Graham Priest gave a colloquium presentation 9/8/2010 on “Contradiction and Unity.” He offered a theoretical construct called a “gluon” which serves the role of unifier, accounting for the constitution of wholes by parts. The presentation was divided into three parts: the problem, gluon theory, and the application of Priest’s solution to Aristotle’s metaphysical problematic of unity.
The problem is that wholes made up of parts must be unified (“bound”) somehow, otherwise they are just congeries of the simples that compose them. In answering the question, “What does the trick?” of unification, we find ourselves responding with something entitative, noun-like. E.g., when asked what makes a group of bricks a house instead of just a pile of bricks, we want to say, “Their form.” Or their arrangement or configuration or principle or relation to one another, etc. But this form is a thing of some kind; if it is not, we have gained nothing, since we find ourselves incapable of characterizing them otherwise. If the form is a thing, however, we have a regress problem, since the form-thing just gets added to the list of things (parts) comprising the whole, and we need to postulate some other thing that unifies the larger set comprising all the original parts plus the form (a “metaform”).
The problem, for Priest, arises from the fact that the extra principle contains a “metaphysical gap.” The gap is the requirement that the principle lacks instantiation; forms must be instantiated by particular objects, generally comprising parts, and instantiation of an object of a certain kind is exactly the problem he is trying to solve: What unifies an object? The motivation he presents first is not physical. Frege’s scheme for the unification of a proposition is just as prone to this metaphysical quandary. For Frege, a term (“Socrates,” say) serves to complete an unsaturated formula (“is mortal,” e.g.), but the nature of this completion or saturation is never addressed. The concept of mortality awaits instantiation in the subject of a proposition of which “is mortal” is the predicate. Together they make a unity, a proposition, but how? So in Frege’s scheme the parts are subject and predicate, and the metaphysical gap is the need for saturation of predicate-mapping functions. Priest’s point in starting with this example is to note that the ontological status of the parts in question, as being either concrete or abstract, is irrelevant to the more general problem of unification.
Priest’s solution is to offer a binding object that is free of the problems outlined above. He is clearly in favor of a realism that conceives of simples, complex objects, physical objects, and nonphysical objects such as forms, tropes, configurations, and the like as bona fide objects. Objects all the way up, objects all the way down. Note that there still can be collections of objects that do not constitute composite objects, that is, bunches of items, or congeries. He just wants to embrace objecthood for abstract as well as physical objects.
Well, what sort of object can unify a group of other objects without introducing a metaphysical gap? Priest’s solution is a special kind of object called a “gluon,” which requires no saturation by the object it unifies. The only way it can manage this is to introduce no difference, no non-identity, with any of the object’s parts. The only way it can do this is to be identical to each of the object’s parts. The only way it can do this is under a logic that permits contradiction, because each part of the object is taken to be non-identical to every other part. The contradiction is that the gluon will be identical to a bunch of distinct items.
Priest’s scheme for the gluon relies on a paraconsistent logic in which some propositions are taken to be true, some false, and some both true and false. The Venn diagram of this arrangement of logical space is two overlapping circles. If the lefthand circle is the set of true statements, and the righthand the set of false ones, the intersection is the set of statements that are both true and false. The region in which gluons operate is this intersection, because the gluons must possess mutually contradictory properties. The reason they need to do this is so that they can be identical to each of the parts. The metaphysical gap, for Priest, is removed if the gluon can be identical to each part (and of course it is identical to itself).
Take an object O with parts A and B, the simplest case of unification. Part A may possess properties that B possesses, and vice versa. In fact the two objects may be qualitatively identical. But they are not numerically identical, and if they are physical objects they are not identical as to location, perhaps among other properties. O’s gluon G must be identical to both A and B. How can it be?
This depends on how one treats identity. Priest’s suggestion is Leibniz’s identity of indiscernibles: x = y iff (AP) P(x) iff P(y). So two things are identical just if they share all and only the same set of properties. This brings in the biconditional as a way of representing in quantified logic the nature of identity.
The interesting properties of parts of an object will be those that differ. If all the bricks in a house are red, we’re not so much interested in the predicate ‘red’, since for the gluon to share redness with any part does not conflict with the non-redness of any other part. But if we take another predicate, such as location or microscopically precise shape, every brick will have different properties. For the gluon G to maintain its identity with A and B by sharing unique properties with both A and B, it must itself possess contradictory properties, e.g., both Thislocation and !Thislocation. Hence Thislocation(G) will be both true and false, as will its negation, so we can see various predications to G occupying the overlap in our paraconsistent logical space.
It’s important to keep in mind that, for Priest, the embrace of contradiction, at least within the paraconsistent limbo, is essential to overcoming the regress problem that arises from postulating a glue element such as a form or arrangement. But is it also important that the system allow the parts of an object besides the gluon to differ from one another. They must differ, or else the scheme would not show how different parts come together to make a unity. The paraconsistent logic works out nicely in this regard, since the biconditional definition of identity Priest uses renders identity reflexive and commutative but crucially not transitive. That is, objects are still identical to themselves (a = a), and if an object a is identical to some object b, then b is identical to a, but a = b and b = c do not imply a = c. As we have seen, if a gluon G plays the role of b in the transitive scheme, two objects with which G is identical need not share all properties with each other, and therefore need not be identical to each other.
That’s the gist. I may make another entry to discuss Priest’s claim about how historical versions of the problem of unity are covered by his gluon approach and to mention some objections raised during Q&A.
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