Appeared in Philosophical Studies 128 (2006), 669-682.

Kripke’s revenge

            Millianism says that the semantic content of a name (or indexical) is simply its referent. This thesis arises within a general, powerful research program, the propositionalist approach to semantics, which sets as a goal for philosophical semantics an assignment of entities – semantic contents – to bits of language, culminating in the assignment of propositions to sentences. Communication, linguistic competence, truth conditions, and other semantic phenomena are ultimately explained in terms of semantic contents.

            Over 100 years ago Frege (1892) pointed out the problem with Millianism: sentences containing co-referential names seem semantically inequivalent. ^éa=a^ù is trivial, a priori, etc.; ^éa=b^ù is not, even if a and b have the same referent; f(a) and f(b) embed differently in the scope of propositional attitude verbs.

            About thirty years ago, Keith Donnellan (1972), David Kaplan (1989), and especially Saul Kripke (1972/1980) pointed out the problem with denying Millianism. Within the propositionalist tradition, the natural alternative to Millianism is that the semantic content of a name is the same as that of an identifying definite description. But, new linguistic data suggested, knowledge of identifying descriptions is not required for linguistic competence. Moreover, definite descriptions do not fix the referents of names, nor do names behave like descriptions in the scope of modal operators.

            The data of Kripke et al. is genuinely puzzling. It in no way undermines the old Fregean arguments against Millianism; it simply is new, conflicting data. Thus, many recent theories seek reconciliation, accommodation of both Kripkean and Fregean data. Such theories often complicate the background propositionalist approach, for instance by incorporating contemporary insights into pragmatics.

            Scott Soames’s excellent book Beyond Rigidity is in this tradition. Soames retains the core of Millianism by claiming that sentences containing names stand in a relation of semantic expression to singular propositions – propositions containing the referents of those names as constituents. But he additionally invokes a relation of assertion. Given an appropriate contextual setting, a speaker can use a sentence to assert a partially descriptive proposition other than the singular proposition semantically expressed by that sentence. Speakers often confuse semantic expression with assertion, and intuit truth values for sentences that match those of asserted rather than semantically expressed propositions. Soames supports his distinction between assertion and expression with convincing evidence, then uses it to reconcile Kripke with Frege.

            Suppose that Clark Kent, chagrined after the failure of his amorous overtures, remarks to Jimmy Olson:

            (L)      Lois Lane does not believe I am handsome.

When dressed in reporter’s clothes and talking to Olson, Kent does not (primarily) intend to assert the proposition semantically expressed by (L), for he knows that proposition is false. (He knows well that Lois does believe that Superman is handsome.) Kent intends rather to assert a partly descriptive proposition, perhaps the proposition Lois does not believe that Kent, the milquetoast reporter, is handsome. In the context, Kent descriptively enriches (the semantic content of) ‘I’ with (the semantic content of) the description ‘the milquetoast reporter’. Our intuition that Kent’s utterance of (L) is true, is explained by the truth of this asserted proposition, despite the falsity of the proposition semantically expressed by (L).

            Soames’s approach appears to accommodate the Fregean data. But the old arguments for Millianism return to haunt Soames’s hybrid Millian view, or so we will argue.

            The Kripkean modal argument against descriptivism was that if ‘Aristotle’ is synonymous with ‘the teacher of Alexander’, then, scope or rigidification tricks aside , we get the clearly incorrect verdict that ‘Aristotle might not have taught Alexander’ is false. Soames’s theory handles this example smoothly. It would be natural not to take a speaker sincerely uttering ‘Aristotle might not have taught Alexander’ to be descriptively enriching ‘Aristotle’ with ‘taught Alexander’ — the enrichment would render the asserted proposition obviously false. The theory correctly predicts that ordinary utterances of ‘Aristotle might not have taught Alexander’ seem intuitively to be true.

            But Soames’s theory allows a context in which a person asserts a true proposition by uttering (A).

            (A)      It is necessary that: (If Aristotle exists, then) Aristotle taught Alexander

The speaker and audience would merely need to descriptively enrich ‘Aristotle’ with ‘teacher of Alexander’. In fact, though, there is no context in which (A) seems true. So, there is no context in which (A) can be used to assert a true proposition. Relatedly, assuming that ‘Michael Jordan’ can be descriptively enriched by ‘is tall’, the theory predicts the possibility of asserting a truth using ‘It would be impossible for Michael Jordan to be short’. In each case the theory overgenerates. It predicts the potential for asserting true propositions with certain sentences, which potential seems not to exist.

            Soames cannot reply that the appearance of falsity in these examples is due to the propositions semantically expressed. These semantically expressed propositions are indeed false, but this reply clashes with what Soames says about (L). The moral there was that intuitive truth value is not a function of semantic truth value, but rather a function of the truth value of the contextual descriptive enrichment. We intuit that Kent’s utterance of (L) is true. We have this intuition, Soames says, because the contextual descriptive enrichment of (L) is true. Why then do we lack analogous intuitions concerning (A)?

            Here is a version of Kripke’s semantic argument, directed against Soames’s theory. About to give a lecture, Gödel is introduced by his host as follows: “We are very pleased to have the person who proved the incompleteness of arithmetic with us today. Professor Gödel will speak on logic.” Gödel’s host believes the partially descriptive proposition Gödel, the person who proved the incompleteness of arithmetic, will speak on logic, and even intends the audience to come to believe this proposition. Thus, it seems that on Soames’s theory, the host descriptively enriches ‘Gödel’ with ‘the person who proved the incompleteness of arithmetic’, and asserts the descriptive proposition when he utters (G).

            (G)      Professor Gödel will speak on logic.

Now suppose that, as in Kripke’s example, Gödel never proved the incompleteness of arithmetic. Someone else, Schmidt, did. Soames must then say that the host asserted something false by uttering (G). Doesn’t that seem wrong?

            Soames might reply that the host asserted a true proposition – the singular proposition that is the semantic content of (G) – and that we intuit that the host’s utterance is true because we consider this proposition. But recall what Soames says about (L). We intuit that Kent’s utterance of (L) is true. Falsity of (L)’s semantic content injects no whiff of doubt; with (L), intuition strongly favors the descriptive enrichment over the semantic content. But in the case of (G), according to the reply under consideration, intuition favors the semantic content over the descriptive enrichment. Intuition is clear that the host’s utterance of (G) was true. The falsity of (G)’s descriptive enrichment injects no whiff of doubt. The reply introduces an inexplicable asymmetry between (G) and (L).

            For a third argument, continue the Gödel example. Smith and Jones arrive late to Gödel’s lecture, miss the first sentence of the host’s introduction, but still hear the host utter (G). Only Smith and Jones know of Gödel’s theft, though they mistakenly think that everyone knows. Smith whispers to Jones: “Gödel stole the incompleteness proof from Schmidt! I really doubt he’ll have the nerve to give a talk on logic. Surely he’ll talk about something else. Still, the host believes that Professor Gödel will speak on logic. So perhaps he will.” According to Soames, by uttering ‘The host believes that Professor Gödel will speak on logic’, Smith primarily asserts the descriptively enriched proposition The host believes that Professor Gödel, who stole the incompleteness proof from Schmidt, will speak on logic. Since the host believes no such thing, this proposition is false. Yet, as with (G), our intuition is that Smith’s utterance is true. There is no whiff of doubt. This example is inspired by Kripke’s (1979) disquotation objection to descriptivism. Kripke points out that if a sincerely utters f, an onlooker can disquote a – truly report her beliefs using the sentence ^éa believes that f^ù. Traditional descriptivism cannot accommodate this datum when the onlooker and a associate different senses with the names in f.

            Soames might reply that Smith not only asserts the false descriptively enriched proposition, but also some true descriptively enriched proposition, for instance The host believes that Professor Gödel, the man standing before us, will speak on logic. This true proposition, Soames might say, explains our intuition that Smith’s utterance is true. We do not find this reply convincing (intuitively, Smith asserts nothing false), but we can avoid it by using a more extreme example in which the beliefs of the attributor and subject differ radically. Imagine that Lex Luthor sincerely utters ‘Superman is strong and Clark Kent is not’. Jimmy then disquotes Luthor and utters (SC) to Perry White.

            (SC)    Lex Luthor believes that Superman is strong and Clark Kent is not.

Suppose Jimmy’s opinions about Superman are extremely different from Luthor’s. Jimmy thinks Superman has X-ray vision, Luthor does not; Jimmy thinks Superman is from Krypton, Luthor thinks he’s from Pocatello. If Jimmy is unaware of this difference of opinion, then nearly any descriptively enriched proposition that Jimmy would assert with (SC) would be false. Yet our intuition that Jimmy’s utterance of (SC) is true remains stable; Jimmy and Luthor’s differing opinions about Superman have zero effect. As before, Soames might say that our intuition pertains to the semantic content of (SC); as before this reply must be squared with what he says about (L). And the present case contains an extra obstacle to this reply: the semantic content of (SC) attributes to Luthor belief in a contradictory (singular) proposition. Why would Jimmy assert such a thing? Soames tends to appeal to descriptive enrichments in such cases.

            So far we have considered anti-descriptivist arguments based on particular intuitions, intuitions about the truth values of particular sentences. Other arguments draw on logical intuitions, intuitions concerning the validity of arguments. Particular intuitions put unconditional pressure on theories to accord a target sentence a certain status. Logical intuitions provide conditional pressure, to accord a certain status to a target sentence (the conclusion of an argument) if one accords that status to certain other sentences (the premises). Logical intuitions are not merely subservient to intuitions about particular sentences. They are independent, and indeed have the potential to clash with particular intuitions. Each sort provides independent data relevant to assessing linguistic theories.

            Is Soames’s theory consistent with anti-descriptivist logical intuitions? The question is not straightforward since Soames gives no account of intuitions about validity. We will argue that any natural extension of his theory to intuitions about validity will be vulnerable to objections similar to those to which descriptivism is vulnerable.

            For Soames, sentences can be used to assert different propositions in different contexts. Thus it is natural, from a Soamesian perspective, to focus on contextual logical intuitions: judgments made in contexts that certain claims follow, or fail to follow, from others. Such judgments may be elicited by questions. After Clark Kent utters (L), we may ask him: does it follow that there is someone such that Lois Lane does not believe he is handsome? If Clark agrees, he contextually intuits the validity of the following argument:

            Lois Lane does not believe that I am handsome.

            Therefore, $x Lois does not believe that x is handsome

            Define the argument asserted by S₁, ..., S_n/C, in a context, as the propositional argument whose premises are the propositions the speaker primarily asserts using S₁, ..., S_n in that context and whose conclusion is the proposition the speaker primarily asserts using C in that context. Similarly, define the argument expressed by S₁, ..., S_n/C, in a context, as the propositional argument consisting of the propositions semantically expressed in the context by S₁, ..., S_n and C. Should Soames take contextual intuitions of validity to be determined by arguments asserted or arguments expressed? Since Soames takes particular intuitions about truth values as concerning propositions asserted, not expressed, one might expect the parallel position on logical intuitions:

Pragmatic Position on Logical Intuitions: Speakers intuit in a context that an argument is valid iff the argument it asserts in that context is (propositionally) valid.

            In addition to its mesh with his position on particular intuitions, there is additional pressure on Soames to adopt the Pragmatic Position. Consider the following argument:

            A1.      Lois Lane believes that Superman flies.

                        Superman = Clark Kent

                        Therefore, Lois Lane believes that Clark Kent flies.

The argument expressed by A1 is valid. Nevertheless, speakers intuit that A1 is invalid (in practically every context). So it is natural for Soames to take these contextual logical intuitions to concern the argument that A1 asserts in those contexts.

            But the Pragmatic Position is problematic, for our logical intuitions are remarkably stable, more stable than one would expect given the above extension of Soames’s ideas to intuitions of validity. For instance, even if Lois descriptively enriches ‘Superman’ with ‘the strongest man on Earth’, she will not intuit that the following argument is valid.

            A2.      Superman flies.

                        Therefore, Superman, the strongest man on Earth, flies.

That is, even in that context, she will be unwilling to say: “Since Superman flies, it follows that Superman, the strongest man on Earth, flies”. Yet, since the argument asserted by A2 in the context is valid, the Pragmatic Position predicts that Lois will intuit, in that context, that A2 is valid.

            So perhaps Soames should say instead that our intuitions about an argument’s validity, in a given context, are sensitive to the arguments that it asserts in other contexts:

Trancontextual Position on Logical Intuitions Speakers intuit in a context that an argument is valid iff for all contexts, the argument asserted by that argument in that context is valid.

This view makes the correct prediction about our intuitions concerning A1, but does not predict that Lois will, in her context, intuit that A2 is valid, for in other contexts A2 can be used to assert an invalid argument.

            We are not altogether sure which account of logical intuitions Soames should prefer. Fortunately, it does not matter for our purposes, because our discussion can focus on (V).

            (V)      If speakers intuit in a context that an argument is valid, then the argument it asserts in that context is valid.

(V) is a consequence of both the Transcontextual and Pragmatic Positions. Moreover, the case that threatened the Pragmatic Position, that of A2, does not threaten (V), only its converse.

            It is difficult to see how Soames could deny (V). If (V) is incorrect, then in some context, a speaker intuits that an argument S₁, ..., S_n/C is valid even though the argument it asserts in that context is invalid. But, on the one hand, if the speaker intuits in that context that the argument is valid, she should be willing to utter ^éNecessarily, if S₁ and S₂ and ... and S_n, then C^ù. On the other hand, if the argument that S₁, ..., S_n/C asserts in that context is invalid, the speaker should also be willing to utter ^éPossibly, S₁ and S₂ and ... and S_n and ~C^ù, for the proposition she would thereby primarily assert in that context would be true. But surely no rational speaker would be willing to utter both of these sentences in the same context.

            Given (V), we can assess the impact of logical intuitions on Soames’s theory. We begin with a traditional argument against descriptivism concerning quantifying-in. Variables – or their natural language equivalents – are paradigmatically directly referential: the semantic content of a variable, relative to an assignment, is simply its referent on that assignment. This threatens descriptivism, given the apparent validity of such arguments as:

            A3.      a.         a believes that b is F

                        b.         $x x=b

                        c.         Therefore, $x a believes that x is F

where b is a proper name and ^éis F^ù is a simple, positive predication. For if b’s semantic content is (purely) descriptive then the premises could be true even if a believes no singular proposition of the form <o,F-ness>, and hence even if the conclusion is false.

            A3 does not threaten Soames, for if he makes certain assumptions he can explain our intuition that it is valid. He might, for instance, claim that if a speaker utters A3a, thus intending to assert a descriptively enriched proposition a believes that b, the G, is F, then in that context, by uttering A3c the speaker would assert the descriptively enriched proposition $x a believes that x, the G, is F. (This requires descriptive enrichment of the variable ‘x’, notice.) The argument asserted by A3 here is thus valid, consonant with (V).

            But now consider the following argument.

            A4.      a.         Superman = the superhero & Lois Lane believes that Superman can fly

                        b.         Therefore, $x (x = the superhero & Lois Lane believes that x can fly)

                        c.         Clark Kent = the milquetoast reporter & Lois Lane does not believe that Clark Kent can fly

                        d.         Therefore, $x (x = the milquetoast reporter & Lois Lane does not believe that x can fly)

                        e.         The superhero = the milquetoast reporter

                        f.         Therefore, $x (x = the superhero & Lois Lane believes that x can fly and Lois Lane does not believe that x can fly) (from b, d, and e)

Lines a, c, and e are the premises; b and d are intermediate conclusions; f is the final conclusion. Consider a context in which ‘Superman’ is descriptively enriched by ‘the superhero’ and ‘Clark Kent’ by ‘the milquetoast reporter’. Then Soames’s account implies that for each premise, the proposition it is used primarily to assert is true. Clearly, the proposition asserted in this context (or any other) by the conclusion, A4f, is contradictory. So the argument asserted by A4 is not valid. (V) then implies that speakers will not intuit that A4 is valid. But that is clearly wrong. Any speaker in the context would agree, for instance, that “if Clark Kent is the milquetoast reporter, and Lois Lane does not believe that Clark Kent can fly, then it follows that there is someone who is identical to the milquetoast reporter, and such that Lois does not believe that he can fly.” Similarly for the other steps in the argument. It is highly intuitive, in the context, that each step in the argument is valid, and so the argument is intuitively valid as a whole.

            Soames might reply that if the second and third occurrences of ‘x’ in A4f are differently descriptively enriched (by ‘the superhero’ and ‘the milquetoast reporter’, respectively), the resultant proposition is true, and the argument asserted by A4 is valid, as required by (V). But this pattern of descriptive enrichment is impermissible (even if descriptive enrichment of variables in some cases, for instance that of ‘x’ in A3c, is allowed). The more nearly English rendering of A4f makes this clear:

Therefore, there is someone who is the superhero, and is such that Lois Lane both believes he can fly and does not believe he can fly.

This sounds like a contradiction. Speakers would be willing to assert its negation, in any context. In no context can the occurrences of ‘he’ make different contributions to this sentence’s meaning. A4f cannot be interpreted as expressing anything other than a contradiction.

            The final section of Sider 1995 advanced a related argument against all “Fregean theories”, i.e., theories that allow the semantic contents of, e.g., ‘Lois believes that Superman can fly’ and ‘Lois does not believe that Clark Kent can fly’ to both be true. The present argument extends the point to the entire class of “pragmatic Fregean theories” (like Soames’s). Consider any theory that says that ‘Lois believes that Superman can fly’ and ‘Lois does not believe that Clark Kent can fliy’ can routinely be used to simultaneously assert, or pragmatically convey, true propositions. Such a theory predicts the legitimacy of uttering the premises of A4. But in any context, any reasonable speaker will intuit the validity of A4 and will be willing to utter the negation of its conclusion. So, any pragmatic Fregean theory legitimates irrational linguistic behavior.

            A4 puts us in an awkward position. Our intuitions clash: we want to utter A4’s premises and the negation of its conclusion, yet we also intuit its validity. Something has to give. Soames’s stand on intuitions about particular sentences, roughly speaking, is that they are correct about something, namely, asserted content. As we have seen, this position cannot be squared with our logical intuitions about A4. We think that the correct stand is rather that, in some cases, speakers’ intuitions about particular sentences are correct about nothing. No way of interpreting our intuitions about A4 renders them all correct. Particular intuitions are best taken as concerning semantic content. Thus taken, some of them are simply mistaken. Speakers intuit the way they do because of “semantic blindness”, to use a phrase of John Hawthorne’s (forthcoming). Speakers fundamentally misunderstand the rules that govern language use. In a sense, then, we are reformers in a way that Soames is not. Speakers regularly utter such sentences as “Lois Lane does not believe Clark Kent can fly”. We think they should stop – such utterances violate the rules of use of English.

Theodore Sider

Department of Philosophy, Davison Hall

Douglass College, Rutgers University

New Brunswick, NJ 08903

sider@philosophy.rutgers.edu

David Braun

Department of Philosophy

University of Rochester

Rochester, NY 14627-0078

david.braun@rochester.edu

References

Braun, David. 2003. “Critical Study of Scott Soames’s Beyond Rigidity”, Linguistics and Philosophy 26: 365-378.

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Everett, Anthony. 2003. “Empty Names and ‘Gappy’ Propositions”, Philosophical Studies.

Frege, Gottlob. 1952/1892. “On Sense and Reference”, in Peter Geach and Max Black (eds.), Translations of the Philosophical Writings of Gottlob Frege (Oxford: Blackwell).

Hawthorne, John. Forthcoming. Knowledge and Lotteries. (Oxford: Oxford University Press).

Kaplan, David. 1989. “Demonstratives: An Essay on the Semantics, Logic, Metaphysics, and Epistemology of Demonstratives and Other Indexicals”, in Joseph Almog, John Perry, and Howard Wettstein (eds.), Themes from Kaplan (New York: Oxford University Press): 481-563.

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Kripke, Saul. 1972/1980. “Naming and Necessity”, in Davidson and Harman: 253-355 and 763-769. Revised edition (with new preface) published as a separate monograph in 1980 (Cambridge, MA: Harvard University Press).

Sider, Theodore. 1995. “Three Problems for Richard’s Theory of Belief Ascription”, Canadian Journal of Philosophy 25: 487-514.

Soames, Scott. 2002. Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity. (New York: Oxford University Press).