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by Corry Shores
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[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
1.4
The Bradley Regress
Brief summary:
(1.4.1) We will now discuss why the gluon cannot be an object on account of a vicious regress. (1.4.2) In the Bradley regress, a binding factor is posited as being a member of the unity it binds. But that only leaves us to find yet another binding factor that would bind the first into the whole. There can be no end so long as the binding factors are consider as object/parts. In terms of gluons, if we make the gluon be an object/part, then we will always need yet another gluon to explain how the prior gluon is bound into the whole. (1.4.3) We cannot simply account for unity by saying it is gluons all the way down. For, no such gluon is sufficient to explain the unity. All of them require something in addition. So, simply saying the unity is found in yet another part never tells us in what the unity consists. (1.4.4) In conclusion, on account of the Bradley Regress, we cannot explain the unity of objects as being another object.
[Preview: The Gluon as a Non-Object on Account of a Vicious Regress]
[The Bradley Regress and Composition]
[Unity is Not Gluons All the Way Down]
[Unity is Not Another Object]
Summary
[Preview: The Gluon as a Non-Object on Account of a Vicious Regress]
[We will now discuss why the gluon cannot be an object on account of a vicious regress.]
[Recall from section 1.3.4 the notion of the gluon. From the brief summary of that section: “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.” And here is the paragraph in full, where the gluon is given a slightly more formal account:
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.
(p.9, section 1.3.4)
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).
(p.9, section 1.3.4)
Although it may seem like the gluon could be an object, as it in some sense is a nameable something with regard to a thing’s unity, Priest now will explain why it cannot be an object.]
It will pay to become clearer about why a gluon cannot be an object. A vicious regress stands behind this.12
12. This kind of regress argument is very old. In the form of the “third man argument” it is used in Plato’s Parmenides as an argument against the theory of forms. Plato is there concerned with what makes all, for example, red things one (namely, red). Invoking a form of redness produces the regress. Being one by being red is not the same thing as being one by being parts of something, and Plato’s form is not (obviously) a gluon. However, structurally, the situations are similar. We will come to the third man argument itself in Chapter 8.
(9)
[The Bradley Regress and Composition]
[In the Bradley regress, a binding factor is posited as being a member of the unity it binds. But that only leaves us to find yet another binding factor that would bind the first into the whole. There can be no end so long as the binding factors are consider as object/parts. In terms of gluons, if we make the gluon be an object/part, then we will always need yet another gluon to explain how the prior gluon is bound into the whole.]
[In section 1.3.3 we discussed Frege’s problem of accounting for the unity of a proposition. The unity is to be found in the relation between a function-part (like a predicate) and an argument part (like a subject to the predicate). That unity comes undone when trying to make statements about concepts themselves, because then something which is not an object is also bestowed that status by means of the propositional structure.] Priest returns now to the problem of unity in a proposition, but this time turning to Russell rather than Frege. [The idea seems to be the Following. Russell wants to account for the unity of the proposition, and he locates it in the copula ‘is’. For, it is what unites the subject and predicate. He furthermore claims that the copula cannot be a constituent of the proposition, and it can only be a “way in which the constituents are put together.” For, suppose that it were a constituent. We would still need to find something else that puts those constituents together (the subject, with the ‘is’, with the predicate). And supposing that binding element to be a component too, we would need yet another such binding factor. Under such a structuring pattern, we would reach no ultimate binding factor, despite that being our very aim.]
Return to the matter of the unity of the proposition again. At one stage in his career, Russell was much concerned with this, and one possibility he considered was that it was the copula, ‘is’, that binds the constituents together. (So, in Fregean terms, there is just one concept, which is the copula.13) He then explains why the copula cannot be on a footing with the other constituents:14
It might be thought that ‘is’, here, is a constant constituent. But this would be a mistake: ‘x is a’ is obtained from ‘Socrates is human’, which is to be regarded as a subject-predicate proposition, and such propositions, we said, have only two constituents [Socrates and humanity]. Thus ‘is’ represents merely the way in which the constituents are put together. This cannot be a new constituent, for if it were there would have to be a new way in which it and the two other constituents are put together, and if we take this way as again a constituent, we find ourselves embarked on an infinite regress.
(10)
13. A discussion of this view, in the context of its regress, is given in Gaskin (1995).
14. Eames and Blackwell (1973), p. 98.
(10)
Priest says that Russell here is using an argument by F.H. Bradley that was also related to the issue of the unity of the proposition and to unity in general.
Russell is using an argument used earlier to great effect by Bradley.15 Again, addressing the problem of the unity of the proposition, Bradley starts by supposing that a proposition has components A and B. What constitutes them into a unity? A natural thought is that it is some relation between them, C. But, he continues:16
[we] have made no progress. The relation C has been admitted different from A and B ... Something, however, seems to be said of this relation C, and said, again, of A and B ... [This] would appear to be another relation, D, in which C, on one side, and, on the other side, A and B, stand. But such a makeshift leads at once to the infinite process ... [W]e must have recourse to a fresh relation, E, which comes between D and whatever we had before. But this must lead to another, F; and so on indefinitely ... [The situation] either demands a new relation, and so on without end, or it leaves us where we were, entangled in difficulties.
And Bradley is, in fact, aware that this is not just a problem concerning the unity of the proposition. It is much more general. Thus, in discussing the unity of the mind, Bradley writes:17
When we ask ‘What is the composition of Mind,’ we break up that state, which comes to us as a whole, into units of feeling. But since it is clear that these units, by themselves, are not all the ‘composition’, we are forced to recognize the existence of the relations ... If units have to exist together, they must stand in relation to one another; and, if these relations are also units, it would seem that the second class must also stand in relation to the first. If A and B are feelings, and if C their relation is another feeling, you must either suppose | that component parts can exist without standing in relation to one another, or else that there is a fresh relation between C and AB. Let this be D, and once more we are launched off on the infinite process of finding a relation between D and C–AB; and so on forever. If relations are facts that exist between facts, then what comes between the relations and the other facts? (10-11)
15. In fact, it had been used some 600 years earlier by Jean Buridan in his Questiones in Metaphysicam Aristotelis (Bk V, q. 8). (See Normore (1985), p. 197f.) It should therefore be called the Buridan/Bradley regress.
16. Allard and Stock (1994), p. 120.
17. Allard and Stock (1994), pp. 78–9. (10)
Priest then reformulates this in terms of gluons. Suppose that the gluon is a member among the other parts. We would then need another gluon to bind it with them. And that gluon would need yet another, and so on without end.
We can state the regress problem generally in terms of gluons. Suppose that we have a unity comprising the parts, a, b, c, d, for example. There must be something which, metaphysically speaking, binds them together.This is the object’s gluon, g. But then there must be something which binds g and a, b, c, d together, a hyper-gluon, g′. There must, then, be something which binds g′, g, and a, b, c, d together, a hyper-hyper-gluon, g′′. Obviously we are off on an infinite regress. Moreover, it is a vicious one.
(11)
[Unity is Not Gluons All the Way Down]
[We cannot simply account for unity by saying it is gluons all the way down. For, no such gluon is sufficient to explain the unity. All of them require something in addition. So, simply saying the unity is found in yet another part never tells us in what the unity consists.]
Priest next explains why we cannot simply say that it is gluons all the way down, or in other words, that there is an infinity of gluons. [I may not capture his insight here. My best attempt for now is the following. What we want is an explanation for unity. Suppose we say it is gluons all the way down. This fails, because at no point in the going down is there a structuring part that unifies the whole. For, given any gluon in the infinite chain, none is sufficient to account for the unity. And to say that it is always to be found in yet another part only makes this problem unsolvable, because it makes it impossible to ever identify the ultimate unifying component. Let me quote, as I am probably not putting that in the best way.]
Perhaps it is not immediately obvious that this is so. Could there not just be a whole lot’a gluin’ goin’ on? To understand why this is not a valid response, we must come back to what is at issue here. Our original problem was how a unity of parts is possible. We need an explanation. Given a bunch of parts, simply invoking another object does not do this. We still have the original problem of how a unity of parts is possible. Thus is a new step triggered, and so on indefinitely. Even invoking an infinite regress of objects does not solve the problem. We still have no explanation of how a unity is constituted. If one is asked how to join two links of a chain together, it helps not one iota to say that one inserts an intervening link. (And adding that one might need an infinite number of such links merely makes the matter worse.) In vicious regresses of this kind (I do not think it is the only kind) the infinity has, in fact, precious little to do with matters. The point is that something has already gone wrong at the first step: a failure of explanation.18
(11)
18. ‘[I]t is the first step in the regress that counts, for we at once, in taking it, draw attention to the fact that the alleged explanation or justification has failed to advance matters; that if there was any difficulty in the original situation, it breaks out in exactly the same form in the alleged explanation. If this is so, the regress at once develops . . . ’ Passmore (1961), p. 31.
(11)
[Unity is Not Another Object]
[In conclusion, on account of the Bradley Regress, we cannot explain the unity of objects as being another object.]
Thus: “As Frege realized, if something is to perform the role of explaining how it is that a unity of objects is achieved, it cannot just be another object” (11).
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:
Allard, J. W., and Stock, G. (eds.) (1994), F. H. Bradley: Writings on Logic and Metaphysics, Oxford: Oxford University Press.
Eames, E., and Blackwell, K. (eds.) (1973), Collected Papers of Bertrand Russell, vol. 7: Theory of Knowledge, London: Allen and Unwin.
Gaskin R. (1995), ‘Bradley’s Regress, the Copula and the Unity of the Proposition’, Philosophical Quarterly 45: 161–80. E
Normore, C. (1985), ‘Buridan’s Ontology’, pp. 189–203 of J. Bogen and E. McGuire (eds.), How Things Are, Dordrecht: Reidel Publishing Company.
Passmore, J. (1961), ‘The Infinite Regress’, ch. 2 of Philosophical Reasoning, London: Duckworth.
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