Davidson and the Problem of Predication

Davidson and the Problem of Predication S¸tefan Ionescu May, 2007 Davidson’s (2005) contains in its second half a discussion of the problem of predication which culminates in the proposal, familiar to his readers, that if any- thing can solve it, a Tarski-style truth-theory can. The basic idea is this: con- verting a Tarski-style truth-definition into an axiomatic theory of a previously understood truth notion can illuminate the nature of predication. My aim in this paper is mostly critical. I shall argue that he rejects alternative accounts by imposing too strict conditions on a satisfactory explanation of predication, and that the solution he envisages fails to do justice to the fact that the original prob- lem arises within natural languages as well. The source of these insufficiencies is Davidson’s focus on truth-conditional semantics explanatorily anchored in the truth-concept; I conclude with a discussion of Davidson’s substantive notion of truth and sketch a different, deflationary approach, together with the possible way to answer the problem of predication. The paper unfolds as follows. In the first section I sketch Davidson’s account of the problem and its history. In the second and third sections I start discussing the constraints he imposes on a solution; the relation between it and Tarski’s program is examined in §4. In §§5–6 I argue that understanding natural lan- guage predication is more basic than its formal counterpart. I do so by examining the possibility of extending Davidson’s solution to sentences containing empty names, and the problem posed by ascribing truth-conditions to sentences in for- eign languages. In the final section I attempt to undermine Davidson’s contention that truth is a fundamental explanatory notion, and point toward a different take on the problem of predication. 1 Davidson’s problem of predication The story goes like this. According to Davidson, the problem of predication goes back (at least) to Plato’s Sophist. It is the semantic task of explaining the unity of simple sentences like “Theaetetus sits” or “Socrates is wise” that appear to be compounds of distinct parts—a name and a verb, or a subject and a predicate. The problem is duplicated at the metaphysical level: it is the problem of explaining how particulars are related to universals (or Forms, in Plato’s case). The entire 1 chapter IV of (Davidson 2005) is devoted to stating the problem and discussing Plato’s and Aristotle’s puzzlement over it. The problem appears to be more disturbing when the semantic task is tackled via metaphysics; for instance, Plato’s theory of participation introduces regress. To say that Theaetetus participates in the Form of Sitting (or resembles it) in- troduces an unexplained relation between Theaetetus, the Form of Sitting, and the relation of participation (or resemblance). This relation has to be explained, in turn, by another relation, and so on. Moreover, whereas the sentence con- tains only two distinguishable parts, the fact that it purports to express contains, apparently, more. Aristotle’s criticism of Plato’s theory of Forms does not take him very close to solving the problem of predication. Though he insists that universals do not exist independently of the particulars (e.g., there are not two distinct entities, Theaetetus and Sitting, but a single one, Theaetetus, who may be sitting or not), when attempting to discuss the semantic problem he agrees with Plato that sen- tences are made of two distinct parts, a noun and a verb. And when forced to explain the function of the parts, he falls back on the error of attributing refer- ents to both1, thus reinstating the problem. The first major step toward a solution is credited to Frege. According to Davidson, Frege’s mature conception is right in noticing the link between the unity of predication and the truth-value of the sentence. Moreover, his concep- tion of logical form as functional in nature allows him a plausible explanation of the relation between subject and predicate. Frege’s solution is plagued, however, by the attempt to justify these insights by ontology. He feels compelled to pro- vide with senses and denotations both predicative expressions and sentences (cf., e.g., (Frege 1892a; 1892b)). But the theory of unsaturated objects that are denoted by concept-words is dubious, and the notion of sentences denoting truth-values is unmotivated; as Davidson points out, sentences are not used in language as sin- gular terms (Davidson 2005, p. 145). From that, it follows that predicates are not functional expressions. However close to a solution to the problem, Frege did not solve it; according to Davidson, the modern history records only sidesteps, for instance, Russell’s struggle with the notion of propositions as concrete objects and Bradley’s regress at the same time (Russell 1903) or Strawson’s reintroduction of predicates indicating universals. Disappointing as it may be, the history of the problem contains nevertheless the hints for a solution, to which I turn. The history of failed attempts allows Davidson to extract the following con- ditions on a theory of predication, which can be summarized as follows (see Davidson 2005, pp. 141–7): 1. Associating predicates with objects (universals, properties, relations, sets) 1 Davidson does not explicitly acknowledges this, but I think he was very much influenced by Peter Geach’s criticism of the “two-name” theory of predication (cf. Geach 1962, §§27–8;1968). Reference and Generality is recommended, though, for covering the historical gap between Antiq- uity and Frege (Davidson 2005, p. 5). 2 must be avoided, because it will always lead to regress; this shows up in Plato, Aristotle, Frege, Russell, and Strawson, but is avoided by Quine2; 2. It is essential to separate the idea that predicates introduce generality into sentences from that that they introduce abstract objects into the subject- matter of sentences; this is a clear consequence of the former; 3. The problem can be met only under a “clear conception” of the logical form of sentences; this is achieved by Frege; 4. A satisfactory account must relate predication to the truth of sentences; this is also Frege’s contribution, though it pushes him directly into the failures noted above. Davidson’s point is that Tarski’s semantic conception of truth (1935) meets all these conditions and can be converted into a theory of predication. Before discussing in more detail Davidson’s positive proposal, I want to comment on the conditions he sets and his arguments that alternative theories cannot meet them. 2 Associating predicates with entities leads to regress This may be so, but semantic theories have usually enough resources for stopping the regress. For instance, Tarski’s own method makes use of set theory in order to convert the recursive definition of satisfaction into an explicit definition. This amounts to taking set-membership as a model for, or representation of, predica- tion; this has become quite standard in the literature. But the solution does not in- troduce regress, for the mentioned relation is assumed as primitive, and its mean- ing is constrained by the membership axioms (e.g., the corresponding Zermelo- Fraenkel axioms), just as the meaning of logical constants is determined by the syntactic clauses of the calculus. A brief survey of recent literature on plural lan- guages shows that this solution is not the only one available; set-membership can be replaced by various relations, e.g. “is/are among” (McKay 2006, Ch. 6), or “is one of” (Yi 1999; Oliver and Smiley 2006). A traditional solution to the same effect is Ben-Yami’s copula, with the meaning determined by the derivation rules of the deductive system (Ben-Yami 2004). What all these approaches have in com- mon is a primitive representation of the predication relation in natural language sentences by means of a formal device. More important, they all rely on a previ- ous understanding of predication as, indeed, a “basic combination” (Quine 1960, p. 96). I do not want to imply that all these solutions are equal, only that the semantic machinery is working. 2 And also by Geach, as mentioned above. Geach explicitly claims that “predicables” (expres- sions that can become predicates) do not name anything (1962, pp. 57–9). Geach’s positive solution is not discussed, being considered too Fregean (Davidson 2005, p. 5). This seems hardly right, given the fact just noted. 3 If this is granted, then Strawson comes out on the part of the angels, together with Quine. Though Davidson is right in criticizing Strawson’s earlier take on Quine (Strawson 1961) for lack of a notion of a predication that assigns a clear role to the copula (Davidson 2005, p. 113), Strawson’s later conception of pred- ication avoids this problem by clarifying how several functions are fulfilled in a sentence. He distinguishes three functions: that of specifying a particular (or several particulars), that of specifying a general concept, and that of presenting the particular(s) and concepts as part of a unitary “propositional combination” (Strawson 1974, p. 22), the function he also calls “predicative linkage or mutual assignment” (p. 30). Strawson is quite explicit in claiming that this last function does not require a separate expression in the sentence, so no more concepts come into play (p. 22). The function is assigned to the predicate as well, and the linguis- tic copula becomes part of it (p. 30). Of course, this does not blur the difference between the two; whereas Quine explicitly denies that predicates contribute enti- ties to the sentence, Strawson explicitly allows that they do. But in stabilizing the status of the copula as part of the “grappling machinery” (Strawson 1974, p. 30), he does not invite any Third Man to crowd the party. The upshot is this: you can have as many kinds of entities you want, if you are able to stop the regress somewhere. Quine may be completely right in not introducing entities for predicates, but his reasons are only in part metaphysical; the other part is that he can do without them. Strawson (as well as the others) may be just as right as Quine for introducing them, both because of metaphysics, and because he can do with them. The “may”, in both cases, is a matter of meta- physics. Davidson does not provide any reason why having two sorts of entities is as bad as three, or many. His argument depends, I think, on assuming that associating predicates with universals etc. is advanced as the complete explanation of predication, and has lit- tle or no force against views that make the predicates’ semantic values only part of the story. In the cases briefly considered in this section syntactic rules, gov- erning the possible combinations of symbols and transformations of sentences, are employed to constrain the semantics of sentences. He seems here to disregard the connection between syntax and semantics. Given Davidson’s own emphasis on compositionality requirements for theories of meaning, this is rather striking. In any event, this kind of argument marks a departure from his earlier view that deflating word-world relations need not have metaphysical impact: The theory gives up reference, then, as part of the cost of going empirical. It can’t, however, be said to have given up ontology. For the theory relates each singular term to some object or other, and it tells what entities satisfy each predicate. Doing without reference is not at all to embrace a policy of doing without semantics or ontology. (Davidson 1977, p. 223) If we want to keep the connection with ontology, it may be that our se- mantics is indifferent to what objects we assign to expressions, not to whether we assign them at all or not. This can be illustrated with an argument from 4 (McGinn 2000, pp. 55–8). The argument involves replicating Tarski-style seman- tics in the following fashion. On the standard approach, the truth-conditions of an atomic sentence “a is F ” are given by assigning to the name “a” an individual a, and to the predicate “F ” the set F of all those objects of which the predicate is true. These are the “first-level” extensions. The truth-conditions emerge in the usual fashion: “a is F ” is true if, and only if, a is a member of F . (1) McGinn proposes that, instead of assigning objects and sets, we assign “second- level extensions”: to names, the set of properties that the named object instanti- ates, and to the predicates, properties. The truth-conditions for the same sentence as above are (where A is the set of properties that a instantiates): “a is F ” is true if, and only if, F is a member of A. (2) A third possibility, he claims, is the “natural” one: assign objects to names and properties to predicates, yielding truth-conditions of the form (where φ is the property referred to by “F ”): “a is F ” is true if, and only if, a instantiates φ. (3) The conclusion he draws is that Tarskian machinery imposes very relaxed constraints on how we interpret the expressions of the language. The three se- mantic theories are (pairwise) isomorphic (there is a one-to-one correspondence between the axioms and theorems of each of the pair). Moreover, if we assume the identity of indiscernibles (two qualitatively identical entities have the same set of properties), we obtain a nice underdetermination argument for the Davidsonian view that truth conditions determine the semantic properties of expressions; for we get a set of sentences that has a unique set of truth conditions under all de- scriptions; but the truth conditions are described by three incompatible theories of the semantic features of the sentences, so the truth conditions are not sufficient to distinguish between the semantic theories. The obvious reply from Davidson is to reject the property theories, on account of making use of “creatures of dark- ness”; but this means doing metaphysics, and it is hard to see how this can be done without semantic guidance. The conclusion I wish to suggest is that understanding predication may re- quire placing the individuals (particulars, or maybe properties construed as such) against the greater scheme of things: classifying them as belonging to a kind, or group, or set, or ascribing them properties. Davidson’s first constraint may be a little too strict for his own good, and yet it does not adequately reject alternative approaches. 3 Predicates’ contribution to sentences The distinction between introducing generality and introducing entities is surely important, but it is equally important to understandmore clearly what it amounts 5 to. Tarski’s original definition (Tarski 1935) is stated for an object language which does not contain non-logical predicates, but only variables ranging over classes. Since there are no predicates, no entities can be assigned. The metalanguage, on the other hand, contains several predicates, interpreted as sets (e.g., the truth- predicate “T r ” is interpreted as the set of all and only the true sentences of the object language). This way of assigning extensions to predicates has become customary in providing semantics for logical calculi (e.g., the predicate calculus) when attempting to study their logical properties. Davidson acknowledges that and comments: We must not confuse the ontology of the explanatory machinery with the ontology of expressions whose semantics we are describing, even if most of the vocabulary of the machinery belongs to the language the semantics of which we are describing. (Davidson 2005, p. 158) Quine is surely aware of the distinction, as we all should be. But interpreting his views on the matter may prove more delicate than it appears to be. His doc- trine of schematic predicate letters, “dummies”, or “blanks” should be linked not only with his interest in spelling out ontological commitments in first-order for- malized languages, but also with his construction of alternative axiomatic set the- ories (see especially Quine 1953, chapters V and VI). The doctrine of schematic letters is partly motivated by ecumenism; if we equate predication with set mem- bership, on some set theories we end up with paradoxes; a way of dealing with this is avoiding that all expressible conditions on variables determine sets, that is, avoiding that all predications can be used to determine set membership. His set theory did not have this kind of problem, but the more common varieties did. Nevertheless, even then he allowed occasions in which predicates were assigned extensions, but the “F ”s and “G”s in symbolic notation are not really predicates, do not denote anything, and do not represent anything; they just mark the spots or gaps to be filled in by predicates. The difficulty of interpreting Quine’s position becomes salient if we contrast this theory of schematic letters with his conception of predication in Word and Object (Quine 1960). There he talks of general terms (usually count nouns) as “possess[ing] built-in modes, however arbitrary, of dividing their reference” (p. 91), and of singular terms as “being true of” only one object (p. 95), and of the “protean” character of mass nouns, that occur in sentences both in subject and in predicate position (p. 99), and of mass occurrences of count nouns. Neverthe- less, “Agnes is a lamb”, “Lamb is scarce”, “The brown part is lamb”, all count as predications, with “lamb” dividing its reference or not, accordingly (these are all Quine’s examples). Their subject-matter is one specific lamb, lamb meat, a piece of lamb meat, respectively. Extensions do not go away at this stage. Later still, in his Philosophy of Logic, he calls predicates “syncategorematic” and insists that they do not name anything, they are just “the other parties to predication” (Quine 1970, pp. 27f). But his focus is again on schematic pred- ication, as it occurs in logical theories. He does not deny that there are at- 6 tributes; only that attributes may enter sentences otherwise than as named en- tities or values of existentially bound variables. However, when it comes to defining truth, things become different. Quine defines sequences as ordered n-tuples of objects, by the Wiener-Kuratowski method, i.e., by construction from sets (p. 36), and defines truth in the usual manner, by defining satisfac- tion by sequences. But the connection between predicates and sets is not re- ally severed by the detour via satisfaction, since sequences are sets. Yet he al- lows, for model-theoretic purposes, use of “set-theoretic analogues” of schematic predication (pp. 51ff). Logicians working in model theory and not sharing all Quine’s scruples have a more direct approach, and talk of predicates as denoting subsets of the domain, just as individual constants name elements thereof (e.g., (Tarski, Mostowski, and Robinson 1953, p. 8)). I think we should bear in mind though that Quine’s scruples arise in the context of logical theories and their for- malized languages. If the interpretation sketched above is correct, for him there is a gap between the natural language and its first-order logic or set-theoretical ana- logues. The former is neither represented by, nor translated, but “paraphrased” into the latter. Given this difference, it may be both useful and correct to distinguish two senses of the generality of predicates3. On the one hand, when the focus is on regimentation in formal languages, we have a kind of non-committal generality that amounts only to: predicates in formal languages are general in that they have argument places open to quantification. This is perfectly similar with Frege’s notion of the “unsaturatedness” [Ungesättigtheit] of concepts (Frege 1892a), but without the weird metaphysical consequences. Here we have a case of subtle employment of the use-mention distinction on Quine’s part: predicate letters are “unsaturated”, not some entities. Indeed, this kind of ge