Abstract
Standard compositionality is the doctrine that the semantic content of a compound expression is a function of the semantic contents of the contentful component expressions. In 1954 Hilary Putnam proposed that standard compositionality be replaced by a stricter version according to which even sentences that are synonymously isomorphic (in the sense of Alonzo Church) are not strictly synonymous unless they have the same logical form. On Putnam’s proposal, the semantic content of a compound expression is a function of: (i) the contentful component expressions; and (ii) the expression’s logical form. Kit Fine recently expanded and modified Putnam’s idea into a sweeping theory in philosophy of language and philosophy of mind. The present paper is a detailed critique of Fine’s “semantic relationism.” Fine’s notion of coordination is explained in terms of the familiar pragmatic phenomenon of recognition. A serious error in Fine’s formal disproof of standard Millianism is exposed. It is demonstrated furthermore that Church’s original criticism of Putnam’s proposal can be extended to Fine’s semantic relationism. Finally, it is also demonstrated that the positive position Fine proffers to supplant standard Millianism is in fact exactly equivalent to standard Millianism, so that Fine’s overall position not only does not displace standard Millianism but is in fact inconsistent.
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Notes
Church (1954). Expressions are synonymously isomorphic if they have the same free variables and one is obtainable from the other by a sequence of applications of: (i) alphabetic changes of bound variable; (ii) replacements of a component expression of a given type (e.g., a predicate) by a strictly synonymous (having the same semantic content) simple (non-compound) constant of that same type; and (iii) replacements of a component simple constant of a given type by a strictly synonymous expression (simple or compound) of that same type. Synonymous isomorphism is a very restrictive notion of synonymy (excluding even, e.g., passive/active transformations), yet synonymously isomorphic expressions need not have the same (most discriminating) logical form.
Fine says that “it will be convenient to think of coordination … as a relation between individual uses of a name,” where “an individual use is, in effect, a way of collecting together internally linked [i.e., intra-idiolect coordinated] tokens” (Semantic Relationism, p. 108). Fine does not speak of occasions of use. He treats the coordination of expression occurrences as a binary relation between occurrences within a sequence of sentences, rather than between occurrences within a single sentence, assigning as content to a sequence of sentences a coordinated sequence of propositions (pp. 52–57). The move to coordination within sequences of sentences is inadequate to take account of the fact that a single occurrence may be differently coordinated on different occasions of use. Occurrences of ‘London’ and ‘Londres’ (as names for London, England) within a sequence of sentences might be coordinated by one bilingual speaker and not by another.
This point is related to the issue, to be addressed below, of whether coordination is a semantic phenomenon, as Fine insists, or pragmatic, as I maintain. Relativization to occasions of use (or to utterances, or the like) is typically pragmatic.
Fine has confirmed this. He defines a coordination scheme for a sequence of uncoordinated propositions as an equivalence relation on their proposition-component occurrences (pp. 55–56). Also, later (pp. 111–112) he appears to assume that coordination is transitive. However, this is in the course of an argument that it is not (pp. 105–121). The assumption of transitivity might be regarded as for a reductio.
Fine prefers to say that the occurrences indicate that their common object “is represented as the same” (comments on an earlier draft—hereafter simply “comments”). This is problematic. (Represented by what? The same as what? What is it to represent a single object x “as R” where R is a binary relation (to represent x as taller, as east, as distinct, as the same), unless it is to represent x as bearing R to x? What is it to represent x without representing x as the same as x?) Presumably Fine means that occurrences x and y jointly represent that there is a single content semantically expressed by the expressions of which x and y are occurrences, or a single individual of which each of x and y is an occurrence.
A pair of occurrences can be neither positively coordinated, nor negatively* coordinated, nor uncoordinated*. There are alternative possibilities. Fine’s text (pp. 54–57) does not clearly decide the relevant issues.
See the preceding note. Fine’s notion of positive coordination might be seen as the existential generalization of a special case of a 4-place relation: x and y jointly represent z and w as the same thing. One may then say that x and y jointly represent z as the same thing (3-place) iff x and y jointly represent z and z as the same thing. Moreover, Fine requires that representing-as-the-same is factive: if x and y jointly represent z and w as the same thing, then z = w (p. 40; but see also p. 136n14). Then to say that x and y are positively coordinated is presumably to say that there is an object z such that each of x and y individually represents z, and x and y jointly represent z as the same thing.
Fine does not use the word ‘jointly’ but it conforms to his intent that coordination is not reducible to semantic attributes of individual expression occurrences other than semantic-relational properties toward other occurrences (p. 22). For x and y to jointly-represent z as the same thing, more is required than the existence of an object w such that each of x and y represents z as w. Occurrences of ‘Cicero’ and ‘Tully’ represent Cicero as Cicero, but an occurrence of ‘Cicero’ and an occurrence of ‘Tully’ do not jointly represent Cicero as the same thing.
See again note 5. That Fine takes representing-as-the-same to be factive suggests, contrary to his assertion that “a coordination scheme does not convey any information” (comments), that the phenomenon he calls ‘coordination’ imparts, or even entails, at least the information that the occurrences in question are co-occurrences—even if the scheme is not itself information and even if the imparted information is trivial. It also suggests that the phenomenon is intimately related to the familiar epistemic notion of recognition. Coordination between occurrences x and y may be, roughly, that of which one is aware in recognizing x and y as co-occurrences, and of which one is ignorant in failing to recognize x and y as co-occurrences.
Fine’s criticism (pp. 69–70) of my account of the semantic content of lambda abstraction misinterprets me as holding that ‘Cicero shaves Cicero’ semantically expresses the same proposition as ‘λx[x shaves x]Cicero’ (i.e., ‘Cicero is a thing that shaves itself’) and a different proposition from ‘Cicero shaves Tully’—the reverse of my actual view.
Fine says that his notion is different from Putnam’s on the ground that Putnam’s is syntactic and pre-semantic (p. 41). Putnam’s idea no less than Fine’s concerns semantic content. Putnam’s tightening of standard compositionality invokes logical form. Fine says that his account instead invokes “semantic connections” or “meaning relationships” among the component expressions (pp. 25–26).
Kripke (1976b). Page references throughout are to this reprinting.
Where ϕβ is any result of substituting free occurrences of a singular term β for free occurrences of the individual variable α in an open formula ϕα, λ-expansion licenses the inference from ϕβ to ⌜λαϕαβ⌝, read: β is an object α such that ϕα.
Fine refers to the argument form ‘Fx; Gx ∴[F&G]x’ as ‘adjunctive inference’ (p. 82). Fine defends his usage (comments) on the ground that one can perform adjunction directly on predicates. This is misleading. The inference is valid only when the predicates share a common argument. Pierre has no difficulty performing adjunction to infer ‘Londres is pretty and London is a capital’ from its separate conjuncts. Reflexive λ-expansion is applicable to propositions p xx that are not of the particular form: Fx & Gx. A variant of Kripke’s puzzle arises with any singular proposition p xx in which a single object recurs, e.g., the proposition that London is not prettier than London.
Salmon (2011a). I do not accept that either of the two attributions, or their conjunction, has more than one (relevant) reading—let alone that there is a natural (semantic) reading of the conjunction on which it is false. Kripke explicitly excludes de re readings as not pertinent to the question raised in the puzzle. I ignore as also irrelevant readings that concern London, Ontario. So do Kripke, Fine, and everyone else.
In my doctoral dissertation I defined intrinsically relational properties as those that involve direct reference to an individual, and purely qualitative properties are those that do not. See my Reference and Essence (Amherst, NY: Prometheus Books, 1981, 2005), pp. 19–20.
The reasoner conceives of R by description, as the property-conjunction of x’s purely qualitative properties, not by acquaintance (Russell). Is this sufficient for the reasoner to infer of R, de re, that x has it and all things that have it are purely qualitatively indiscernible? Millianism per se is neutral.
This assumption is curious. The proof’s reliance on it would weaken the theorem slightly. In fact, however, it appears that the assumption plays no role in the argument.
On Fine’s definition of ‘manifest consequence’ in Semanitc Relationism (pp. 48–49), every proposition is a “manifest consequence” of any proposition that lacks multiples occurrences of a single individual. Also, the proposition that Fb & Gb is a manifest consequence of the proposition that Fa & Ga, whereas the proposition that ∃xFx is not. These results clash with Fine’s intent. (Fine also offers an explanation of manifest validity in terms of coordination, at p. 136n14.) Here is a possible patch: Say that a proposition p′ is an occurrence-substitution instance of a proposition p if p′ is the result of replacing all individual-occurrences in p by individual-occurrences (allowing for replacement of distinct occurrences of the same individual—i.e., of co-occurrences—by occurrences of distinct individuals). Where K and K′ are sets of propositions, say that K′ is an occurrence-substitution instance of K if K′ is a set of occurrence-substitution instances of the elements of K. Where a set K′ of propositions is an occurrence-substitution instance of K and a proposition p′ is an occurrence-substitution instance of p, say that 〈p, p′〉 is a reflection of 〈K, K′〉 if for any individuals x and x′, if p′ replaces an occurrence in p of x with an occurrence of x′, then some element of K′ replaces an occurrence of x in some element of K with an occurrence of x′. Then p is a manifestly* valid consequence of K if for any occurrence-substitution instance K′ of K there is an occurrence-substitution instance p′ of p such that 〈p, p′〉 is a reflection of 〈K, K′〉 and p′ is a classically valid consequence of K′. If an argument is manifestly* valid, then perforce it is classically valid (Thanks to Luke Manning and Max Weiss for discussion).
See the preceding note. Say that an argument is recurrence-independently valid if every occurrence-substitution instance of it is classically valid. If an argument is recurrence-independently valid, then perforce it is manifestly* valid.
Cf. also Semantic Relationism, pp. 119–120.
The description “the city called ‘Londres’” may be replaced with ‘the city called by a name that may be transcribed using a sequence of geometric figures of the sort …’ to be filled in by a purely qualitative characterization of the sequence of geometric figures 〈‘L’, ‘o’, ‘n’, ‘d’, ‘r’, ‘e’, ‘s’〉; similarly mutatis mutandis with regard to the description “the city called ‘London’”. The replacement descriptions might be thoroughly descriptional.
Even the expanded premise-set {x = the ϕ; y = the ψ; the ϕ = the ψ; the ϕ has F; the ψ has G; ∃x(Fe x & Px); ∃x(Ge x & ~Px)} is perfectly consistent.
Special thanks to Teresa Robertson and Nathaniel Tabris for discussion of this point. Tabris first suggested to me that Fine might be assuming that in order for I to legitimize applications of the relevant instances of reflexive λ-abstraction, they must be replaced with arguments that invoke I as a premise and are manifestly valid in Fine’s sense. Fine has confirmed (comments) that Tabris’s suggested interpretation is correct. I had dismissed Tabris’s suggestion at the time because it seemed a poor fit with the text, excessively speculative, and even uncharitable. As I shall argue, the proposed interpretation has Fine tacitly and gratuitously attributing to standard Millianism a thesis incompatible with it, or at least completely contrary to its spirit, and then refuting the straw-man theory by deriving from the fabricated thesis a consequence completely contrary to the spirit of Millianism.
The first conjunct expresses that R is quasi-reflexive, e.g., that anyone who loves is narcissistic. In the general case, Fine tacitly assumes that the natural hypothesis, and apparently the only hypothesis to which the standard Millian can appeal, is that the reasoner who appears to perform reflexive λ-expansion on p xx , if rationally justified, does not in fact do so, and instead is in possession of information either entailing that for any individual y, if p yz is true for some individual z then p yy is also true, or else entailing that for any y, if p zy is true for some z then p yy is also true.
Two pages before presenting his objection Fine says that the standard Millian “must work with a conception of propositional knowledge that is closed under manifest rather than classical consequence” (pp. 80–81). It should be noted that no notion of proposition knowledge is closed under logical consequence, manifest or classical. If knowledge were closed under logical consequence, mathematicians could never discover any new theorems. More to the point, recurrence-dependently valid inferences require recognition on the part of the reasoner of a recurring individual in order to be justified, but this does not have the consequence that only manifestly valid inferences are justified.
Fine maintains that the burden of proof is not on him to justify his tacit assumptions, but on me to show that the assumptions are unjustified (comments). I leave it to the reader to adjudicate this issue.
Fine says that on his account, “given the appropriate coordination, the content of the argument as a whole has a form that renders it manifestly valid” (comments). The coordinated argument—‘Fx; Gx ∴ x has F&G’ together with a coordination scheme that “represents x as the same” in the two premises—is indeed valid (cf. Semantic Relationism, p. 136n14). However, reflexive λ-expansion is not manifestly valid according to Fine’s definition (pp. 48–49). Nor is it manifestly valid according to the patch suggested in note 17 above, or according to Fine’s explanation in terms of coordination (p. 136n14). Let C be a scheme that coordinates the two occurrences of ‘x’ in the premises. If the argument as a whole is manifestly valid, as Fine asserts, then does invoking C in lieu of I at line 11 validate the deduction as a whole? (see note 7). Fine’s remarks might even be modified accordingly: “Since the inference to ⊥ [together with C, as a whole] is manifestly valid, the thinker is justified in inferring ⊥ from ∃x(Fe x & Px) and ∃x(Ge x & ~Px) [together with C, as a whole].” If so, then Fine’s version of Millianism faces the very problem he misattributes to standard Millianism. Be that as it may, as regards Fine’s argument, his own alternative to standard Millianism fares no better.
Cf. Frege’s Puzzle (Atascadero, CA.: Ridgeview, 1986, 1991), at pp. 103–118. See also note 7 above.
See the preceding note.
Frege’s Puzzle, pp. 119–121; Salmon (1989a, at p. 1040).
Fine rejects this suggestion (comments). He says that if we suppose that Pierre grasps the proposition that London is pretty by means of different guises, we can hardly think of these guises as coordination schemes because they are not connected. I would have thought that it is essential to the nature of coordination schemes that one coordination scheme s might positively coordinate distinct occurrences, x-on-occasion-o and y-on-occasion-o′, while another scheme s′ negatively coordinates x-on-o and y-on-o′. Cousteau might positively coordinate any relevant occurrence (on an occasion) of ‘London is pretty’ with any relevant occurrence of ‘Londres est jolie’, while Pierre negatively coordinates any occurrence of the first sort with any occurrence of the second.
Cf. Kaplan, “Words,” loc. cit., note 1 above. I believe by ‘common-currency expression’ Kaplan means a specific expression.
Matthew Griffin suggests that Fine’s proposal might be expanded to provide a necessary and sufficient condition in cases where the auditor understands the discourse, but not more generally. For example, Fine might be prepared to say that if an auditor understands ϕαβ on o, then x and y are coordinated on o iff the auditor knows by his/her understanding of ϕαβ that x and y are co-occurrences on o.
Later in Semantic Relationism, again discussing the phenomenon of distinct individuals with the same generic name, he says that “it will be convenient to think of coordination not as a relation between tokens of a name but between what one might call individual uses of a name. Thus Peter, whose use of the name is fractured, will have two individual uses of the name ‘Paderewski,’ while we, whose use is unfractured, will have one individual use of the name.” Furthermore, in cases of intra-idiolect interpretation “any failure of the speaker to see two names that are in fact the same as the same should be attributable to a deficiency in his attempt to apply the semantics of the language [idiolect] rather than to a deficiency in the semantics itself” (pp. 108–109; see note 7 above). Knowing of two men by the generic name ‘Cicero’ and asking whether the two occurrences of ‘Cicero’ as used co-designate, the auditor is unaware that the occurrences were given the same “individual use.” In that sense, the auditor is ignorant of the pre-semantic fact that, as used, both occurrences are of the same disambiguated name. He does not interpret while missing the intended identification; he wishes to know what specific expressions are to be interpreted.
Fine contrasts ignorance of intra-idiolect coordination, evidently wherein such ignorance is pre-semantic, with ignorance of inter-idiolect coordination. However, both types are in this respect completely on a par: Ignorance concerning an occurrence of a generic expression, of what specific expression it is an occurrence of on a given utterance-occasion, is pre-semantic. (As he sets it up, Fine’s test case is in fact intra-idiolect. It can also be modified into a case in which the two relevant uses of ‘Cicero’ were made by the auditor himself, now not remembering which use he made in one of the two occurrences. “Was it Cicero 1? Or Cicero 2?”).
Fine evidently believes (comments) that whereas co-designative occurrences of ‘Paderewski’ are positively coordinated in English, not all co-occurrences (on occasions) of ‘Paderewski’ are coordinated in Peter’s idiolect. Presumably he believes likewise that occurrences of ‘London’ are not positively coordinated with occurrences of ‘Londres’ in Pierre’s idiolect of Frenglish. I believe this misplaces pragmatic-epistemic phenomena within semantics proper. Co-designative occurrences of ‘Paderewski’ are as much alike purely semantically in Peter’s idiolect as they are in English. Similarly for occurrences of ‘color’, ‘colour’, different pronunciations of ‘tomato’ or ‘either’, etc.
A potential case in point is provided (ironically) by Kripke’s views on alternate-base notations for natural numbers. Kripke believes that the binary-number two, designated by the binary-notation ‘10’, is composed in a particular way of the binary-number one and the binary-number zero, and is therefore not the very same entity as the decimal-number two, which is not so composed. In short, Kripke does not coordinate binary-notation occurrences of ‘10’ with decimal-notation occurrences of ‘2’. But even if Kripke’s view of alternate-base notations is incorrect (as I believe), he understands bi-notational discourse as well as anyone.
That two expressions are synonymous is a purely semantic fact but it is typically not a basic (axiomatic) fact of pure semantics. It is instead a derived purely semantic fact, a consequence of the purely semantic facts concerning each expression that it means what it does. Fine attempts to get at what is significant about this case by drawing a bewildering array of related, and inter-related, distinctions (ibid., pp. 43–50): between semantic in the broad sense and semantic in the narrow sense; between the domain of semantic facts and the domain of semantic information; between semantic facts and the special sub-class of semantic requirements (Fine’s text does not consistently adhere to this terminology); between facts that are semantic as to topic and the special subclass of facts that are semantic as to status; between classical consequences of semantics and the special sub-class of manifest consequences; even Kant’s distinction between noumena and phenomena; and more (see note 17 above). I believe, perhaps incorrectly, that in the present case these fine distinctions, excluding the last cited, can be reduced to two, with which they are in any case at least very closely related: (i) a Carnapian distinction between pure and applied semantics, analogous to the distinction between pure and applied mathematics (cf. p. 135n5); and (ii) the distinction between manifest and non-manifest validity. Regarding the former distinction, cf. Salmon (1993a, b), both reprinted in Content, Cognition, and Communication, chapters 9 and 10, pp. 169–190. Regarding the latter distinction, cf. Salmon (1986, 1992), both reprinted in Content, Cognition, and Communication, chapters 2 and 3, pp. 32–66; and Salmon (2011b) (Perhaps a third distinction is needed: that between basic and derived semantic facts).
Cf. Salmon (1991); reprinted in Content, Cognition, and Communication, chapter 16, pp. 298–308.
Cf. Frege’s Puzzle, pp. 103–109.
Recall also that on Fine’s view, coordination is a binary relation, so that a pair of expression occurrences are either positively coordinated absolutely or negatively coordinated absolutely, not relative to a cognizer on an occasion of use.
Fine has responded (comments) that the foregoing criticisms ignore the fact that he takes a reductive stance toward the notion of coordinated content. Fine’s reductionism will be considered in the closing paragraphs of the present essay.
The defining condition for positive coordination could be modified to require that A recognize x and y as co-occurrences. See note 7. Other options are possible.
A fourth mode of coordination should be acknowledged. Pierre could come to wonder, “Maybe London and Londres the same city.” In that case he positively coordinates the occurrences of London in the proposition that London is no prettier than London (“London is no prettier than London”)—and consequently he does not uncoordinate them—but he also reserves judgment without negatively coordinating (“Londres is no prettier than London”). We may say that in this case Pierre both positively coordinates the relevant occurrences and withholds coordinating them, although he neither negatively coordinates nor uncoordinates them.
We may assume that in considering an individual z, A takes z in a certain way, by means of a certain guise, where these ways of taking individuals or guises satisfy the following conditions: A can take a single individual by means of distinct guises; A positively coordinates occurrences x and y iff there is guise g such that A takes the object as occurring in x by means of g and A takes the object as occurring in y also by means of g; and if A negatively coordinates occurrences x and y, then ∃g∃g′(g ≠ g′ & A takes the object as occurring in x by means of g & A takes the object as occurring in y by means of g′), but the converse does not obtain. A might wonder instead of negatively coordinate. We may posit that A withholds coordinating x and y iff ∃g∃g′(g ≠ g′ & A takes the object as occurring in x by means of g & A takes the object as occurring in y by means of g′).
Church, “Intensional Isomorphism and Identity of Belief”; see note 2 above. Putnam originally proffered his modification of compositionality in response to the problem of nested attitude operators posed by Mates (1950, p. 215). Church’s response (which employs ‘fortnight’ and ‘period of fourteen days’ in place of ‘bachelor’ and ‘unmarried man’) was aimed primarily at Mates, and secondarily to rebut Putnam’s proposed modification “in the sense of showing it to be superfluous.” Church’s criticism is here applied directly against Putnam’s and Fine’s versions of compositionality (see note 9 above), in the sense of showing them to be not merely superfluous but seriously implausible. I reply to objections in Salmon (2001); reprinted in my Metaphysics, Mathematics, and Meaning (Oxford University Press, 2005), pp. 344–364.
On Fine’s claim of ambiguity, see for example Semantic Relationism, pp. 54–57, 97–98, 104. See also note 13 above. Assuming Millianism, the same argument is applicable to (1′) ‘Tully admires Cicero’ and (2′) ‘Cicero admires Cicero’. The full force of the argument is revealed once it is acknowledged that the Putnam view cannot plausibly be restricted to proper names of individuals. It must be extended, for example, at least to single-word natural-kind terms like ‘groundhog’. If it applies to ‘vixen’, then it applies equally to ‘bachelor’. Cf. my “Generality,” Philosophical Studies (forthcoming 2012).
Cf. Kripke (1979).
According to standard Millianism, it is a semantic requirement (a manifest theorem of pure semantics) that
R α=β: For any designating proper names α and β, ⌜α = β⌝ expresses the singular identity proposition in which the designatum of α occupies the subject position and the designatum of β occupies the object position.
Here ‘α’ and ‘β’ are bound syntactic variables ranging over specific proper names. It is a manifest consequence of R α=β, and hence according to standard Millianism it is also a semantic requirement, that
R α=α: For any designating proper name α, ⌜α = α⌝ expresses the singular identity proposition in which the designatum of α occupies both the subject and object positions.
The deduction of R α=α from R α=β involves reflexive λ-expansion, but no individual recurs in the contents of R α=β or R α=α to render the entailment non-manifest (see note 17 above). Given the further semantic requirement that Cicero 1 is a specific proper name of Cicero/Tully, according to standard Millianism it is a semantic requirement that ⌜Cicero 1 = Cicero 1⌝ expresses the singular identity proposition in which Cicero/Tully occupies both the subject and object positions.
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Acknowledgments
I presented some of this material at a number of venues. I am grateful to my audience’s reactions. I am especially grateful to Murat Aydele, Roger Clarke, Teresa Robertson, Ori Simchen, Lourdes Valdivia, Max Weiss, and Dean Zimmerman for comments and discussion of an early draft, and to the participants in my seminars at UCSB during Spring 2010 and at the CUNY Graduate Center during Fall 2010 for comments and observations concerning some of the arguments and issues raised here, especially Luke Manning, Ian Olasov, Clark Sexton, and Nathaniel Tabris. Special thanks go to Kit Fine, who participated in the CUNY seminar and clarified many aspects of his book, and also provided detailed responses to an earlier draft.
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Salmon, N. Recurrence. Philos Stud 159, 407–441 (2012). https://doi.org/10.1007/s11098-011-9773-7
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DOI: https://doi.org/10.1007/s11098-011-9773-7