy rather than their consistency with a totalizing worldview. Here the measure of truth is not based on the extent of the correspondence between an idea and its intended object, but based on the extent of the power afforded by this idea to produce intended results.
I think this is all fine, to a certain extent. I think if we consider the Madhyamaka solely from a philosophical point of view, we could say that it is anti-foundationalist. But the attitude or disposition of this view seems to be a bit off the mark, or rather, a bit out of balance. The axiomatic suspicion I mentioned earlier is perhaps entirely unnecessary, and lends itself too much for an enthusiasm for polemics and a readiness to refute others’ views. I think it actually indicates an incredibly subtle metaphysical assumption at the base of the disposition, which is the notion that for something to have a foundation it must necessarily have an ultimate foundation. When you take on this assumption, taken in tandem with the Madhyamaka rejection of ultimate foundations, what you essentially have is a sort of nihilistic activism constantly operating under the shadow of a totalitarian absolutism.
My preferred way of rendering the Madhyamaka is as non-foundationalist rather than anti-foundationalist. Often the two are conflated, and perhaps in some contexts their uses are not distinguished. But I think it is very useful to make a clear distinction between the two.
First, I think non-foundationalism (nF) is not only distinct from foundationalism (+F), but should also be understood as distinct from the way in which +F and anti-foundationalism (-F) are distinct from each other. Which is to say, that +F and -F are distinct from each other as views only insofar as they are identical in their being views at all. I think it would be fruitful to distinguish nF from both +F and -F in that nF is not a view per se, but an attribute; not a noun but an adjective.
A project understood as +F or -F in view would be characteristically different from a project with a nF attribute, because while the former only operates through the medium of a transcendental idea (whether in the mode of affirmation with F or the mode of denial with -F), the latter only operates in terms of a direct engagement with its object of concern. So in spite of their apparent opposition, +F and -F are united in their being different modes by which one is subjected to determination by conceptual constructs. The only real difference then, the one that truly matters, is the difference between nF and +F/-F.
To understand nF as an attribute of a project and not as a view or basis of a view is to say that to the extent that the Madhyamaka operates, it operates without recourse to self-sufficient entities or ultimate foundations. This leaves open the possibility of the provisional use of temporary expressions of self-sufficiency or foundation. It avoids the +F extreme because it does not require, and does not operate in terms of, notions of self-sufficiency or foundations dependent upon some absolute ground, and it avoids the -F extreme because it can meaningfully make use of such notions for the same reason, because that there is no final foundation does not exclude the possibility of there being some foundations to work off of. Since it avoids the extreme of +F, it avoids the charge of circularity (the prime issue for all absolutisms). Since it avoids the extreme of -F, it avoids the charge of self-refutation (the prime issue for all relativisms).
As well as allowing us to make use of conventions, a nF Madhyamaka would also allow us to challenge them on grounds that transcend them, rather than remaining immanently limited to the logic that governs that convention. An -F Madhyamaka does not really have this ability, since it must adopt conventions on their terms without subjecting them to evaluation in terms of something that could be considered more valuable or true.
Lastly, a curious point. Perhaps to the extent that we give name to it, the “Madhyamaka” is invariably anti-foundationalist. Perhaps that which is non-foundationalist is the “Madhyamaka” that is without name, if such a thing can be even called something anymore at this point. Drawing from some Tibetan Madhyamikas, we can make an analogy here between the Madhyamaka-in-name with the notion of the Categorized Ultimate, and the Madhyamaka-without-name with that of the Uncategorized Ultimate. To the extent that we refer to the ultimate nature in terms of conceptual categories, the Madhyamaka view of anti-foundationalism is adequate. To the extent that we orient ourselves to the ultimate nature in a non-conceptual mode devoid of proliferating categorizations, we embody the Madhyamaka-without-name. Perhaps similarly, the Madhyamaka-in-name is a useful stepping stone that gradually prepares the agent to the Madhyamaka that is without-name, without form. So in order to articulate a bridge between the two, I will refer to the Madhyamaka neither as a view of rational anti-foundationalism nor that of mystical foundationalism, but as merely being non-foundationalist in character.