Connectives and Necessity

Connectives and Necessity

In Naming and Necessity Kripke argues against the description theory of names and offers a theory-sketch to be put in its place, often labeled the causal theory. He then extends his critique to apply to common nouns (natural kind terms) contending that they too are not to be defined by means of descriptions but rather owe their reference to certain kinds of causal chain. What he doesn’t do is inquire into whether the critique can be extended yet further. Here I will do just that, focusing initially on logical connectives such as “and”, “or”, and “not”. The question, then, is whether these terms satisfy a description theory, and if not what kind of theory should be put in its place. Instead of employing the notion of reference, which may appear tendentious, we may prefer to formulate the issue in terms of the “semantic value” of such terms, so the question becomes whether (say) the term “and” has the semantic value of conjunction in virtue of the fact that speakers associate certain individuating descriptions with “and”. To fix ideas, we might cite a description like “the truth function that has such and such a truth table”, though a description like “Russell’s favorite truth function” is not to be ruled out on logical grounds. When a speaker uses “and” to refer to (express) conjunction does she do so by having a description in mind along these lines? Does she pick out conjunction with a description like “the truth function with such and such a truth table” and then abbreviate that with the monosyllable “and”? Does she have a little logician in her head that knows how to characterize conjunction uniquely? This would be the analogue of having a little historian in your head that enables you to refer to Winston Churchill using “Winston Churchill” by knowing various historical facts about that individual, such as that he was the prime minister of Great Britain during World War II.

It is easy to see that this kind of theory runs up against the same kinds of problems Kripke diagnosed for ordinary proper names. The main one is the problem of error: speakers may make mistakes about the properties of the things they refer to. In the Godel/Schmidt example, the obscure Schmidt is the inventor of the incompleteness theorem not Godel, yet people still refer to Godel with “Godel” and not Schmidt despite associating “the inventor of the incompleteness theorem” with the name “Godel”—their mistaken belief does not direct their reference towards Schmidt. Similarly, a logically inept speaker might wrongly suppose that a conjunction can be true if only one of its conjuncts is true (he would be a very logically inept speaker), but that wouldn’t mean that his use of “and” expresses disjunction not conjunction. The reason in both cases (according to Kripke) is that there is an historical and social dimension to the meaning of the relevant terms in a given speaker’s mouth—the speaker refers to what people in the past in general referred to with “Godel” or “and”. He just happens to have a false belief about what he is referring to (this would be even clearer if the description the speaker had in mind were “Russell’s favorite truth function” in the situation in which actually Russell liked disjunction more). Likewise, just as a speaker might refer to Feynman with “Feynman” even if all he knows about the physicist is that he is some famous physicist or other, a speaker might refer to conjunction with “and” even if all he can tell you is that conjunction is some kind of truth function or other. The community’s use of the word in question ensures its reference in an individual’s mouth; his ignorance of facts about the reference doesn’t undermine that. This applies as much to connectives as to proper names. It is in fact an instance of a perfectly general point, namely that what people believe about the things they talk about is not determinative of the reference of their words. You can have all sorts of false beliefs about things and still mean what other people mean by their words. Clearly, the point about “and” can be carried over to “or” and “not”, so our logical vocabulary is not subject to a description theory (assuming Kripke is right about proper names).[1]

Here is another instructive case: the word “necessary”. How does it refer? First, note that it can refer to two different things—metaphysical necessity and epistemic necessity (compare a single name with two referents). Suppose we take it to refer to metaphysical necessity: is this because speakers have true individuating beliefs about metaphysical necessity? Hardly: they might have quite wrong ideas about this kind of necessity. Suppose someone believes that such necessity is truth in all possible worlds whereas in fact there are no possible worlds and metaphysical necessity is a primitive modal property. Then they have a false belief about the reference of their words, but the words still have a determinate reference, viz. metaphysical necessity. Or suppose the speaker thinks the notion corresponds to some outdated and supernatural concept of the metaphysical whereas in fact it is definable in elementary modal logic. That doesn’t cause them to refer to nothing or to something supernatural with the word “necessary”; their personal beliefs are irrelevant to the semantic content of the communal words they use. Or again, they might just know that metaphysical necessity is some kind of necessity or other—they can’t personally distinguish it from epistemic necessity—and yet they still refer to metaphysical necessity not epistemic necessity. The same might be said of the word “causation”: does it refer to whatever satisfies the speaker’s descriptive beliefs? Clearly not, since the speaker might have quite erroneous beliefs about the nature of causation (she might think that causation is nothing but constant conjunction). Ditto for the words “identity” or “true” or “beauty” or “good” or “space” or “time” or any number of other words. The reference of these words will not follow the idiosyncratic false beliefs of individual users. We can’t find out what they refer to in a given speaker’s mouth by surveying the descriptive contents of his or her mind. Just consider all the erroneous beliefs that surround such words as “democracy”, “God”, “morality”, “death”, “consciousness”: none of this matters to the actual semantic content of the word as it is used in a given linguistic community. The point has nothing specifically to do with proper names; it is a general point about the relation between meaning and belief.[2]

Compare syntax and phonetics. No one thinks that the syntactic and phonetic properties of an utterance are determined by the speaker’s beliefs about them. They are a matter of the language itself not what the speaker believes about the language. People can have all sorts of false beliefs about syntax and phonetics—they are not made true by the fact that beliefs about language fix the nature of language, because there is no such fact. Why should semantics be different? What people believe about the reference of their words is not what fixes the actual reference of their words. Kripke claims that causal chains fix the reference of proper names, but the same kind of point applies to any meaningful word—the meaning-determining facts are not facts about individual belief. This is why false beliefs don’t alter meaning. We might put this by saying that the language faculty is independent of the belief faculty (compare the perceptual faculty). A pure causal theory of reference removes reference altogether from belief as a means of reference fixation, but the falsity of description theories already undermines such a theory. So the defects of the description theory of names reflect a much more general point about belief and meaning, as we can see by considering other types of word. It is certainly not true that each word in a sentence has its reference (semantic value) fixed by descriptive knowledge possessed by the speaker; and it is demonstrable that no word is semantically equivalent to a definite description (except a definite description).[3] The point I have been making is that Kripke’s critique of names is just part of a larger critique, and in the light of that larger critique is entirely predictable.[4]

[1] It wouldn’t be difficult to construct a similar case for quantifier words by imagining speakers with false beliefs about the properties of quantifiers.

[2] I haven’t discussed rigid designation in connection with the generalized description theory, but an analogue of it holds for connectives and the like (de jure rigid semantic value). The most effective argument Kripke deploys is the error argument, so I have focused on that.

[3] It is true that there can be “descriptive names”, i.e. names stipulated to be equivalent to descriptions (“Let ‘Stanley’ be synonymous with ‘the lizard in my living room’”). But that is not the situation with ordinary proper names.

[4] Another line of argument is that the description theory presupposes reference because the components of descriptions are themselves referential, as in “the father of that girl”. Kripke does not deploy this type of argument and I will leave it aside here.