If and when duality (the mode in which phenomena appear as different from each other and occupying the states of presence or absence) is found to be erroneous, there is the tendency or urge to move towards a “higher” mode in which phenomena are seen in some sense as actually identical to one another and as going beyond the dichotomy of presence and absence. This higher mode is often considered to be an ultimate state, state of non-duality or a state of affairs in which there are no phenomena that appear to exist dualistically.
However, this notion of non-duality does not really meet the full measure of its own concept. That is to say, that this conception of non-duality is itself often dualistically opposed to the state of duality. This results in the interpretation of non-duality in terms of the dichotomy of presence and absence, where non-duality is the truly present state by which the state of duality is made absent. So this notion of non-duality only deals with the negation of duality at a certain level (that of the existence of observable phenomena) while still allowing duality to remain at another level (that of the concept itself). So if this expression of non-duality were to be established, it would really only amount to one kind of duality being replaced by another kind. Thus, it is better considered to be a “monism,” where there is the subsumption of one aspect of duality over the other, rather than a complete transcendence from duality as such.
In order for non-duality to be expressed in the fullness of its concept, non-duality (the negation) itself must not be dualistically opposed to duality (the negandum) lest it re-assert duality in a different form.
To do this, we must first understand the two different ways in which the negation operation can be deployed: one as an implicative or relative negation and the other as a non-implicative or absolute negation.
Wth an implicative negation, the negandum (the thing to be negated) is made absent only by way of substitution in which the intent is to replace the negandum with an alternative proposition. Because this form of negation can only operate by reference to something other than the negandum itself, it can also be called a relative negation.
With a non-implicative negation on the other hand, the negandum is simply eliminated by way of denial; nothing is implied to take its place. Because this form of negation has no recourse to anything other than the negandum itself, it can also be called an absolute negation.
So the notion of a state of non-duality in which it is opposed to the state of duality merely replaces one state of affairs with another, and as such can be considered to be a form of relative negation. However as we have established previously this notion of duality does not meet the full expression of the concept; it is not “pure” non-duality because it is “tainted” by its own dualistic opposition to duality.
However the failure of this form of non-duality to fully meet its own concept does not mean that we have to abandon the need for an adequate concept of non-duality and remain content with the state of duality. We can consider non-duality as a form of absolute negation in which duality is simply being denied reality.
At first, it may seem that an absolute negation is too nihilistic. It seems to rest content with a simple absence in which things are eliminated but nothing is constructed. It also seems paradoxical with how it takes something as given only to deny that thing reality, which begs the question as to why that thing was given in the first place if it can only be denied in the last place? These would indeed be problems for us, but only if we do not interrogate the way or manner in which the denial itself is being performed.
What exactly is being denied when we deny duality in an absolute negation? If we deny the complete reality of duality, then we have indeed eliminated it. This form of denial is common to both the monistic conception of non-duality as a relative negation as well as the nihilistic conception of non-duality as an absolute negation. Both monistic and nihilistic conceptions are faulty in their inability to fully express the concept of non-duality because while the monistic conception only replaces one form of duality with another, the nihilistic conception of duality leaves us nothing else to work with and in some sense remains still attached to duality through its exclusive focus on it.
If we deny not the entire reality of duality, but only deny it a certain claim to reality, something different happens. If we first make a distinction between two levels of reality, where there is a relative reality and an ultimate reality, and then subsequently deny duality a claim to the ultimate level, we leave open the possibility for duality to remain at the relative level. Duality is not entirely eliminated but rather becomes situated in its proper place.
So a concept of non-duality which operates by way of a non-implicative or absolute negation that denies duality existence on the ultimate level is a form of non-duality that is not dualistically opposed to duality and hence can rise to fully express the essence of its concept as being beyond duality. This concept of non-duality does not bear a dualistic relationship to duality because we do not have a state of non-duality being compared to a state of duality. In fact, we are asserting nothing at all, unlike the monistic and nihilistic conceptions which try to assert at the ultimate level that either non-duality exists or that duality does not exist, respectively. We are merely denying that duality exists ultimately, and by consequence establishing that it exists relatively. This leaves open the fact that there is an ultimate level of reality, but nothing is being said about it. In a way you can consider this to be a self-reflexive feature of this form of the concept of non-duality, where the one who deploys it knows that the ultimate is not the sort of thing that can be named and expressed verbally, but must be embodied and experienced as living praxis. If duality presents itself in any ultimate way, it must be denied this level of existence in order to eliminate further obstructions to the genuine ultimate—this is the real purpose of our concept of true non-duality. Once duality is denied in this way, we are allowed to remain fully open to the ultimate as it really is, independent of our conceptions of it.