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by Corry Shores
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[Logic and Semantics, entry directory]
[Graham Priest, entry directory]
[Priest, One, entry directory]
[The following is summary. You will find typos and other distracting mistakes, because I have not finished proofreading. Bracketed commentary is my own. Please consult the original text, as my summaries could be wrong.]
Summary of
Graham Priest
One:
Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness
Ch.1
Gluons and Their Wicked Ways
1.3
Unities and Their Parts
Brief summary:
(1.3.1) Things have parts. To understand the relation of the parts to the whole, we need a sense of how their arrangement composes that whole. (1.3.2) There is something over and beyond the sum of something’s parts which explains its unity, and we will call it “form.” There are many philosophical questions we can ask about unity and parthood, but they will not have bearing on what we will determine here. (1.3.3) We face a contradiction when thinking of there being something over and beyond the parts that explains their unity in a whole, namely, that on the one hand it is not an object as a part, but on the other hand, it is a thing that is “part” of that whole. (1.3.4) The unifying factor in a thing is called its gluon. It both is and is not an object/part. It is an object insofar as we name it and conceive it. But it is not an object insofar as it is what constitutes the organizing and unifying factor of the thing, because as such it needs to be over and beyond any of the parts rather than simply being another part. (1.3.5) An object is both a plurality and a unity. So, all objects are fundamentally inconsistent.
[Parthood and Configuration into Wholeness]
[Form as What is More than the Parts’ Sum and as What Explains the Unity]
[The Contradiction of a Form Being Both a Part/Object and a Non-Part/Non-Object.]
[The Inconsistent Gluon as the Unifying Form.]
[Inconsistency and Objectivity.]
Summary
1.3
Unities and Their Parts
[Parthood and Configuration into Wholeness]
[Things have parts. To understand the relation of the parts to the whole, we need a sense of how their arrangement composes that whole.]
If something is a thing, then it (probably) has parts. Later we will discuss whether all objects have parts. Priest lists a number of examples to illustrate this parthood, including both spatializable and temporal parts: “A computer has components, a country has regions, a history has epochs, a piece of music has notes, an argument has statements, and so on” (8). So we now ask, “What is the relationship between a thing and its parts?” (8). Priest then notes that such a relationship might not even hold in the first place: “For a start, the parts can exist when a unity they compose does not. The bricks of a house, for example, can lie scattered around in a field before the house was built, or after it is destroyed” (8, boldface mine). [So while a thing has parts, not all parts have a thing in the sense of a greater unity.] Priest then quotes Aristotle on this idea:
Aristotle made the point this way (Top. 150a15–21):
In general, too, all the ways of showing that the whole is not the same as the sum of its parts are useful in meeting the type . . . [of man who defines an object to be its parts]; for a man who defines in this way seems to assert that the parts are the same as the whole. The arguments are particularly appropriate in cases where the process of putting the parts together are obvious, as in a house and other things of that sort; for there, clearly, you may have the parts yet not have the whole, so that the parts and the whole cannot be the same.7
(8)
7. Quotations from Aristotle through this book are taken from Barnes (1984), unless otherwise indicated.
(8)
Priest then notes what is important here with regard to parthood in relation to wholeness. It is not enough to think just of the parts on their own to understand their relation to the whole. Rather, we need to understand the way they relate and are configured in the particular ways that compose the whole.
The parts of the house are not sufficient: they have to be configured in a certain way. Similarly, a piece of music has to have its notes arranged in the right way. And an argument has to be structured into premises and conclusion.
(8)
[Form as What is More than the Parts’ Sum and as What Explains the Unity]
[There is something over and beyond the sum of something’s parts which explains its unity, and we will call it “form.” There are many philosophical questions we can ask about unity and parthood, but they will not have bearing on what we will determine here.]
As we saw in section 1.3.1, as with the example of a pile of bricks not composing a house, a unity is something over and beyond the sum of its parts. Priest suggests that we use Aristotle’s term “form” to name this “more” that is over and beyond the sum of the parts and that explains the wholeness they compose. It is not easy to define this notion of form, especially since, as we later see, Aristotle’s definition will not suffice. And also, it could be that forms are different in kind for different cases. For example, “what constitutes the unity of a house would seem to be different from what constitutes the unity of an argument” (8). And even for one type of form, it is still not obvious what “constitutes the unity of an object”: “is it the geometric shape, or the causal interaction between the bricks, or the design in the mind of the architect, or is it something entirely sui generis?” (8) Priest then says “Never mind” (8). [I am not sure why yet. It could be that we will be able to discuss form or unity more generally, where it will not matter how more precisely we come to define it, because whatever we say would apply in any possible case. What he says next might give the explanation here.] Priest also says that what makes a part what it is is also something that is not obvious. “Do the parts of a human body comprise, for example, its organs, the cells in these, the atoms in these, all of the above?” Priest then notes that “For our purposes, it does not matter. Virtually nothing this book has to say will presuppose an answer to that question” (8). [So it would seem that we will discuss parts and wholes in a way where we can still determine important features without also needing to answer these questions.]
[The Contradiction of a Form Being Both a Part/Object and a Non-Part/Non-Object.]
[We face a contradiction when thinking of there being something over and beyond the parts that explains their unity in a whole, namely, that on the one hand it is not an object as a part, but on the other hand, it is a thing that is “part” of that whole.]
[Priest next moves on to his potent philosophical thinking on this matter. We first note that the form of the thing performs a certain function, namely, to bind the parts into a whole. Then Priest notes a problem that I may missummarize, so please consult the quotation to follow. We should first note a point he makes with regard to section 1.2. Let us look at our brief summary before relating it to our current paragraph:
Frege’s theory of meaning on the one hand accounts for the unity of a proposition while on the other hand makes it impossible for there to be such unity when making statements about concepts and their important structures. A concept has the same structure as a function. This means there are two elements involved. {1} There is an unsaturated function part, in which there is a ‘gap’ or variable where the argument can go. And when a specific argument is put in that open place, then the concept has {2} an object. For example, ‘is unsaturated’ is a concept, and it has a gap (at the beginning) where we could place one or another particular concept (which is something that structurally speaking is unsaturated) so that it takes ‘is unsaturated’ as its predicate. However, this structure does not allow such an expression about concepts to be made, despite the fact that the theory requires we do so and also despite the fact that our intuition tells us we should be able to do so. Were we to use a name for concepts, like ‘a concept is unsaturated’, then we have a false sentence. For, the name ‘a concept’ is not unsaturated, because it itself, as the name taking that predicate, is an object and not a concept. It is in this way that Frege has a problem of unity with regard to his notions of concept and proposition.
(Our brief summary of section 1.2)
And here is a quotation from that section:
Frege’s problem, then, is this. If concept-senses and function-senses are to play their role in accounting for the unity of complexes, they cannot be objects. But they are. One might avoid Frege’s problem simply by rejecting his account of meaning. The situation in which Frege finds himself is, however, but an example of a much deeper problem which cannot be avoided in this way. At root, the problem is not about meaning at all. It is about how parts cooperate to form a unity of any kind. Let me spell this out.
(7, from section 1.2)
The main point as I gather is that Frege is not just explaining some particular structure of propositions that is relevant to logic and mathematics. He is trying to explain what unifies a proposition. That unifying factor is a function, which takes objects, but is not itself an object. Nonetheless, we also come to treat it as an object (specifically when making a function be the object in another function). But, the binding factor of a proposition should not be objectifiable, for then it would be a part like other parts. (Priest is probably making a different point, so please judge from the quotation below). Now, returning to objects understood more generally so as to also include things like houses, whatever it is that is over and beyond the parts cannot itself be a part. For then it is not over and beyond them. (And suppose we do take it for a part. Then we have the same question again, what unifies the parts? It would need to be something else, and we return to the same problem regarding whether or not this new unifying factor is a part or not. That might be something we deal with in the next section, 1.4.]
Whatever the parts are, though, and whatever form is, the form is something that binds the parts into a whole. But now we have a contradiction. It is, after all, something, an object. (I have just spoken about it.) On the other hand, it cannot be an object. If it were, the collection of parts plus the form constitute a plurality, just as much the original. So the problem of binding would not be solved. In Frege, note, the role of binding is played by concept-senses; it is therefore these which occupy the contradictory role.
(9)
[The Inconsistent Gluon as the Unifying Form.]
[The unifying factor in a thing is called its gluon. It both is and is not an object/part. It is an object insofar as we name it and conceive it. But it is not an object insofar as it is what constitutes the organizing and unifying factor of the thing, because as such it needs to be over and beyond any of the parts rather than simply being another part.]
Priest then makes this point more precise. He has us think of an object with a certain set of parts. [Using the house example, we think of the bricks. But as we saw, we can have a scattering of bricks or we can have a brick house, both with the same set of parts.] A thing cannot simply be a set of things, it must also be a unity, which itself is not nothing. Let us call the unity the gluon. It both is and is not an object. It is an object, because we can name it, think about it, refer to it, etc. But it is not an object, because then it would just be another part rather than what unifies the whole. [It would be like another brick in the field.]
Here, then, is our problem of unity. Let me lay it out in abstract terms. Take any thing, object, entity, with parts, p1, .. , pn. (Suppose that there is a finite number of these; nothing hangs on this.) A thing is not merely a plurality of parts: it is a unity. There must, therefore, be something9 which constitutes them as a single thing, a unity. Let us call it, neutrally (and with a nod in the direction of particle physics), the gluon of the object, g.10 Now what of this gluon? Ask whether it itself is a thing, object, entity? It both is and is not. It is, since we have just talked about it, referred to it, thought about it. But it is not, since, if it is, p1, .. , pn, g, would appear to form a congeries, a plurality, just as much as the original one. If its behaviour is to provide an explanation of unity, it cannot simply be an object.
(9)
9. Or some things; but it will turn out that there is only one.
10. The name was coined, with essentially this meaning, in the Conclusion to Priest (1995a).
(9)
[Inconsistency and Objectivity.]
[An object is both a plurality and a unity. So, all objects are fundamentally inconsistent.]
[I may get the next point wrong, but it could be the following. What we noticed above is that an object is made of a plurality of parts. But an object itself is a unity, implying it is not made of parts. But maybe we can say that when we speak of an object as a plurality of parts or as a “congeries,” we are referring not to the parts but to the unity or at least just one thing. Yet, Priest notes that we cannot predicate “congeries” to a singular thing. We can only predicate it to a plurality of things. Thus every object (and not just “square circles” for example) is an inconsistent object, being both a plurality and not a plurality. Let me quote, as I think I missed the point here:]
As is clear, the problem is posed by the contrast between an object, which has a unity, and a congeries, which is a plurality. It might be thought that when we refer to a plurality, we are referring to some one thing, in which case the supposed distinction disappears. But ‘is a congeries’ is not a predicate that applies to a single object. It is a predicate of a plurality, the parts of the object. I will return to the topic of plural reference in Section 6.10.11
(9)
11. Relatedly, one might be tempted to ask what it is in virtue of which a bunch of objects is a plurality. Are there anti-gluons? But such a question would make little sense. A gluon is whatever it is that answers the question about how parts cooperate to form a whole. If one asks how it is that objects cooperate to form a plurality, the answer is that they do not. No cooperation of any kind is necessary to be a disparate and disconnected bunch of things.
(9)
Priest, Graham. 2014. One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University.
Or if otherwise cited:
Barnes, J. (ed.) (1984), The Complete Works of Aristotle, Princeton, NJ: Princeton University Press.
Priest, G. (1995a), Beyond the Limits of Thought, Cambridge: Cambridge University Press; second (extended) edn., Oxford: Oxford University Press, 2002.
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