Abbott, B. & Hauser, L. (1995) Realism, model theory, and linguistic semantics. Annual Meeting Linguistics Society of America, January.
1995 Annual Meeting Linguistics Society of America, January 8, 1995.{*}

Realism, model theory, and linguistic semantics

Barbara Abbott & Larry Hauser

1. Introduction

George Lakoff (in his book Women, Fire, and Dangerous Things (1987) and the paper "Cognitive semantics" (1988)) champions some radical foundational views. Strikingly, Lakoff opposes realism as a metaphysical position, favoring instead some supposedly mild form of idealism such as that recently espoused by Hilary Putnam, going under the name "internal realism." For what he takes to be connected reasons, Lakoff also rejects truth conditional model-theoretic semantics for natural language.

Realism is defined in Anthony Flew's A Dictionary of Philosophy as: "Most commonly the view (contrasted with idealism) that physical objects exist independently of being perceived."{1} As such, it seems to be purely a metaphysical position, logically independent of semantics. However, realism is frequently held to have semantic consequences and, in particular, it seems, at least, to strongly encourage a claim that our words and phrases refer to mind independent things. Model-theoretic semantics (MTS) is an approach to semantics developed originally for formal languages of logic. On this approach the semantics for a language must first define what a model or interpretation for the language is -- minimally a domain of individuals and a function assigning referents from that domain to the language's nonlogical constants (essentially the content words, in the case of a natural language). Then it must provide rules which determine truth conditions relative to such a model for all the sentences of the language generated by the syntax.{2}

This paper examines an argument, given by Lakoff, against realism and MTS. We claim that Lakoff's argument has very little, if any, impact for linguistic semantics.

2. Model-theoretic semantics

Since Lakoff's argument modifies an argument developed by Putnam, let us look first at Putnam's version.{3}

2.1. Putnam's model-theoretic argument. There are two parts to the argument. The first elaborates on Quine's thesis of the indeterminacy of meaning.{4} Putnam 1980 explains that, for any consistent set of sentences in a language, a model can be constructed using any domain of individuals that is not of the wrong size.{5} To see this, note that by Gödel's Completeness Theorem (Gödel 1930) any consistent set of sentences has at least one model -- call it M -- with a domain of individuals D. Now consider an arbitrary domain D'. If D' is not of the wrong size a mapping can be given from the elements in D to those in D'. (This also holds true if D' = D, where the mapping would essentially reshuffle the elements.) Now a new model M' may be constructed by reinterpreting the predicates in the original set of sentences using D', so that M' is isomorphic to M. M' will also satisfy the original set of sentences. Putnam 1981 shows how to extend this result to intensional models. He gives the following example (1981, 32-35): A cat* is on a mat* will express the same proposition (be true in the same possible worlds) as A cat is on a mat where cat* denotes (i) cherries, in worlds where a cat is on a mat and a cherry is on a tree, (ii) cats, if a cat is on a mat and no cherry is on a tree, and (iii) quarks otherwise; and similarly for mat*. And he gives a formal proof that such examples are, in general, constructable (1981, 217-8).

Putnam's explicit target is metaphysical realism. For suppose we have an epistemically perfect or ideal theory of the world, T. T is consistent with all the observations we will ever be able to make and satisfies all of our theoretical constraints. The metaphysical realist believes that T, nonetheless, might be false; but according to Putnam's "model-theoretic argument" it could always be made true simply by reinterpreting the predicates.

This situation arises under the assumption that the predicates of the language can be assigned wild interpretations which are 'unintended', allowing members of D' to be included or excluded from the denotation of a particular predicate solely to make the original set of sentences true. The problem is that fixing the truth conditions of sentences does not fix the denotations of the words in them. To this, the natural response would seem to be to supplement the model theoretic picture with constraints on reference. Here the second part of Putnam's argument comes into play.{6} Putnam supposes some reference determining mechanism, say a causal theory, has been proposed. He then remarks that, even so, the indeterminacy problem is not solved because "adding to our hypothetical formalized language of science a body of theory entitled 'Causal theory of reference' is just adding more theory" (1980, 18). In other words, such statements merely become part of the consistent set of sentences, T, that may be satisfied in unintended ways.{7}

Against this, David Lewis 1984 suggests the world itself imposes constraints on reference which rule out the wild unintended interpretations of Putnam's argument. Lewis writes:

Among all the countless things and classes that there are, most are miscellaneous, gerrymandered, ill-demarcated. Only an elite minority are carved at the joints, so that their boundaries are established by objective sameness and difference in nature. Only these elite things and classes are eligible to serve as referents. (p.227)

Lewis views this kind of referential eligibility as a matter of degree. A degree of indeterminacy remains, but the kind of crazy reinterpretations allowed with no constraints are ruled out. This reply of Lewis, seems to motivate Lakoff's modification, which is our main focus.

Clearly, Putnam intends his model-theoretic argument to defeat metaphysical realism. With regard to our concern, the use of MTS for natural languages, Putnam's intentions are less clear. In any case, given the central importance of reference to the argument, together with the fact that MTS by itself has nothing to say about how elements of the language come to be in correspondence with elements of the model, it is difficult to see how this kind of argument could be turned against MTS. MTS presupposes and merely registers those relations. What's more, fixing truth conditions for sentences fails to determine reference for words no matter what semantic framework one is assuming; so, again, it's difficult to see how this kind of argument could be aimed specifically at MTS?{8}

2.2. Lakoff's version of Putnam's argument. We have just suggested that Putnam's model-theoretic argument does not impugn the practice of using model theory to describe natural language semantics. Lakoff strenuously disagrees. He asserts, "Putnam argues . . . model theoretic semantics fails as a theory of meaning . . ." (1987, 230). "If Putnam is right, model theory cannot be made into a theory of meaning at all" (ibid.). "Anyway you look at it...meaning is not definable in terms of truth in a model...." (1987, 252).{9} Let us look, then, at Lakoff's modification of Putnam's argument to see if it holds some threat for MTS not apparent in Putnam's version.

Lakoff repeats many of the specific steps in Putnam's argument, but the overall form is different due to a short cut Lakoff takes. The short cut involves putting forward a 'constraint' or 'fundamental requirement' which, Lakoff claims, "any theory of meaning at all, model-theoretic or not, must obey" (1987, 230). He then uses Putnam's examples to argue that MTS cannot meet this constraint.

The constraint that Lakoff introduces is given in (R).

(R) The meanings of the parts cannot be changed without changing the meaning of the whole.

As far as we know this constraint is not mentioned anywhere by Putnam. Lakoff does not justify it very extensively; pretty much the entire rationale is given in the following few sentences:

It is the nature of meaning that the meanings of the parts of a sentence contribute to the meaning of the whole in a nontrivial way. Requirement [(R)] is a way of stating that. It is such an obvious requirement, that it is usually taken for granted in empirical semantic theories and not stated explicitly. Yet any putative theory of 'meaning' that violates requirement [(R)] is not really a theory of meaning. (1987, 230)

Note that (R), viewed as a general statement about language, is the converse of the principle of compositionality. Compositionality requires that the meaning of a sentence be determined by the meanings of the words plus the way they are put together syntactically. Thus, it insures that fixing the meaning of the words in a sentence should fix the meaning of the whole sentence. (R) suggests the existence of an inverse type of function that would fix the meanings of the words in a sentence given the meaning of the whole. Thus (R) imposes a kind of determinacy on the meaning of the parts. (R) is obviously different from compositionality, and not so obviously supportable. In particular Lakoff's one supporting observation, "it is the nature of meaning that the meanings of the parts of a sentence contribute to the meaning of the whole in a nontrivial way," does not in fact imply (R), despite his claim that (R) "is a way of stating that." Shortly, we will give examples where the meanings of the parts do contribute to the meaning of the whole in a nontrivial way but where, nevertheless, (R) does not hold.

Lakoff declares that (R) must hold universally "for all sentences of all languages. If a given theory cannot guarantee that requirement [(R)] will hold for every sentence, then it fails as a theory of meaning" (1987, 231; emphasis in original). Apparently Lakoff modifies Putnam's argument in this way hoping to strengthen it by lowering the threshold of failure. He notes:

...Putnam makes an infinitely stronger claim, that in model-theoretic semantics condition [(R)] can be violated for every sentence of a language. ... But any number of violations of requirement [(R)] will be sufficient to show inconsistency. To make his point Putnam only needs to demonstrate the inevitability of moderate indeterminacy of reference. (1987, 321-2).

Here, Lakoff seems to have Lewis' reply to Putnam specifically in mind. Noting Lewis' admission that his proposal to invoke naturalness as a constraint on reference will still leave a moderate degree of indeterminacy, Lakoff responds, "But...even moderate indeterminacy is enough to guarantee inconsistency with requirement [(R)]" (1987, 243).

Viewed as an absolute constraint, as Lakoff views it, (R) imposes a kind of radical determinacy on language. It rules out on a case by case basis any examples constructed to demonstrate that fixing truth conditions does not fix reference, like Putnam's cat*/mat* example; but notice that in so doing (R) also rules out actual paraphrases which evince the kind of local indeterminacy illustrated in examples (1)-(3) on the handout. When we go from the (a) sentences to the (b) sentences in each case we change the meanings of the corresponding parts while keeping the truth conditions of the whole the same.


a. Kim is taller than Sally.

b. Sally is shorter than Kim.


a. The woman sold a car to the man.

b. The man bought a car from the woman.


a. Mary forgot the quotation.

b. The quotation was forgotten by Mary.

Probably similar examples could be found in any language. Contrary to Lakoff's claim that (R) must hold "for all sentences of all languages," then, it probably does not hold for all sentences of any language.{10} Natural languages just do show a certain amount of this type of local indeterminacy.{11}

Furthermore, even were (R) to hold for every sentence of every natural language, it is still difficult to see how this would show MTS not to be viable. Again, the problem highlighted in Lakoff's argument, like Putnam's, is the determination of reference for words, not the determination of truth conditions for sentences given referents for their words. But the latter is all MTS claims to do.

In several places Lakoff's comments suggest that he believes MTS to be intended not just as a framework for describing existing semantic facts in an explicit way but as a mechanism for creating meaning in natural language. For instance, he summarizes his conclusion thusly: ". . . meaning is not definable in terms of truth in a model . . . . The reason is clear: Meaningless structures cannot give meaning to meaningless symbols" (1987, 252; emphasis in original). But linguists who work on the semantics of natural languages within a model-theoretic framework do not, thereby, undertake to explain the ultimate origins of meaning. The task is rather to give a rigorous compositional account of the meaning that exists, whatever its ultimate origins. Here, Lakoff's denigration of model theoretic semantics seems rooted in a misunderstanding much like Justice Scalia's misunderstanding of evolution as a theory about the ultimate "origin of life." As Stephen J. Gould notes, in his essay "Justice Scalia's misunderstanding,"

Evolution is not the study of life's ultimate origin as a path toward discerning its deepest meaning. Evolution, in fact, is not the study of [life's ultimate] origins at all. Even the more restricted (and scientifically permissable) question of life's origin on our earth lies outside its domain. . . . Evolution studies the pathways and mechanisms of organic change following the origin of life. Not such a shabby subject either (Gould 1992, 455).

Similarly, MTS is not the study of the ultimate sources of meaning with a view to -- as Lakoff puts it -- "what human beings are like in the most fundamental sense" (1988, 122). Even more restricted (scientifically permissable) questions of linguistic meaning's origins lie outside its domain. MTS studies the pathways and mechanisms of semantic composition following the origin of meaning. Neither is this such a shabby subject.

Comments to: B. Abbott; L. Hauser

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*We owe many thanks to Rich Hall, Grover Hudson, and Charles McCracken for their comments on earlier drafts of this paper and for much helpful discussion and clarification of the issues in it. We are also grateful to Mark Richard and two anonymous referrees for their insightful comments. Undoubtedly many flaws remain for which the aforementioned are not responsible.^

1. Flew's definition continues "Thus understood, realism obviously reaffirms the standpoint of common sense, and it achieves the status of a philosophy only because a case against it has been seriously argued." It is quite ironic that Lakoff, in opposing realism and promoting idealism, takes himself to be opposing philosophy, which he apparently views as some kind of single-minded monolith devoted to realism (as well as model-theoretic semantics).

Lakoff names the realist doctrines he opposes "objectivism" and in the paper "Cognitive Semantics" he concludes: "Objectivist cognition is a false philosophical doctrine that stands in the way of research on the nature of meaningful thought" (1988, 149). Similarly a section of this paper aimed at showing the wrongness of objectivism is labelled "A Case of Philosophy versus Science" (1988, 122). Lakoff 1987 argues in a similar vein at much greater length (see especially the Preface and chapters 11-15).

Lakoff's apparent confusion about what philosophy is may account for some anomalies in his presentation. In addition to his failure to be able to cite any examples of actual objectivist philosophers (cf. 1987, 157), the philosophers he does cite (e.g. Wittgenstein, Austin, Putnam (who himself acknowledges his antecedent Kant)) are primarily opposed to objectivism (although David Lewis is a natural exception to this generalization), whereas the "Defenders of the Classical View" cited in 1987, chapter 9, are all psychologists!^

2. See Kalish 1967 for a clear presentation of this type of semantics and many historical references. It has been pointed out to us that some of the issues discussed in this paper arise in the context of other semantic frameworks (a fact that will be further acknowledged below), but we confine ourselves to model-theoretic semantics since that is the target named explicitly by Lakoff. Part of our purpose in fact is to clarify the extent to which the arguments given by Lakoff apply specifically to MTS.^

3. More recently Putnam has adopted a position called "natural realism" -- see Putnam 1994. In this work he explains that when he used the term "internal realism" in Putnam 1978 he meant it to refer to his earlier views and not the new ones he was putting forward at that time (1994, 461, n. 36). See also Dreben 1992, 300-301 for critical commentary on Putnam's use of terms containing the word "realism".^

4. An interesting question is the exact relation between Putnam's argument and Quine's views, full consideration of which unfortunately goes beyond the scope of this paper (not to mention these writers, but see Dreben 1992 for some interesting insights). We'll just note here that while Quine apparently believes that this indeterminacy simply exists, Putnam finds it unacceptable. (Cf. Putnam 1983, xiif.) Hence his argument that it exists on the metaphysical realist view is intended as a reductio of that view. (This point is made forcefully by Anderson 1992.)^

5. The reason for this cautious wording is that there may be more than one possible right size. If an infinite model is required then, by the Löwenheim- Skolem theorems, a model of any infinite cardinality will do. Otherwise, whether an exact size is required may depend, in part, on whether the identity predicate is taken to be a logical constant. See Myhill 1951 for some clear and helpful discussion.^

6. Somewhat confusingly, in "Cognitive semantics" (1988, 128-9) Lakoff puts forward the two parts in reverse order, as two separate arguments. He also cites the indeterminacy result prior to and independently of the examples given by Putnam to establish it! We do not know whether this is just carelessness on Lakoff's part or whether it reveals some confusion about the argument itself.^

7. The problem of reference is really at the heart of Putnam's concerns, and we regret having to give it such short shrift here. In addition to the 'just more theory' argument just cited, Putnam has also put forward what is known as the 'brain-in-a-vat' argument. See the exegetical works cited above for further discussion.^

8. David Lewis also wonders why this argument is called "model-theoretic". Cf. Lewis 1984, 229f. Oddly, even Lakoff seems to see this at some points in his discussion, e.g. when he says "The problem lies not with the use of model theory per se. It lies with objectivist philosophy and the attempt to base a theory of meaning on truth . . . ." (1987, 256). However comments like this tend to get swamped by the many contrary statements such as those given in the text immediately below, which seem to take Putnam's argument as aimed specifically at MTS.^

9. It must be noted that, in addition to these strong statements about the hopelessness of MTS, Lakoff also makes weaker statements, including some which seem to contradict the strong ones. Compare the quote cited in the preceding footnote with the following: "The problem lies in the use of model theory in the service of a theory of meaning" (1987, 230). Lakoff even describes his own approach as "cognitive model theory" (1987, 259). However it is not really recognizable as MTS (see 1987, ch. 17).^

10. Grover Hudson has suggested to us that Lakoff actually might have meant to impose, not principle (R), but rather the principle in (i):

(i) The meaning of one part cannot be changed without changing the meaning of the whole.

There would be two things to say in that case. The first is to note that we can find examples in natural language where (i) is violated, viz.:


a. Someone is buying a car.

b. Someone is selling a car.

Of course (iia) and (iib) differ in meaning in some sense, but their truth conditions are the same and that is all that is at issue here (since that is all that MTS claims to represent). And the other is that it is not clear that it is possible to construct the kind of example Putnam uses in making his indeterminacy argument (e.g. the cat*/mat* example described above) but changing the reference of only one word rather than two. Put in more general terms, this would require showing that the model M' above could agree with the model M on all but one predicate, and we're not sure that that can be shown.^

11. Of course the meanings of the parts of the sentences in (1)-(3) are not globally indeterminate due to the existence of other sentences which conclusively 'disambiguate' those given. We do not know if it would be possible to demonstrate a pathological indeterminacy -- the unavoidability of unintended reference -- for only a part of a language. Quine 1969 gives an example of what, if he were right, we might call "enduring" local indeterminacy. Japanese NPs consisting of a number word, a classifier, and a head noun may in principle be parsed semantically in two different ways. Either the noun is taken as inherently count, and the classifier in effect inflects the number word, or the noun is neutral between count and mass readings and the classifier word 'countifies' it. (See Quine 1969, 35-38.) The problem with this example of Quine's is that data from the rest of the language determines a constituent structure within the NP which combines the classifier with the number word, and this in turn (assuming compositionality) determines the semantics. See Miyagawa 1989, and the references cited there.^

References, and Some Related Works

Abbott, Barbara. 1994. Realism, model theory, and linguistic semantics. Ms, Michigan State University, East Lansing.

Anderson, David L. 1993. What is the model-theoretic argument? The Journal of Philosophy 90, 311-322.

Dreben, Burton. 1992. Putnam, Quine -- and the facts. Philosophical Topics 20, 293-315.

Flew, Antony. 1979. A dictionary of philosophy. New York: St. Martin's Press.

Gould, Stephen Jay. 1992. Bully for brontosaurus. New York: W.W. Norton & Co.

Gödel, Kurt. 1930. Einige metamathematische Resultate über Entscheidungsdefinitheit und Widerspruchsfreiheit. Anzeiger der Akademie der Wissenschaften in Wien, mathematische-naturwissenschaftliche Klasse 67, 214-215.

Lakoff, George. 1987. Women, fire, and dangerous things: What categories reveal about the mind. Chicago: University of Chicago Press.

Lakoff, George. 1988. Cognitive semantics. U. Eco, M. Santambrogio, & P. Violi, eds., Meaning and mental representations, Bloomington, IN: Indiana University Press, 119-154.

Lewis, David. 1984. Putnam's paradox. Australasian Journal of Philosophy 62, 221-236.

Myhill, John. 1951. On the ontological significance of the Löwenheim-Skolem theorem. M. White, ed., Academic freedom, logic, and religion, Philadelphia: University of Pennsylvania Press, 57-70.

Putnam, Hilary. 1978. Realism and reason. Meaning and the moral sciences, London: Routledge & Kegan Paul, 123-140.

Putnam, Hilary. 1980. Models and reality. Journal of Symbolic Logic 45, 464-82. Reprinted in Putnam, 1983, 1-25.

Putnam, Hilary. 1981. Reason, truth and history. Cambridge: Cambridge U. Press.

Putnam, Hilary. 1983. Philosophical papers vol. 3: Realism and reason. Cambridge: Cambridge University Press.

Putnam, Hilary. 1994. The Dewey Lectures 1994: Sense, nonsense, and the senses: An inquiry into the powers of the human mind. The Journal of Philosophy 91:9, 445-517.