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Commentary on Jamie Mellway's "Enduring Aristotle's Dialectic: The Discipline of Non-Contradiction"
by Tom Radcliffe

Date: 2001-05-26
Forum: Enlightenment's First Annual Meeting
Copyright: Tom Radcliffe

The paper that inspired this commentary, Enduring Aristotle's Dialectic: The Discipline of Non-Contradiction will be defended at the Annual Meeting. The paper and the comment will appear in the published proceedings.

Mellway asks and interesting question of minimalist ontology: if we deny the Principle of Non-Contradiction (PNC) as Aristotle formulates it in Book Gamma 3 of the Metaphysics, is there a weaker principle we might adopt that will allow us to withstand or endure the dialectical attacks Aristotle makes on deniers of the PNC?

By examining Aristotle's argument Mellway is able to answer affirmatively, and while I think Mellway's argument is essentially sound there are some clarifications that could be made. Also, he perpetuates an assumption that is not required for his argument and that I believe is incorrect, which is that we are either conceptual beings or engaged in understanding reality as it is (the noumenal). After a short review of Mellway's argument, I consider an alternative to this assumption.

A valuable addition to the paper would be to explicitly state the PNC:

that the same attribute cannot at the same time both belong and not belong to the same subject and in the same respect [Metaphysics, 1005b, W.D. Ross Tr.]
Aristotle's initial defense of this principle is that it must be used by anyone who wants terms to mean something definite, regardless of any ontological commitments about the nature of meaning. As Mellway says: "The source of meaning, whether intrinsic or nominalistic, is a different issue than whether a term has a definite meaning."

But this is not precisely true, because there is an extent to which Aristotle's argument depends on a false alternative: the key word in the PNC is "cannot", and the alternative is "can". To claim the PNC is false is just to claim that in at least one case a thing can both have and not have the same attribute in the same respect and at the same time. There is nothing to stop me from asserting this of just one thing or one class of things, while denying it of everything else. The source of meaning becomes important to making this argument because it is far more plausible, as Mellway shows when moving on to Aristotle's ontological concerns, that the PNC may be false generally even while something like it applies in most cases if meaning is intentional rather than intrinsic.

With regard to Aristotle's ontological considerations, Mellway correctly identifies the position taken by Ray and myself as being:

the radical view that there are no intrinsically distinct objects and that an entity is a part of noumenal reality that has been intentionally isolated
This view is indeed a kind of ultra-accidentalism: there are nothing, in Aristotle's terminology, but accidents, and all accidents are accidents of accidents. The potential for infinite regress Aristotle is concerned with is brought to an end by the choice of the knowing subject, who treats some accident(s) as essential, which is something like what Mellway describes as the "Discipline of Non-Contradiction".

However, in introducing the Discipline of Non-Contradiction, Mellway says, "we are concerned with constraining our terms/concepts and not with describing the noumenal." This is a view I take issue with, as I do not see the two as being at odds with each other--to describe the noumenal to ourselves we must ensure our descriptions fulfill a consistency constraint that is something like the PNC. For much the greater part of the noumenal this is an easy constraint to fulfill because the noumenal itself fulfills it. It is only in rare and extremely artificial cases--experimental violations of Bell's Inequalities--that we are able to infer those modes of existence that do not admit of non-contradictory description by virtue of being nonlocal, and therefore incapable of definite description in time.

In the passage quoted above, Mellway correctly describes the view Ray and I have taken of entities as "part of noumenal reality" that have "been intentionally isolated." Both poles of this relationship are important: our concepts are about reality, even though they are constrained by conditions (the PNC) that do not in general constrain the reality they describe. This merely means that there may be modes of existence that we cannot describe in a non-contradictory manner. But it does not follow from this that we are not describing reality in every case where we can describe it.