Abstract This chapter is a technical digression with two aims: The first is to make explicit the proof theory and model theory for the first-order modal logic that has been proposed as a framework for regimented languages. The model theory is a version of possible-worlds semantics that allows the domains of individuals to vary from world to world. The second task is to make explicit a representation of the formal theory of propositions proposed in Chapter 2 in this modal framework. The first task includes giving a completeness theorem for the modal logic. The second task includes an argument that there is no paradox in a theory of propositions with a truth predicate that applies to the propositions expressed in the language of that theory.

Abstract While this book endorses an ontological commitment to propositions, properties, and relations, it rejects a commitment to the existence of merely possible worlds or merely possible individuals. The aim of this chapter is to reconcile the rejection of these ontological commitments with a model theory for modal logic that seems to require them. It is argued that a model structure of a Kripke model that is intended to represent some aspect of reality should be regarded as a representational device that may contain artifacts that do not correspond to anything in the reality being modeled. The role of the artifacts is to represent a relational structure that is realized in the domains of entities being modeled. The modeling strategy is a generalized supervaluation strategy that uses refinements of models to facilitate the compositional semantics for domains with relational structure that is not grounded intrinsic properties.

Abstract This chapter provides an interpretation of W. V. Quine’s methodology and metaphysical theory, in order to provide a background for the neo-Quinean theory of propositions that will be developed later in the book. It emphasizes Quine’s naturalism (his rejection of a transcendent a priori perspective from which to do philosophy) and his way of characterizing the project of regimentation (the construction of a formal language for representing one’s philosophical and scientific commitment). It discusses Quine’s distinctions between ontology and meta-ontology, and between the commitments of logic and the substantive commitments of a specific regimented theory. In the discussion of Quine’s views about logic, it considers the logical status of identity theory and of set theory, and the role of singular terms.

This Commentary on Mark Richard’s Meaning as Species raises three sets of questions about Richard’s project: first about the relation between his conception of meaning and the determination of reference and propositional content; second, about its relation to Paul Grice’s notion of speaker meaning, and more generally to the Gricean program for a theory of conversation, and third about way meanings evolve while maintaining their identity.

Kripke's arguments in Naming and Necessity that there are necessary truths that are knowable only a posteriori are convincing, but his examples that purport to be cases of contingent truths that can be known a priori are more problematic. These examples bring out something important about reference and meaning, but this paper argues that the knowledge of speakers who fix the reference of a name or word by stipulation is not appropriately classified as a priori knowledge. The paper discusses the factual presuppositions required for the success of the acts that establish semantic connections between both simple names and theoretical terms and the objects, properties, and relations to which they refer.

Two puzzles are described: a problem about necessary a posteriori truths and a problem about propositional attitudes with singular propositions as their contents. Two strategies for solving them are compared. The first is the diagonalization strategy, which distinguishes possible worlds that are compatible with what is actually expressed by a given sentential clause from possible worlds that are compatible with what would be expressed by the clause if that possible world were actual. The second strategy is the fragmentation strategy, which represents the intentional states described by sentential clauses as separate nonintegrated representational states. It is argued that these are complementary, not competing, strategies. Both play a role in the solutions to the problems. In conclusion, it is suggested that these strategies can also help to clarify a number of further problems—about self-locating attitudes, about the nature of computation, and about knowledge of phenomenal experience.

Dorothy Edgington has been a resolute defender of an NTV account of conditionals, according to which a conditional does not express a proposition that makes a categorical claim about the world, but instead make a qualified claim, or express a conditional belief, qualified by or conditional on the proposition expressed by the antecedent. Unlike some philosophers who defend an NTV view for indicative conditionals, but not for subjunctive or counterfactual conditionals, Edgington argues for the more radical thesis that both kinds of conditionals should be given a non-propositional analysis. This chapter considers Edgington’s NTV account of subjunctive conditionals, the role of objective probability in the account, and its relation to the possible-worlds propositional analysis of subjunctive conditionals.

A defense of a version of Allan Gibbard’s expressivist analysis of normative judgments, focusing on his account of what he calls “normative logic.” The version defended interprets his analysis in a way that is significantly different from his own interpretation, which ties expressivism to a deflationary notion of truth. It is argued that Gibbard’s general account blurs the line between expressivism and normative realism, and that a more robust notion of truth that draws a sharper line can be defended, and can be reconciled with his normative logic. The chapter concludes by considering the application of this expressivist account to epistemic norms, and more specifically to norms for assessing degrees of belief and measures of degree of confirmation.

A discussion of contextualist accounts of knowledge, and of the epistemic logic that is appropriate to them. David Lewis’s account is compared and contrasted with an alternative, a version of an information-theoretic, “normal conditions” analysis of knowledge. The two accounts are formulated in a common abstract framework making it possible to clarify the structural features they share, and those on which they differ. Central concerns of the discussion are the interplay between facts about the attributor’s context and facts about the subject of the knowledge attribution, and the dynamics of knowledge attribution as contexts shift in response to changes in the epistemic situation of both the attributors and the subject.

This chapter concerns a reflection principle discussed by David Christensen and Adam Elga according to which a rational agent’s credence in ϕ‎ ought to be his or her expectation of the ideal credence for the agent, which is the degree to which the evidence ideally supports ϕ‎. The principle seems to have paradoxical consequences, illustrated in its application to an example to which the title of this chapter refers, but it is argued that the paradox arises from mistaken assumptions about what determines the agent’s epistemic situation. The principle may still need qualification, and it needs to be reconciled with the possibility of epistemic modesty (uncertainty about whether one’s credences are ideal), but the clock paradox can be dissolved, and doing so helps to clarify issues concerning higher-order evidence.

A mental state is luminous if and only if being in a state of that kind always puts one in a position to know that one is in the state. This chapter is a critique of Timothy Williamson’s margin-of-error argument that no nontrivial states are luminous in this sense. While I agree with Williamson’s rejection of a Cartesian internalist conception of the mind, I argue that an externalist conception (one based on information theory) can be reconciled with the luminosity of intentional mental states such as knowledge. My argument, which uses an artificial and simplified model of knowledge, is not a direct rebuttal to his argument, as applied to a more realistic notion of the knowledge of human beings, but I argue that it shows that a luminosity assumption is compatible with externalism about knowledge, and it suggest an intuitively plausible strategy for resisting his argument.

This chapter was the first exposition and defense of an axiom system and model theory for a conditional logic in the possible worlds framework, a theory designed to model counterfactual propositions. It is argued, using a version of the Ramsey test, that the truth-conditions for conditionals that are provided can explain why we assess counterfactuals in the way we do. Counterexamples are given for various principles that are often taken to be valid for conditionals, but that are invalid on the semantics provided. It is argued that the theory helps to explain how propositions that are ostensibly about counterfactual possible situations can be confirmed or disconfirmed by evidence about the actual world.

It is argued, following David Lewis, that we should model a cognitive state by a set of centered possible worlds, since this is required to represent the believer’s self-locating or indexical knowledge and belief. But it is also argued, contra Lewis, that we should take the contents of belief to be propositions, represented by sets of uncentered possible worlds, since this is required to give a perspicuous account of agreement and disagreement of different agents, and of change of belief over time. Reconciling these two thoughts requires a defense of Propositionality: roughly, the thesis that any ignorance of where one is in the world is also ignorance about what the world in itself is like. This thesis is defended against some criticisms, and motivated by an externalist picture of knowledge and intentionality.

AbstractA critical discussion of David Lewis’s two-dimensional framework for doing semantics. Lewis’s framework has the same abstract structure as David Kaplan’s semantics for demonstratives, where the truth-value of a sentence is defined as a function of two parameters, one of which is a context. This chapter focuses on the notion of context that is common to the two frameworks, arguing that it is not suited to play the pragmatic role that we need a notion of context to play. The technical notion that both Kaplan and Lewis call ‘context’ plays several different roles in the explanation of speech that need to be distinguished, and this notion also needs to be distinguished from a pragmatic notion of context as the body of information that is available for the determination of what is said.

This is a discussion of Delia Fara’s theory of vagueness, and of its solution to the Sorites paradox, criticizing some of the details of the account, but agreeing that its central insight will be a part of any solution to the problem. I also consider a wider range of philosophical puzzles that involve arguments that are structurally similar to the argument of the Sorites paradox, and argue that the main ideas of her account of vagueness helps to respond to some of those puzzles.

Semantic-pragmatic theorizing took a dynamic turn in the 1970s, but at the time the dynamics remained in the pragmatics and retained a more or less traditional static conception of compositional semantics. Later dynamic semantics built rules for context change into the semantics. This essay argues that the phenomena that motivated the dynamic turn are best explained at the pragmatic level, retaining a notion of propositonal content, and a distinction between content and force. It is argued that while a partial notion of propositional content can be recovered from a dynamic conception of semantic value as context-change potential, some information that plays an important role in the broader explanation of discourse is lost. It is then argued that it is important to retain a notion of speech act force, separated from content.

ion can be used in the way discussed above, however, to produce a reading of (8o) that is valid. (82) (A( Aez(XPxb) (y)) (c)) (a) a=al (zg(y 'z(x~Pxb) (y)) (c)) (a,) And still another reading of (8o), namely (83) (83) ea(jA(QPxb) (y)) (c) a=al 6an ( Av (XPxb) (y) v(c ) This content downloaded from 207.46.13.113 on Thu, 06 Oct 2016 04:28:46 UTC All use subject to http://about.jstor.org/terms A SEMANTIC THEORY OF ADVERBS results from reversing the order in which the adverbs of (8o) are regarded as applying. This reading of (8o), in which only the flying is intentional and not its destination, is harder to associate with the English sentence. But such a reading is readily associated with slightly different examples, such as He intentionally flew his plane within a few feet of the rooftops, over a town called Hadleyville. 8. Adverbial Constructions and Validity Logical validity is not a palpable, overt property of inferences couched in natural language. For one thing, questions of validity depend on a syntactic analysis of the language: if adverbs that are sentence modifiers are not distinguished from those that are predicate modifiers, then inference (67) must be considered invalid, since it has the same form as (72). Logical validity also depends on the extent to which the semantic theory of the language has been developed. A theory that does not treat few and most as having fixed semantic interpretations will be unable to account for the difference in logical validity between the following two inferences. (84) Most doctors are men. Most doctors are nonsmokers. Therefore, some men are nonsmokers. (85) Few doctors are women. Few doctors are smokers. Therefore, some women are smokers. If the theory puts no restrictions whatever on the quantifiers that interpretations may assign to few and most, then an interpretation in which the customary meanings of these expressions are exchanged is not excluded. In fact, the semantic theory of logical validity will givefew and most only those inferential characteristics that can be ascribed to all expressions that are construed as denoting quantifiers.28 Moreover, any syntactic-and-semantic theory of a language will determine a relation of sameness of form among inferences such that all inferences sharing the same form are alike valid or invalid. This means that imaginative talent is required in testing inferences for validity, since an inference that strikes the ear as appropriate and correct 28 Inadequacies such as the one exemplified by (84) and (85) can be alleviated by adding certain meaning postulates that serve to rule out unwanted interpretations, thus defining a nonlogical type of validity that renders more inferences valid. As a referee of this paper pointed out, for instance, one could introduce a meaning postulate for most to the effect that P(most X) entails P(more than half X). But though meaning postulates render a semantic theory less abstract, in no nontrivial case will they make it so concrete that there will fail to be many significantly different interpretations, each of which satisfies all the meaning postulates. And there are methodological reasons for seeking to avoid the use of meaning postulates. They detract from the coherence and systematic character of the resulting theory. This content downloaded from 207.46.13.113 on Thu, 06 Oct 2016 04:28:46 UTC All use subject to http://about.jstor.org/terms 2I6 RICHMOND THOMASON AND ROBERT STALNAKER may well have the same form as one that does not. Consider, for instance, the pairs (86)-(87) and (88)-(89): (86) This is a tiger. Therefore, this is an animal. (87) This is a cigar. Therefore, this is an animal. (88) John realizes it is raining. Therefore, it is raining. (89) John believes it is raining. Therefore, it is raining. A theory that does not distinguish between the ways in which tiger and cigar, or knows and believes, interact with interpretations cannot distinguish between the validity of (86) and (87), or that of (88) and (89). These cautions are appropriate because many inferences in which adverbs figure seem correct but nevertheless are invalid relative to our theory. We have put no restrictions whatever on the set _s10 of functions that can be assigned to predicate adverbs. In particular, these functions need not commute with one another: where f,g E a? f(g(p)) may differ from g(f(p)) for various p E bY1. Consequently, it is not the case that (UeP) (a) IF (U4P) (a); therefore inferences such as (go) (go) John carried the eggs quickly to the wrong house Therefore, John quickly carried the eggs to the wrong house are classified as invalid, a result that clashes with the strong feeling we all have that this inference is correct. But in the absence of a theory that enables us to distinguish between quickly and carefully we must assign (go) the same form as (gi). (gi) John carried the eggs carefully to the wrong house. Therefore, John carefully carried the eggs to the wrong house. This inference does not appear valid. To be fair, however, we should add that it does not appear invalid, either; the first impression it presents is one of puzzlement. But the following account of (9I) explains why this should be so. In one of its senses, the premiss means (92): (92) that John was careful in his manner of carrying the eggs, but not necessarily in carrying them to the wrong house. And in one of its senses, the conclusion means (93): (93) that John was careful in carrying the eggs to the wrong house, but not necessarily careful in his manner of carrying them. This content downloaded from 207.46.13.113 on Thu, 06 Oct 2016 04:28:46 UTC All use subject to http://about.jstor.org/terms A SEMANTIC THEORY OF ADVERBS Word order in English is not in general a very reliable clue to adverbial scope; an adverb can usually be inserted in a variety of positions in a sentence without obtaining results that differ in meaning. Thus, though the word order of (9I) is slightly more natural in association with the senses we chose above, the premiss of (9i) can mean (93) and the conclusion of (9 I) can mean (92). Since (93) clearly does not follow from (92), this explains why (9i) should not appear valid; it has a sense in which its conclusion can be false while its premiss is true. On the other hand, since (9i) also has senses in which its conclusion and premiss say the same thing, we can explain why it does not appear invalid. Notice that it is natural to explain the ambiguity of John carefully carried the eggs to the wrong house as one of scope.29 On the reading associated with (92) the scope of carefully is carried the eggs; on that associated with (93) it is carried the eggs to the wrong house. If this is so, then commutativity must fail. Another principle that holds for many adverbs and at first appears plausible is that for all f, g e Q1, f(p, A P2) = f(pl) A f(P2)230 This corresponds to the joint validity of inferences such as (94) and (95) (94) E(XPx) (a) A t(fQx) (a) 5e((Px A Qx))(a) (95) e(X(Px A Qx))(a) Q(fPx) (a) A e( Qx) (a) But there are counterexamples to this principle, at least insofar as it implies (95): (8) is such a counterexample. It is more difficult to find evidence against (94), and it may be that this inference embodies a meaning postulate that could reasonably be imposed on all predicate adverbs of English. Perhaps the best known and most controversial inference pattern involving adverbs is exemplified by John walks slowly; therefore, John walks. Formally, this is (96).

Kripke models, interpreted realistically, have difficulty making sense of the thesis that there might have existed things that do not in fact exist, since a Kripke model in which this thesis is true requires a model structure in which there are possible worlds with domains that contain things that do not exist. This paper argues that we can use Kripke models as representational devices that allow us to give a realistic interpretation of a modal language. The method of doing this is sketched, with the help of an analogy with a Galilean relativist theory of spatial properties and relations.