Simplicity made difficult
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KeywordsFormal Semantic Propositional Truth Truth Predicate Operator Argument Explanatory Priority
In their new book Relativism and Monadic Truth, Herman Cappelen and John Hawthorne (2009) seek to defend a “mainstream” view of the contents of thought and talk, which they call Simplicity, against recent “analytic relativist” heresays (including my own). Simplicity consists in five theses:
There are propositions and they instantiate the fundamental monadic properties of truth simpliciter and falsity simpliciter.
The semantic values of declarative sentences relative to contexts of utterance are propositions.
Propositions are, unsurprisingly, the objects of propositional attitudes, such as belief, hope, wish, doubt, etc.
Propositions are the objects of illocutionary acts; they are, e.g., what we assert and deny.
Propositions are the objects of agreement and disagreement. (1)
The real locus of dispute, though, must be T1. After all, analytic relativists tend to accept T3, T4, and T5.1 T2 is a technical claim; whether it is correct is a matter of what sorts of abstract objects it is most useful to assign to embedded occurrences of sentences in a compositional semantic theory. There are relativists and nonrelativists on both sides of the issue, and Cappelen and Hawthorne concede that much of what they have to say is consistent with the falsity of T2. So the central issue has got to be T1. The mainstream view that Cappelen and Hawthorne seek to defend from relativist attacks is that propositions—the contents of our beliefs and assertions—instantiate the “fundamentally monadic properties” of truth simpliciter and falsity simpliciter.
It is not at all obvious what this view comes to. In what follows, I will say how I think Cappelen and Hawthorne understand it. I will then argue that, so understood, it is not in fact what is at issue between analytic relativists and their opponents.
Old school relativists might have refused to call propositions “true” or “false” without adding a qualification, but the analytic relativists Cappelen and Hawthorne are discussing are happy to make room for a monadic propositional truth predicate that behaves disquotationally. This is because analytic relativism is proposed not as a piece of revisionary metaphysics, but as a framework for doing empirical semantics. Competent speakers who assent to “Joe’s chile is tasty” will also assent to “it is true that Joe’s chile is tasty,” and speakers who assent to “Joe might be in Boston” will also assent to “the claim that Joe can’t be in Boston is false.” As empirical semanticists, analytic relativists had better have some account of how the monadic predicate “true” works in these discourses. Of course, they could chalk these uses of “true” up to error—false folk beliefs about the nature of truth—but not much recommends that path. After all, even committed relativists about some area of discourse will want the conveniences afforded by a disquotational truth predicate when they are engaging in that discourse. Moreover, it is easy to give a semantics for monadic “true” and “false” that works in an analytic relativist framework and ratifies the disquotational inferences. Roughly stated: “true” expresses a property, truth, whose extension at a circumstance of evaluation is the set of propositions that are true-at that circumstance of evaluation. Since this simple and natural account is consistent with relativist semantics and accords perfectly with speakers’ use of the monadic propositional truth predicate, there is no reason for a relativist not to adopt it.
Thus, as Cappelen and Hawthorne acknowledge, relativists are happy to accept the coherence of a monadic predicate “true” that applies to propositions, and even of a monadic property truth that applies to propositions. So, we can infer, Cappelen and Hawthorne must hold that this property, though monadic, is not fundamentally monadic. What does that mean?
A natural first thought is that a monadic property is not fundamentally monadic if things have it only in virtue of standing in certain relations to other things. The property of being a brother is not fundamentally monadic in this sense, because one counts as having this property in virtue of standing in a relation to someone else. Though this seems the most natural thing to mean by “fundamentally monadic,” I am hesitant to interpret Cappelen and Hawthorne this way, since on this interpretation T1 would be inconsistent not just with relativism, but with most substantive theories of truth, including correspondence theories (according to which a proposition is true in virtue of standing in a relation of correspondence to something else—a fact or a bit of reality). What, then, are they getting at?
According to Simplicity, truth and falsity are fundamental monadic properties of propositions. … This contrasts with those who think that the fundamental properties in the vicinity of truth are relational—for example, ‘being true at a world’ or ‘being true at a time’. Of course, and as we emphasize in Chapter 3, T1 is compatible with their being relational properties of being true or false at a world; but what is important is that such relational properties are to be explained in terms of the more fundamental properties of truth and falsity simpliciter. (2)
Thus, for example, we might introduce a dyadic predicate—true at—that holds between a sentence and a context of utterance. What is important, from the perspective of Simplicity, is that this and other derivative uses are explained in terms of the more fundamental monadic properties of propositional truth and falsehood—for example, we may naturally explain the truth of a sentence at a context in terms of the truth of a proposition expressed by the sentence in that context. (3)
Explanatory Priority of Monadic Truth
One can talk of “truth at a context” without running afoul of this principle, provided one uses “S is true at a context c” to mean something like “S would express a true proposition if used at c.” Similarly, one can talk of propositions being true or false “at a world,” if (for example) one thinks of possible worlds as maximal consistent propositions, and defines “p is true at a world w” as “w entails p” (78–9 n. 18).
All legitimate uses of relativized truth predicates must be explained in terms of a monadic truth predicate.
I think there is an interesting issue here about how the relational notions of truth used in semantics are to be understood—whether by definition in terms of monadic truth or in some other way. But it seems to me that this issue cross-cuts the debate between analytic relativists and nonrelativists. For a relativist can coherently endorse the Explanatory Priority of Monadic Truth, and a nonrelativist can coherently reject it.
To substantiate these claims, I will need to say a bit more about what I mean by “relativist.” As I have argued (MacFarlane 2005, 2007, and elsewhere), to be a relativist is not just to engage in “profileration”—to countenance unusual parameters of propositional truth. One is only a relativist if one takes the accuracy of some assertions or beliefs to vary with the context from which they are assessed (the “context of assessment”).2 The notion of accuracy is connected to assertoric and doxastic practice roughly as follows: we should assert or believe something only if in doing so we would assert or believe accurately, and we should retract an earlier assertion if it was inaccurate. So allowing accuracy to be assessment-sensitive has definite consequences for the predictions we make about when speakers will take themselves to be warranted in making assertions, when they will feel normative pressure to retract earlier assertions, and when they will take themselves to be in disagreement. Understood in this way, relativism about a particular domain of thought and talk is not a metaphysical thesis but a testable, empirical hypothesis—at least to the extent that any semantic theories are testable.
It is easy to see that proliferation need not imply the assessment-relativity of accuracy. Cappelen and Hawthorne point out themselves that a metaphysical presentist who takes the present to be the only real time could introduce abstract times and do semantics with a relational notion of “truth at a time,” without abandoning Simplicity (82). Such a theorist would say that an assertion is accurate just in case its content is true at the abstract time that corresponds to the present (the one real time), so this position would not be “relativist” in the sense I have described. Similarly, a naive realist about taste properties could take propositions to be true relative to a standard of taste, but hold that an assertion is accurate just in case its content is true at the one true standard of taste. Thus proliferation is consistent with full-blooded objectivism about taste claims.
Proliferation can also go along with a kind of contextualism (MacFarlane 2005, 2007, 2009). Consider a theorist who relativizes propositional truth to times, but is not metaphysically a presentist (someone like Kaplan 1989). Such a theorist will say that an assertion is accurate just in case its content is true at the time the assertion occurs (the time of the context of use). So, even though the proposition Sally asserted 12 h ago—the proposition that it is raining here—is not now true, her assertion was correct, because its content was true when she made it. No scary relativism here: just ordinary dependence of truth on the time of utterance. Similarly, a theorist who relativized propositional truth to a standard of taste could hold that an assertion is accurate just in case its content is true at the asserter’s standard of taste. Such a theorist would agree with standard contextualists about which taste claims are accurate, and would join them in holding that there is no real disagreement between two parties with different standards of taste who say (respectively) “this chile is tasty” and “this chile is not tasty.” (I have dubbed this kind of view “nonindexical contextualism” to distinguish it from more familiar kinds of contextualism, which posit contextual variation in propositional content.)
A relativist approach to taste predicates, by contrast, would say that there is no assessment-independent answer to the question whether an assertion is accurate. Rather, an assertion is accurate, as assessed from a context c, just in case its content is true at the standard of taste relevant at c (normally, the assessor’s standard). On this kind of view, there can be real disagreement between the parties described above, despite their different standards of tastes. For, relative to each party’s context of assessment, the accuracy of his own assertion precludes the accuracy of the other’s.
Cappelen and Hawthorne argue (17–18) that there is no need to discuss assessment sensitivity, since it is trivially implied by proliferation (provided that the truth of the proposition varies with the proliferated parameter). As the above examples show, this is incorrect. We cannot conclude that a proposition whose truth varies with some factor X is assessment-sensitive, even if we know that it is true relative to the value of X that is relevant at one context and false relative to the value of X that is relevant at another context. To decide whether the proposition is assessment-sensitive, we would also have to know what the theory says about the relation between accuracy (relative to a context of assessment) and truth-at-X. As we have seen above, various answers are possible:
An assertion of p at c 0 is accurate, as assessed from c 1, just in case p is true at X *, where X * is “the one true value of X.”3
An assertion of p at c 0 is accurate, as assessed from c 1, just in case p is true at X c0, where X c0 is the value of X relevant at c 0.
An assertion of p at c 0 is accurate, as assessed from c 1, just in case p is true at X c1, where X c1 is the value of X relevant at c 1.
Only given the third answer will the proposition be assessment-sensitive.
To see the difference, we need to look at what the realist and the relativist say about accuracy.4 The realist will say that the accuracy of an assertion that something is tasty is independent of anyone’s standard of taste, while the relativist will say that it depends on the standard of taste relevant at the context of assessment. Given plausible principles connecting accuracy to norms for assertion and retraction, the two views will imply different things about which tastiness assertions are warranted, and hence (indirectly) make different predictions about usage.5
…a realist can perfectly make room for a family of properties expressed by constructions of the form ‘true by so-and-so’s standards’, properties that are distinct from those of truth and falsity. Adopting now the perspective of such a realist, it will be natural to interpret the relativist’s talk of some proposition being true at a standard of taste index as expressing the claim that the proposition is true by such and such standards, a perfectly legitimate claim even by the realist’s lights. Meanwhile, it will be very natural to interpret the relativist’s disquotational truth predicates as expressing the very properties that the realist expresses by ‘true’ and ‘false’. According to this proposed translation manual, the so-called relativist and the realist do not differ at all. (137)
Let us return, now, to the question that prompted this digression: How can a relativist endorse the Explanatory Priority of Monadic Truth? Recall that Explanatory Priority does not forbid working with relational notions of truth, so long as they are introduced by definition in terms of monadic truth. So suppose that we start with a monadic truth predicate and an operator “by standard of taste s.”6 We can then define a notion of truth at a standard of taste as follows: a proposition p is true at a standard of taste s iff by standard of taste s, p is true. Using this relational notion of truth, we can give a formal semantics for taste predicates, and even, if we like, for the monadic truth predicate.7 If we then say that an assertion of p is accurate, as assessed from c, just in case p is true at s c, where s c is the standard of taste of the agent of c (the assessor), then our semantics counts as relativist in the sense defined above, and yields the empirical predictions characteristic of a relativist semantics. Despite that, we have respected the Explanatory Priority of Monadic Truth. Though we have employed a relational notion of truth in our formal semantics, this notion is defined in terms of monadic truth. We can even restate our condition for the accuracy of an assertion in terms of monadic truth: an assertion that p is accurate, as assessed by a at c, just in case, by a’s standards of taste at c, p is true.
The upshot is that a relativist can embrace the Explanatory Priority of Monadic Truth. Conversely, a nonrelativist can reject it. To reject the Explanatory Priority of Monadic Truth is simply to deny that the relational truth notions one uses are to be understood in terms of monadic truth. One need not endorse the opposite order of explanation, since it may be that our grasp of truth is independent of our grasp of one or the other notion of truth-at. Of course, any semanticist who uses a relativized notion of truth but declines to explain it in terms of monadic truth needs to explain it in some other way. But that goes for the relativist and the nonrelativist alike. In my own work, I have sought to explain the notion of truth relative to a context of use and context of assessment by exhibiting its role in a broader theory of linguistic communication. That is very much the same kind of explanation that nonrelativists (like Donald Davidson, Michael Dummett, and David Lewis) have offered of truth relative to a context of use.
One would think that, after explaining the issue over T1 as an issue about the Explanatory Priority of Monadic Truth, Cappelen and Hawthorne would devote their attention to arguing that analytic relativists are, in fact, committed to rejecting the Explanatory Priority claim. But the arguments that they take to be relativist arguments against T1 do not have anything to do with Explanatory Priority. They say, for example, that “Lewis and Kaplan use an ‘Operator Argument’ against T1” (31). It is true that Lewis (1980) and Kaplan (1989) both employ an “Operator Argument” to motivate their use, in formal semantics, of parameterized truth predicates. But this argument, by itself, implies nothing about the relative explanatory priority of monadic and relational truth. Indeed, Lewis makes it clear that he does not think that the operator argument has any ramifications for propositional truth; it establishes only that the semantic values of sentences must have relativized truth values, and Lewis explicitly denies that the semantic values of sentences must be propositions. His target is T2, not T1.
To recap: I have argued that, since the relativist is happy to accept a monadic property of propositional truth—the property expressed by the ordinary English word “true” when it occurs without explicit relativization—T1 cannot be interpreted as the bare claim that there is a monadic propositional truth property. It must be interpreted as the stronger claim that all relational truth properties must be explained in terms of monadic truth. However, while this is a claim worth discussing, the issue seems orthogonal to the debate over analytic relativism. An analytic relativist could in principle endorse T1; conversely, one can reject T1 without being a relativist in any interesting sense. Nor do the “pro-relativist” arguments Cappelen and Hawthorne discuss have any obvious bearing on T1, construed as an explanatory priority claim.
In fact, many of the “pro-relativist” arguments they discuss seem to have little to do with analytic relativism on any understanding. Half of their book is devoted to criticism of “two styles of argument [that] are particularly important in the anti-Simplicity literature” (31): says-that arguments for sameness of content (Chapter 2) and operator arguments for the relativization of truth for sentential semantic values (Chapter 3). The reader who is not familiar with the literature might reasonably infer that these arguments are the central pillars on which relativist views rest. Nothing could be more misleading.
I agree that Says-That and its variants are not good tests for sameness of content, for all the reasons Cappelen and Hawthorne give. This is bad news for work that relies heavily on such tests, such as the defense of semantic minimalism in Cappelen and Lepore (2004). But I don’t see why it is bad news for analytic relativism. Even if Says-That were a successful diagnostic for sameness of content, it could not support relativism against realist or nonindexical contextualist alternatives, which also posit sameness of content. For this reason, relativists have always relied much more heavily on intuitions about agreement, disagreement, and retraction, and have sought theoretical motivations for positing sameness of content that have nothing to do with our reporting practices (see especially Recanati 2007).8
Turning, finally, to Chapter 3: it is true that in Kaplan one can find an “operator argument” for proliferation of parameters of truth for sentential contents. Against this Cappelen and Hawthorne argue, first, that the constructions Kaplan treats as operators do not syntactically embed sentences, and second, that one can give semantics for operators without parameterizing truth. There is room for debate here, but since I’m not aware of any analytic relativists who motivate proliferation on the basis of an operator argument, the whole issue seems irrelevant to the debate over analytic relativism.9 It is more directly relevant to T2—the thesis that the semantic values of embedded sentences are propositions—but as I have noted, the debate about T2 is orthogonal to the issues that divide relativists, realists, and contextualists.
It is not clear to me what T5 comes to, exactly. If it means that people can disagree about whether p, where p is a proposition, then I know of no relativist who would reject it.
In MacFarlane (2005), I put the point slightly differently: to be a relativist is to countenance propositions whose truth varies with the context of assessment. Following Kaplan, I employ two different relativizations of truth, truth at a circumstance and truth at a context (or, for the relativist, truth at a context of use and context of assessment). As Kaplan emphasizes, it is important not to conflate these relativizations, which have different roles in semantics. Since people are prone to conflate them, through careless use of phrases like “true at” or “true for,” I here put the point in terms of “accuracy.” A translation manual: an assertion or belief occuring at context c 1 is accurate (as assessed from context c 2) just in case its content is true as used at c 1 and assessed from c 2.
Alternatively, using truth-at-contexts instead of accuracy: p is true as used at c 0 and assessed from c 1 just in case…
Or, alternatively, at truth relative to a context of use and context of assessment.
The main difficulty with the realist position is that it has to posit a high degree of chauvinism or self-delusion in order to explain why people make tastiness claims on the basis of nothing more than their own affective reactions, even when they know that only one of them will thereby satisfy the norm.
Alternatively, we could use a counterfactual construction: “if s were the correct standard of taste, it would be the case that…”
Cappelen and Hawthorne may be supposing that using “true at s” to give a semantics for “true” would commit one to the explanatory priority of relational to monadic truth. But if that were enough to establish an explanatory priority claim, then standard Tarskian semantics would be committed to the implausible idea that truth relative to an infinite sequence of objects is explanatorily prior to conjunction, and to the even more implausible idea that conjunction is explanatorily prior to itself. Truth conditional semantic clauses are not explanations of concepts.
Cappelen and Hawthorne embrace an agrees-that test, which lacks some of the deficiencies of says-that tests. However, they beg the question when they attempt to deploy this test against temporalism. Suppose that 2 days ago Bill said “It is raining in Boston,” and 2 weeks ago Janet said “It is raining in Boston.” Cappelen and Hawthorne say that the inappropriateness of saying “Bill and Janet agreed that it was raining in Boston” is “powerful evidence against the Kaplanian approach” that takes Bill and Janet to have asserted the same proposition—the time-neutral proposition that it is raining in Boston (98). But the validity of the negative part of the agrees-that test is one of the things at issue between temporalists and eternalists; the Kaplanian will just take this case to be a counterexample to the test. One cannot dismiss a putative counterexample to a test by ruling out the counterexample on the basis of that very test.
See MacFarlane (2009), §6.3 for an explict rejection of the idea that only the presence of an operator could motivate parameterizing propositional truth.
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