Having recently returned from the Geneva conference on Bradley's regress, I have much to ruminate upon and digest. I'll start my ruminations with some comments on Richard Gaskin's work.
In an earlier post I suggested that we ought to make a tripartite distinction among vicious, benign (harmless), and virtuous (helpful) infinite regresses. To put it crudely, a vicious regress prevents an explanatory job from getting done; a benign regress does not prevent an explanatory job from getting done; and a virtuous regress makes a positive contribution to an explanatory job's getting done. I gave an example of a putative virtuous regress in the earlier post which example I will not repeat here. In this post I draw your attention to a second putative example from the work of Richard Gaskin, whom I was happy to meet at the Geneva conference on Bradley's Regress. Gaskin's proposal is that "Bradley's regress is, contrary to to the tradition, so far from being harmful that it is even the availability of the regress which guarantees our ability to say anything at all. Bradley's regress is the metaphysical ground of the unity of the proposition." ("Bradley's Regress, the Copula, and the Unity of the Proposition," The Philosophical Quarterly, vol. 45, no. 179, April 1995, p. 176) In terms of my schema above, Gaskin is claiming that Bradley's regress is positively virtuous (not merely benign) in that it plays a positive explanatory role: it explains (metaphysically grounds) the unity of the proposition.
I will now attempt to summarize and evaluate Gaskin's position on the basis of two papers of his that I have read, and on the basis of his presentation in Geneva. (I should say that he has just published a book, The Unity of the Proposition, which I have not yet secured, so the following remarks may need revision in light of his later work.)
1. First, a rough characterization of the problem of the unity of a proposition. A proposition is a whole of parts. Thus the proposition expressed by the declarative sentences Sokrates albus est and 'Socrates is white' is a whole the parts of which are the semantic values (referents, Bedeutungen) of 'Socrates,' 'is,' and 'white' -- assuming that two if not all three of these words have referents. Now the whole in question has the property of being either true or false, a property that the parts taken singly do not have. Thus the referent of 'Socrates' is neither true nor false. And the same holds for the other constituents of the proposition. It is also the case that the constituents taken collectively, as a collection, as a mere many, is neither true nor false. What then accounts for the proposition's being truth-valued when its parts are not?
We can also approach the problem from the side of the declarative sentence. To utter such a sentence is not to recite a list. Listing the words in 'Socrates is white,' even if they are listed in the order they have in the sentence, is not the same as asserting the sentence. A sentence is not a list of the words featured in it. The problem, then, is to specify what it is about a declarative sentence that distinguishes it from a list of its constituent words, or what it is about a proposition that distinguishes it from the mere aggregate of its constituents. This amounts to specifying what it is about a declarative sentence or a proposition that gives it the property of being either true or false. Since a proposition is a unity of constituents, and not a mere aggregate, the problem is to explain, ground, account for, the peculiar unity of a proposition whereby its several constituents form a whole that is either true or false.
2. Gaskin operates with the basic assumption that "components of a proposition have reference on the model of proper name and bearer. . . ." (177) Thus both names and predicates have referents. This strikes me as a reasonable assumption, though I won't say much in defense of it here. Setting aside vacuous names, it is obvious that names have referents. That predicates also refer is perhaps not obvious, but is reasonably maintained. Gaskin holds that predicates must have reference if a semantic theory of natural language is to be possible. (177) I myself find it impossible to credit the sort of nominalism that maintains that 'white' is true of white things because English speakers apply tokens of 'white' to them. By my realist lights there must be something in reality that grounds the correctness of the application of 'white' to white things. White things are not white because we predicate 'white' of them; we correctly apply 'white' to them because, in reality, they are white. So there must be something in reality to which predicates refer.
3. Now if predicates refer like names, then the problem of the list arises, the problem of explaining the difference between a sentence (which is a unitary structure capable of being true or false) and the corresponding list (which is not a unitary structure capable of being trut or false). Obviously, a sentence is not a list of names; you cannot say anything by listing names, and a list of names is neither true nor false; so if predicates are a species of name, the problem of the list arises. One solution is the Fregean one: concept-expressions and concepts are essentially (as opposed to accidentally) unsaturated. Thus '___wise' and the referent of this concept-expression are essentially unsaturated or gappy or incomplete unlike names and their referents which are saturated or complete. Predicates refer to concepts but do not name them; names refer to objects by naming them. Now if the referents of predicates, namely concepts, are essentially incomplete then -- or so the theory goes -- they fit together with the referents of names without the services of a tertium quid such as a relation of instantiation. This is supposed to defuse the Bradley regress: there simply is no regress if object and concept fit together like plug and socket. In the proposition, there is no need for a logical copula: the copulative function is discharged by the gap in the concept. It is the essential incompleteness of concepts and their radical difference from objects that is supposed to make it possible for predicates to have reference without igniting a Bradley-type regress or giving rise to the problem of the list.
4. Unfortunately, the Fregean solution to the problem of the list, with its radical dichotomy of objects and functions (concepts being a species of function), engenders the paradox of the horse, the paradox illustrated by the claim that the concept horse is not a concept. The reason this claim is thought to be true is because 'The concept horse' is a name whose referent is an object (Gegenstand). So, making the claim, one picks out an object and says truly of it that it is not a concept (Begriff). But of course this is paradoxical because it seems we do in fact talk about concepts as concepts and quantify over them. A Fregean, for example, needs to be able to say, without contradiction, that every concept is such that it is not an object, that every concept is a function, that concepts are unsaturated, that some concepts have objects falling under them, that some don't, etc. But he cannot say any of these things without contradiction if reference to concepts as concepts is impossible.
One cannot eliminate the paradox of the horse by saying that concepts cannot be named, but only referred to by the use of predicates as predicates. For again, we cannot dispense with quantification over concepts.
5. The task is to solve the problem of the list without engendering the paradox of the horse. Gaskin, following David Wiggins, proposes that we re-introduce the copula by distinguishing in every predicate a strictly predicative element (the copula) and a strictly non-predicative conceptual component available to be quantified over. Now it is the copula, rather than the concept, that is the vehicle of unsaturatedness. (173). But the copula cannot designate a relation on pain of Bradley's regress. Nor can we say that the copula designates nothing, that it is an "insignificant piece of syntax." (175) For we can talk about "predicative being." "The copula must, in some way, refer." (175). This strikes me as correct. The 'is' in 'Socrates is white' is not a mere syntactical element. It contributes to the meaning of the sentence. As I would put it, it expresses that Socrates' whiteness is.
6. We now come to Gaskin's proposal. It is that the copula has reference, but that it is "endlessly deferred." (176) The idea, I take it, is that the copula in 'Socrates is white' refers to : . . .the instantiation of the instantiation of the instantiation of whiteness by Socrates. The copula has a referent, but it is infinitistic. "The unsaturatedness of the copula is, then, underwritten by Bradley's regress. For the copula introduces unsaturatedness into the proposition in just the infinitistic way embodied by the regress." (176) Bradley's regress is thus virtuous (and not merely benign or harmless): it first makes possible our ability to say anything at all. "Bradley's regress is the metaphysical ground of the unity of the proposition." (176) What prevents a proposition from being a mere list is its being an infinite list. (176)
Gaskin's view avoids two extremes. One would be to say that the copula refers to a finite something such as a relation of instantiation. But then we succumb to the problem of the list. The other extreme would be to say that the copula refers to nothing. Gaskin finds a via media: the copula refers to an infinite something, namely, an actually infinite series of instantiation relations. Or at least that is what he seems to be saying in his 1995 Phil. Quart. paper.
7. Should we adopt Gaskin's view? The answer to this depends on exactly what his view is. From his Geneva presentation it is clear that the infinite regress is an external one in that it deploys itself between propositions and not within any given proposition. Let Socrates is wise be our example. Symbolize this as Ws. We then get the following regress: Ws, E2Ws, E3E2Ws, . . . , En+1EnWs, . . . . where En is n-adic exemplification (instantiation). This regress is supposed to provide "the metaphysical condition of unity." Gaskin writes:
My suggestion: don’t treat the regress as vicious, but regard it as providing the
metaphysical condition of unity. Each stage in the regress supplies necessary and sufficient
conditions for the unity of the relevant proposition at each stage (if any) on either side of it.
[. . .] Bradley’s Regress, like the structure of the real line, is infinitistic in a metaphysical, not an
epistemological, sense, and for that reason is not vicious: it represents an infinitistic condition
on the structure of the world, and not an infinitistic, and so uncompletable, task for the
understander. The condition imposed by Bradley’s regress on the proposition, and on the
world, can be captured in a finitely based theory of meaning, and so is within the grasp of the
understander. Accordingly, though acquaintance with the unified proposition involves
acquaintance with an infinity of entities, the process of becoming acquainted with it and them
does not involve performing the impossible feat of, in Aristotle’s phrase, ‘going through
infinitely many things’. The regress unpacks the original proposition into an infinity of
further propositions, and it structures, infinitistically, our understanding of that original
proposition, but it does not present us with a series of discrete epistemic tasks: we do not
have to perform an infinity of such tasks corresponding to the stages of the regress before we
can assure ourselves of the unity of a given proposition. Even so, its unity depends on the
presence, in the unspoken and unwritten background, of the members of the regress: were
that background not fully in place—if the regress did not get going, or if it faltered at some
point—the proposition in question would not be unified, but would fall apart into a mere
aggregate.
My main problem with Gaskin's proposal is that I fail to see how it does anything to explain the unity of the proposition. What he does is simply presuppose the unity of the proposition. We want to know what makes a proposition more than the mere aggregate of its constituents, what makes it be a unity capable of being either true or false, when neither the aggregate nor any member of the aggregate is capable of being true or false. What is the unifier of a proposition's constituents? Using some terminology that Gaskin himself employs, we want to know what is the "metaphysical ground of the unity of the proposition." But now consider the (admittedly benign) infinite series of propositions . . . En+1Ws, EnWs, . . . , E3Ws, E2Ws, Ws. Surely the metaphysical ground of the unity of the base proposition Ws cannot be E2Ws; nor can E3Ws be the ground of E2Ws, and so on. This is because the infinite series cannot exist unless the base proposition is already constituted as a unitary structure capable of being true or false. Gaskin's explanation, in other words, is circular: his explanation of the unity of Ws presupposes the unity of Ws. And the same goes for every proposition 'to the left' of Ws in the regress as above depicted: in every case, the explanation of EnWs in terms of En+1Ws is circular in that ir presupposes that EnWs is on hand as a full-fledged unity.
I grant that Gaskin's Bradley-type regress arises, that it is actually (not potentially) infinite, and that it is benign. I also admit that the regress furnishes us with a criterion, in the epistemological sense of a test, for distinguishing between a proposition and its corresponding aggregate and a declarative sentence and its corresponding list. The criterion or test is that, if the analysis of the proposition/sentence gives rise to Bradley's regress, then it is a proposition/sentence, while if it does not, then it is an aggregate/list. What I deny is that the regress has any explanatory value as regards the metaphysical question of the unity of the proposition. Thus, although the regress is benign, it is not virtuous in my sense: it does not do an explanatory job. It does not do an explanatory job because, as an external regress between propositions, as opposed to an internal regress within a proposition, it presupposes the very datum that needs explaining, namely, the unity of the base proposition Ws in our example.
My point, then, is that Gaskin has not furnished us with the metaphysical ground of the unity of the proposition, as he seemed to be promising he would judging from his papers published in the '90s. He has instead furnished us with a criterion or test for distinguishing sentences from lists and propositions from aggregates. But this criterion or test cannot be what makes or constitutes a proposition a unity any more than turning blue litmus paper red, or red litmus paper blue is what constitutes the difference between an acid and a base.
This leads to the question as to what exactly the problem of unity for a proposition/sentence is. Could it be that Gaskin understands this problem differently than I do? If the problem were merely to furnish a criterion or test for telling apart propositions/sentences from their corresponding aggregates/lists, then I would say that Gaskin has solved the problem. But the problem as I see it lies deeper, and I suggest that for Gaskin too it lies deeper. He formulates the question as follows in the first paragraph of his Geneva talk: "What are propositions and what unifies them, i.e., what distinguishes them from mere aggregates and enables them to be true or false?" At the beginning of paragraph 4 he writes, "So the question of unity is: what unites object and concept?" There are perhaps two quite different questions here, the first properly metaphysical, the second epistemological:
Q1. What makes the sub-propositional constituents of a proposition into a unity capable of being true or false? What unites object and concept in a monadic proposition? A proposition is more than its constituents as their unity: what is the ground of this unity?
Q2. What distinguishes propositions from mere aggregates?
I believe that Gaskin has provided an answer to (Q2). The answer is that propositions but not aggregates give rise to an instantiation regress. But in answering (Q2) he has not thereby answered (Q1). Or so it seems to me. Furthermore, I do not believe I am foisting (Q1) upon him; he himself is asking (Q1); it is just that he conflates (Q1) with (Q2) as the passages suggest without however definitely proving.
A final thought. Gaskin may be waffling between internal and external understandings of the regress. What he needs to secure metaphysically the unity of the proposition is an actually infinite regess internal to the proposition. Such an internal regress, being actually infinite, would at least have a chance of gluing together all the proposition's constituents. (I would argue, however, that the internal regress is vicious, but that is beside the present point.) For one could then argue that no constituent remains 'unglued.' This internal regress would also comport well with Gaskin's talk of the referent of the copula as the vehicle of unsaturatedness. On this way of looking at the problem, the 'is' in 'Socrates is wise' refers to an infinity of instantiation relations within the proposition Socrates is wise, a proposition which, because of this infinity, cannot be faithfully represented by the simple sentence 'Socrates is wise.' But on Gaskin's preferred way of looking at the problem, the 'is' in 'Socrates is wise' refers to the dyadic instantiation relation in the proposition Socrates instantiates wisdom, and not to an infinity of instantiation relations of ever increasing adicity.
So let me end with a dilemma for Gaskin. Either he construes the ensuing infinite regress of instantiation internally or externally. If construed internally, the regress has a chance of actually securing the unity of the proposition. That's the good news. The bad news is that the regress so construed is vicious. (I have not argued this point here, but Francesco Orilia has in his Geneva paper.) If, however, the regress is construed externally, as Gaskin certainly does in his Geneva presentation, then his metaphysical explanation of the unity of the proposition is circular and no explanation at all, as I argued above.
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