Axioms for Non Duality

Question

I am interested in teachings about non-duality and I was wondering whether there are any texts that build up assertions of non-duality from a set of axioms. I am aware of Spinoza's ethics and already started reading it. But are there any other works on this topic?

Answer 1

Not a direct example, maybe, but look into positive set theory, where the axiomatic function that generates sets from general descriptions is restricted to positive descriptions, i.e. non-negative ones. Just as such, the system is still consistent with a background logic with substantive negation propositions, but so see also about e.g. negation-free paraconsistent logic for non-dualistic options in that direction, too.

Justification of references: I am assuming, for the sake of the OP question, that a "rigorous" axiomatization of non-duality would mean effacing most or all of the dichotomies that lead to substantive negation. On its face, of course, non-duality still uses the prefix "non-" in the expression of the standpoint itself, so a complete absence of negation seems impossible. (Even when, in classical logic, we find a way to collapse all the connectives, including the negation one, to the Sheffer stroke, we still know behind-the-scenes that this connective has the effective meaning of NAND, "not and" or "not both," so negativity is not entirely dispelled.) Indeed, that very phrase "absence of negation" is self-defeating if taken naively, since an absence can be styled a sort of weak or trivial negativity, after all.

Now, consider that there is an element of arbitrariness in calling electrons negatively charged and positrons positively charged. There is another level of representation where we could switch the descriptions per particle type as long as between the two types, a symmetrical relation held. This would be a perhaps helpful way to interpret/apply non-duality: to strongly relativize (almost) all negations, while maintaining a form of absolute positive representation attendant upon everything in sum.

All that being said, I don't know that set theorists and logicians who favor such systems are implicitly committed to non-duality. Positive set theory does have a proper universal set instead of a universal proper class, and sometimes the absolute set is looked upon as an ultimate oneness containing all possible being. Other times, though, absolute infinity in the theory of proper classes is adapted to the concept of absolute divine infinity, where the divine nature is sufficiently transcendent to dualize the world apart from Itself, or more often an extremely pluralistic worldview, that of the set-theoretic multiverse, has been found helpful in navigating the multitude of set theories. Attempts to weaken (if not eliminate) ontological commitments to "the" multiverse as such are variously more or less successful; still, offhand, the prevalence of mathematical and logical pluralism nowadays tends against non-duality in abstracto (even if the mathematical multiverse is a convenient fiction, say, it still ends up being a fiction that is separate from the range of more stable, monism-friendly facts in the physical world, such as they are).