The Argument

This chapter is devoted to Putnam’s model-theoretic argument. This argument presents the most formidable obstacle to the view of meaning outlined so far. I touch upon the following questions: What exactly is Putnam's model-theoretic argument? Exactly which theories are susceptible to the argument? What type of externalist constraints upon reference have been invoked to solve the model-theoretic argument? Does Putnam's ‘just more theory’-response to these answers work? Is it feasible to invoke internalist constraints to answer the model-theoretic challenge?

Here is a common reading of Putnam’s model-theoretic argument (an early version of which was given by Newman).66 _{Consider a theory T that is consistent and}

empirically confirmed. A corollary of Gödel’s completeness theorem tells us that if T is consistent, it has a model. A model is an ordered pair <W, V>, consisting of a domain and an interpretation function. The domain W is a set of elements that can be

considered the domain of discourse of T, and the interpretation function V is a function that maps the terms of T onto sets of elements from W in such a way that (all, or many of) the sentences in T come out true.

66 _{Putnam 1978, 1983. Newman 1928. There is some controversy as to the correct interpretation of}

Putnam’s model-theoretic argument. My interpretation resembles that of Anderson 1993, Bays 2008, Lewis 1983a, 1984, and Merrill 1980.

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A consistent theory T, then, can be considered true-in-the-model <W, V>. Putting aside issues of size, the real world can be turned into a model of theory T as well. The domain W can be replaced with a set of elements from the real world and the

interpretation function V can be replaced with a mapping onto elements from the real world. Consequently, T is true-in-the-real-world. In other words, it is true simpliciter. If we identify reference with this mapping from terms onto elements in the real world, Putnam’s argument shows that every consistent theory T comes out true. This is a

reductio ad absurdum, for it should be possible for such a theory to be false.

A different way to understand the model-theoretic argument is by considering the notion of functional definition. The Ramsey-Carnap-Lewis view of theoretical terms provides the default account.67 _{Consider a theory T that contains terms t}

1 through tn. It

also may contain already interpreted terms (O-terms). This theory T(t1, …, tn) can be

transformed into its Ramsey sentence: x1 … xn T(x1, …, xn). This Ramsey sentence, in

turn, can be transformed into an open sentence by removing the quantifiers: T(x1, …,

xn). Functional definition, then, is the view that the referent of t1 is the first member of

the unique n-tuple that realizes, or comes close enough to realizing, this open sentence. The meaning of t1 is how the referent of t1 depends on the state of the world.

Putnam’s model-theoretic argument poses a problem for the view that all terms are so functionally defined. On this view—called ‘global descriptivism’—there are no already-interpreted O-terms. Lewis writes, “global descriptivism… leads straight to

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Putnam’s incredible thesis. For any world (almost), whatever it is like, can satisfy any theory (almost), whatever it says. … It is (almost) certain that the world will afford the makings of an interpretation that will make the theory come out true” (1984: 60). He continues, “Global descriptivism… may be part of the truth about reference, but it cannot be the whole story. There must be some additional constraint on reference; some constraint that might, if we are unlucky in our theorizing, eliminate all the allegedly intended interpretations that make the theory come true” (61).

Before I discuss proposed solutions, it is important to address the following question: Exactly for what view does Putnam’s argument pose a problem? Have

philosophers even seriously considered global descriptivism as a theory of the meaning of terms in a public language? In fact, does global descriptivism not commit the error of attempting to analyze linguistic meaning in terms of word-world relations? Is this not a type of error that ignores the Gricean insight that linguistic intentionality should be explained in terms of mental intentionality?

Lewis agrees. He writes, “It would be better, I think, to start with the attitudes and go on to language”, but a proper restatement of Putnam’s argument, “would

relocate, rather than avoid, the problem” (1984: 57-8; italics added). Elsewhere, he

writes, “If the problem of intentionality is rightly posed there will still be a threat of radical indeterminacy” (1983a: 49; italics added). So what would the model-theoretic argument as applied to mental content –a ‘rightly posed’, ‘relocated’ version—look like?

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Some philosophers have defended a language of thought-hypothesis.68

According to this hypothesis, human thinking takes place in a symbolic language that is realized in the brain. Thoughts, on this view, are composed of ‘sub-thought’ parts (i.e. concepts) in much the same way as sentences are composed of sub-sentential parts (i.e. words). In fact, Putnam himself considers an application of his argument to a language of thought. He writes, “‘Mentalese’ is thought to be a medium whereby the brain constructs an internal representation of the external world… If thinking is ultimately done in ‘mentalese’, then [my argument shows that] no concept we have will have a

determinate extension.” (1983a: 17; italics original).

Does that mean the model-theoretic argument only poses a problem if we accept a language of thought? No, the argument can be viewed as being both about language and mind without having to adopt ‘Mentalese’—here is how.69 _{On the}

functionalist approach sketched in Section 1.2, ‘belief’ and ‘desire’ are theoretical terms from folk-psychology. This theory consists of generalizations that capture regularities about how the environment affects subjects, how subjects’ internal states affect

behavior, and how these states affect each other. A properly regimented, more rigorous version of this folk-theory will ascribe certain beliefs to subjects. Such ascriptions

capture what subjects really believe and desire.

This regimented psychological theory will generate belief ascriptions on the basis

68 _{Fodor 1975.}

69 _{My claims about the proper target of the model-theoretic argument is inspired by remarks from}

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of behavioral and environmental evidence. As suggested earlier, this psychology will ascribe to a subject a belief in a modified Ramsey sentence. It will have the form: S believes that !x1 … !xn T(x1, …, xn). (The exclamation marks add a uniqueness

condition.) Putnam’s model-theoretic argument can be understood as saying that the world cannot fail to provide a model that makes the Ramsey sentence from this content clause come out true. And this is the reductio that has to be avoided. Ultimately, then, Putnam’s model-theoretic argument does not pose a problem for theories of reference, but rather a challenge for theories of intentionality.70