This is a free book, 165 pages. It is for anyone who has had a solid introductory logic course and wants more. Topics covered include soundness and completeness for first-order logic, Tarski's theorem on the undefinability of truth, Gödel's incompleteness theorems, the undecidability of first-order logic, a smattering of second-order logic, and modal logic (both propositional and quantificational). I wrote it for use in my own course, because I thought I could present the most important results and concepts more clearly (...) than the available textbooks. (shrink)
This is the text of my comments on the project of dynamic semantics for the session on that topic at the Central Division APA meeting on April 21, 2007. The other speakers were Jeroen Groenendijk, Frank Veltman and Thony Gillies. I question the philosophical basis for dynamic semantics. My doubts have to do with the nature of information states and the norms of semantics. I also question the data that inspire the project. In particular, I question the data concerning presupposition (...) and the data concerning modal operators and conditionals. (shrink)
This is not a research paper. It is just a handout that I prepared for a course some years ago. It is a presentation of Kripke's theory of truth that I intend to be understandable even to people who have had only a first course in logic. Although elementary, it is completely precise. All the terms are defined and all the proofs (except one trivial induction) are given in detail. I am putting this on the web because I think there (...) are probably a lot of people who want to think about truth and who recognize that they need to know something about Kripke's theory but who are not sure whether they have the necessary background to follow the precise presentations that have been published. (shrink)
A lot of us have given up on the idea that there will be a naturalistic account of the relation of semantic reference and so have resolved to formulate our theories of semantics and communication without appeal to semantic reference. Still, there is a resilient intuition to the effect that I know the extensions of the terms of my language. This paper explicates that intuition without yielding to it. The key idea is to give a “skeptical” account of what it (...) is to “know the meaning” of a word, by which I mean an account of the status that is granted to a person in saying that he or she “knows the meaning” of a word. (shrink)
It is often assumed that, though we may speak in sentences that express propositions only inexplicitly, our thoughts must express their propositional contents explicitly. This paper argues that, on the contrary, thoughts too may be inexplicit. Inexplicit thoughts may effectively drive behavior inasmuch as they rest on a foundation of imagistic cognition. The paper also sketches an approach to semantic theory that accommodates inexplicitness in mental representations as well as in spoken sentences.
Recanati takes for granted the conveyance conception of linguistic communica- tion, although it is not very clear exactly where he lies on the spectrum of possible variations. Even if we disavow all such conceptions of linguistic communication, there will be a place for semantic theory in articulating normative concepts such as logical consistency and logical validity. An approach to semantics focused on such normative concepts is illustrated using the example of “It’s raining”. It is argued that Recanati’s conception of semantics (...) as involving the pragmatics of saturation and modulation cannot account for the logical properties of “It’s raining. (shrink)
In recent years, many philosophers have supposed that perceptual representations have propositional content. A prominent rationale for this supposition is the assumption that perceptions may justify beliefs, but this rationale can be doubted. This rationale may be doubted on the grounds that there do not seem to be any viable characterizations of the belief-justifying propositional contents of perceptions. An alternative is to model perceptual representations as marks in a perceptual similarity space. A mapping can be defined between points in perceptual (...) similarity space and points in an objective quality space. The correctness of perceptual representation can then be defined as a kind of accuracy of mapping rather than as the truth of a proposition. The phenomenon of seeing-as can be accounted for as a matter of the location of marks in perceptual similarity space relative to other marks in perceptual similarity space. Perceptual representations, on this account, will not justify beliefs, but they may nonetheless guide judgment. (shrink)
Semantics deals with the literal meaning of sentences. Pragmatics deals with what speakers mean by their utterances of sentences over and above what those sentences literally mean. However, it is not always clear where to draw the line. Natural languages contain many expressions that may be thought of both as contributing to literal meaning and as devices by which speakers signal what they mean. After characterizing the aims of semantics and pragmatics, this chapter will set out the issues concerning such (...) devices and will propose a way of dividing the labor between semantics and pragmatics. To semantics belongs the job of defining the conditions under which a sentence is true relative to a context. To pragmatics belongs the job of explicating the conditions under which a given context pertains to a given conversation. (shrink)
This paper presents a precise semantics for incomplete predicates such as “ready”. Incomplete predicates have distinctive logical properties that a semantic theory needs to accommodate. For instance, “Tipper is ready” logically implies “Tipper is ready for something”, but “Tipper is ready for something” does not imply “Tipper is ready”. It is shown that several approaches to the semantics of incomplete predicates fail to accommodate these logical properties. The account offered here defines contexts as structures containing an element called a proposition (...) set, which contains atomic propositions and negations of atomic propositions. The condition under which “Tipper is ready” is true in a context is defined in terms of the contents of the proposition set for the context. On this account, the content of the context pertinent to a conversation must be determined not by what speakers have in mind but by relations of objective relevance. (shrink)
Carey speculates that the representations of core cognition are entirely iconic. However this idea is undercut by her contention that core cognition includes concepts such as object and agency, which are employed in thought as predicates. If Carey had taken on board her claim that core cognition is iconic, very different hypotheses might have come into view.
At least since Locke, philosophers and psychologists have usually held that concepts arise out of sensory perceptions, thoughts are built from concepts, and language enables speakers to convey their thoughts to hearers. Christopher Gauker holds that this tradition is mistaken about both concepts and language. The mind cannot abstract the building blocks of thoughts from perceptual representations. More generally, we have no account of the origin of concepts that grants them the requisite independence from language. Gauker's alternative is to show (...) that much of cognition consists in thinking by means of mental imagery, without the help of concepts, and that language is a tool by which interlocutors coordinate their actions in pursuit of shared goals. Imagistic cognition supports the acquisition and use of this tool, and when the use of this tool is internalized, it becomes the very medium of conceptual thought. (shrink)
Recent philosophical literature has debated the question of how much context-relativity needs to be countenanced in precise semantic theories for natural languages and has displayed different conceptions of the way in which it might be accommodated. This article presents reasons to think that context-relativity is a phenomenon that semantic theory must accommodate and identifies some of the issues concerning how it ought to be accommodated.
Jason Stanley has argued that in order to obtain the desired readings of certain sentences, such as “In most of John’s classes, he fails exactly three Frenchmen”, we must suppose that each common noun is associated with a hidden indexical that may be either bound by a higher quantifier phrase or interpreted by the context. This paper shows that the desired readings can be obtained as well by interpreting nouns as expressing relations and without supposing that nouns are associated with (...) hidden indexicals. Stanley’s theory and the present alternative are not equivalent, however. They differ over the status of sentences such as “Every student is happy and some student is not happy”. On Stanley’s theory, this sentence will be true in some contexts, while on the present alternative it will be true in no context. Considerations in favor of the present theory’s verdict on such sentences are presented. The broader question at issue is the correct way to incorporate context-relativity into formal semantics. (shrink)
Some expressions, such as “all” and “might”, must be interpreted differently, relative to a single context, when embedded under “says that” than when unembedded. Egan, Hawthorne and Weatherson have appealed to that fact to argue that utterance-truth is relative to point of evaluation. This paper shows that the phenomena do not warrant this relativistic response. Instead, contexts may be defined as entities that assign other contexts to contextually relevant people, and context-relative truth conditions for indirect discourse sentences can be satisfactorily (...) formulated in terms of such contexts. (shrink)
Jill de Villiers has argued that children's mastery of sentential complements plays a crucial role in enabling them to succeed at false-belief tasks. Josef Perner has disputed that and has argued that mastery of false-belief tasks requires an understanding of the multiplicity of perspectives. This paper attempts to resolve the debate by explicating attributions of desires and beliefs as extensions of the linguistic practices of making commands and assertions, respectively. In terms of these linguistic practices one can explain why desire-talk (...) will precede belief-talk and why even older children will have difficulty attributing incompatible desires. (shrink)
This paper criticizes the dominant approaches to presupposition projection and proposes an alternative. Both the update semantics of Heim and the discourse representation theory of van der Sandt have problems in explicating the presuppositions of disjunctions. Moreover, Heim's approach is committed to a conception of accommodation that founders on the problem of informative presuppositions, and van der Sandt's approach is committed to a conception of accommodation that generates over-interpretations of utterances. The present approach borrows Karttunen's idea that instead of associating (...) presuppositions with sentences, we should define the conditions that contexts must meet in order to satisfy-the-presuppositions-of a sentence. However, in place of Karttunen's conception of contexts in terms of common ground, the present theory substitutes a conception of contexts as objective entities that are independent of the attitudes of the interlocutors. Contexts, so conceived, may be defined as containing sets of relevant possibilities. This allows us to define the conditions under which a context satisfies-the-presuppositions-of a disjunction. (shrink)
The proposition expressed by a sentence is relative to a context. But what determines the content of the context? Many theorists would include among these determinants aspects of the speaker’s intention in speaking. My thesis is that, on the contrary, the determinants of the context never include the speaker’s intention. My argument for this thesis turns on a consideration of the role that the concept of proposition expressed in context is supposed to play in a theory of linguistic communication. To (...) illustrate an alternative approach, I present an original theory of the reference of demonstratives according to which the referent of a demonstrative is the object that adequately and best satisfies certain accessibility criteria. Although I call my thesis zero tolerance for pragmatics, it is not an expression of intolerance for everything that might be called “pragmatics.”. (shrink)
A similarity space is a hyperspace in which the dimensions represent various dimensions on which objects may differ. The similarity space theory of concepts is the thesis that concepts are regions of similarity spaces that are somehow realized in the brain. Proponents of such a theory of concepts include Paul Churchland and Peter Gärdenfors. This paper argues that the similarity space theory of concepts is mistaken because regions of similarity spaces cannot serve as the components of judgments. It emerges that (...) although similarity spaces cannot model concepts, they may model a kind of nonconceptual representation. (shrink)
It is obvious that there are kinds of cognition -- mental problem solving -- that do not require spoken language. But it should not be obvious that peculiarly conceptual thought is independent of spoken language. This paper is a critical survey of arguments concluding that conceptual thought must be independent of language. The special emphasis is on arguments that John Searle has put forward, but others are considered as well. These include the claim that only the intentionality of thought is (...) "intrinsic", arguments from the nature of speech acts, appeals to the fact that animals and babies think, and the computational theory of mind (this last not being one of Searle's arguments). Finally, there is an argument from a certain conception of linguistic communication. (shrink)
The question whether semantics is a normative discipline can be formulated as a question about the meaning of the word “means”. If I assert, “The word ‘gatto’ in Italian means cat,” what have I done? The naturalist about meaning claims that I have asserted that a certain natural relation obtains between Italian speakers’ tokens of “gatto” and cats. Or at least, I have asserted something about the way Italian speakers use the word “gatto”, which way presumably has something to do (...) with cats. The normativist claims, on the contrary, that what I have said is that in speaking Italian one ought to use the word “gatto” in a certain way, which way has something to do with cats. What I have done is endorse a certain proposal about how to use the word, which, if accepted, will have normative force. (shrink)
A number of philosophers have argued that the key to understanding the semantic paradoxes is to recognize that truth is essentially relative to context. All of these philosophers have been motivated by the idea that once a liar sentence has been uttered we can 'step back' and, from the point of view of a different context, judge that the liar sentence is true. This paper argues that this 'stepping back' idea is a mistake that results from failing to relativize truth (...) to context in the first place. Moreover, context-relative liar sentences, such as 'This sentence is not true in any context' present a paradox even after truth has been relativized to context. Nonetheless, the relativization of truth to context may offer us the means to avoid paradox, if we can justifiably deny that a sentence about a context can be true in the very context it is about. (shrink)
"If you turn left at the next corner, you will see a blue house at the end of the street." That sentence -- a conditional -- might be true even though it is possible that you will not see a blue house at the end of the street when you turn left at the next corner. A moving van may block your view; the house may have been painted pink; a crow might swoop down and peck out your eyes. Still, (...) in some contexts, we might ignore these possibilities and correctly assert the conditional. In this book, Christopher Gauker argues that such context-relativity is the key to understanding the semantics of conditionals. Contexts are defined as objective features of the situation in which a conversation takes place, and the semantic properties of sentences -- conditionals included -- are defined in terms of assertibility in a context. One of the primary goals of a theory of conditionals has to be to distinguish correctly between valid and invalid arguments containing conditionals. According to Gauker, an argument is valid if the conclusion is assertible in every context in which the premises are assertible. This runs counter to what Gauker sees as a systematic misreading of the data by other authors, who judge arguments to be invalid if they can think of a context in which the premises are judged true and some other context in which the conclusion is judged false. Different schools of thought on conditionals reflect fundamentally different approaches to semantics. Gauker offers his theory as a motive and test case for a distinctive kind of semantics that dispenses with reference relations and possible worlds. (shrink)
Language acquisition is often said to be a process of mapping words into pre-existing concepts. Some researchers regard this theory as an immediate corollary of the assumption that all problem-solving involves the application of concepts. But in light of basic philosophical objections to the theory of language acquisition, that kind of rationale cannot be very persuasive. To have a reason to accept the theory of language acquisition despite the philosophical objections, we ought to have experimental evidence for the existence of (...) concepts in prelinguistic children. One of the few lines of research that attempts to provide such evidence is the work of Paul Quinn, who claims that looking-time results show that four-month old infants form "category representations". This paper argues that Quinn's results have an alternative explanation. A distinction is drawn between conceptual thought and the perception of comparative similarity relations, and it is argued that Quinn's results can be explained in terms of the latter rather than the former. (shrink)
This paper spells out the positive theory sketched at the end of "Against Stepping Back".): According to deflationists, [p] is true is in some sense equivalent to p. The problem that the semantic paradoxes pose for the deflationist is to explicate this equivalence without relying on a semantics grounded in the sort of real reference relations that a deflationist thinks do not exist. More generally, the deflationist is challenged to give an account of logical validity that does not force us (...) to countenance such relations. (The usual model-theoretic definition seems to presuppose that there is some special interpretation, the intended interpretation, such that truth simpliciter is truth on that intended interpretation. So if the deflationist adopts this sort of definition, the deflationist will be challenged to identify the intended interpretation without positing real reference relations.) Fortunately, a precise semantics compatible with the deflationist philosophy can be had as follows: First, we define a context as a certain sort of set constructed from a basis of literals (atomic sentences and negations of atomic sentences). This formal account of contexts has to be supplemented with an account of the conditions under which a structure satisfying the formal definition is the structure of that kind pertinent ot a given conversation. For each syntactic type of sentence, we define the conditions under which a sentence of that type is assertible relative to a context. In particular, we define the conditions under which sentences of the form " [p] is true" are assertible in a context, and we define the conditions under which sentences of the form "[p] is assertible in context G" are assertible in a context. Finally, logical validity is defined as preservation of assertibility in a context. It is demonstrated that this approach to semantics resists the semantic paradoxes. (shrink)
Many philosophers hold that for various reasons there must be psychological laws governing beliefs and desires. One of the few serious examples that they offer is the _belief-desire law_, which states, roughly, that _ceteris paribus_ people do what they believe will satisfy their desires. This paper argues that, in fact, there is no such law. In particular, decision theory does not support the contention that there is such a law.
Many philosophers hold that beliefs and desires are theoretical entities postulated for the sake of predicting and explaining people's behaviors. This paper offers a very different perspective on the nature of beliefs and desires. According to this, the first step is to understand the nature of assertion and command. Then, to understand the nature of belief and desire, what one must do is extend one's understanding of assertion and commandto assertions and commands on behalf of others; for to attribute a (...) belief is to make an assertion on someone's behalf, and to attribute a desire is to make a command on someone's behalf. From this perspective we can recognize that explanation and prediction are not the primary rationale for attributions of beliefs and desires. A number of foundational issues will also be addressed, having to do with cognition, semantics and ontology. (shrink)
According to the expressive theory of communication, the primary function of language is to enable speakers to convey the content of their thoughts to hearers. According to Tyler Burge's social externalism, the content of a person's thought is relative to the way words are used in his or her surrounding linguistic community. This paper argues that Burge's social externalism refutes the expressive theory of communication.
Carruthers labels as “too strong” the thesis that language is necessary for all conceptual thought. Languageless creatures certainly do think, but when we get clear about what is meant by “conceptual thought,” it appears doubtful that conceptual thought is possible without language.
As Grice defined it, a speaker conversationally implicates that p only if the speaker expects the hearer to recognize that the speaker thinks that p. This paper argues that in the sorts of cases that Grice took as paradigmatic examples of conversational implicature there is in fact no need for the hearer to consider what the speaker might thus have in mind. Instead, the hearer might simply make an inference from what the speaker literally says and the situation in which (...) the utterance takes place. In addition, a number of sources of the illusion of conversational implicatures in Grice's sense are identified and diagnosed. (shrink)
I define T-schema deflationism as the thesis that a theory of truth for our language can simply take the form of certain instances of Tarski's schema (T). I show that any effective enumeration of these instances will yield as a dividend an effective enumeration of all truths of our language. But that contradicts Gödel's First Incompleteness Theorem. So the instances of (T) constituting the T-Schema deflationist's theory of truth are not effectively enumerable, which casts doubt on the idea that the (...) T-schema deflationist in any sense has a theory of truth. (The argument in section 2 of "Semantics for Deflationists" supercedes this paper.). (shrink)
Inference rule deflationism is the thesis that the nature of truth can be explained in terms of the inference rules governing the word "true". This paper argues, first, that, in light of the semantic paradoxes, the inference rule deflationist must reject some of the classical rules of inference. It is argued, secondly, that inference rule deflationism is incompatible with model theoretic approaches to the definition of logical validity. Here the argument focuses on the question whether the number of primitive referring (...) expressions in a natural language is denumerably infinite. Finally, it is argued that these conclusions pertain to T-schema deflationism and Horwich's minimal theory as well. (shrink)
[Written in 1999. Still relevant, but references are not up-to-date.] If one asks about the relation between thought and language, people expect the issue to concern such matters as whether we think in language, whether creatures without language can "think", and the way language shapes our concepts. In my opinion, there is a much deeper question, which concerns the nature of linguistic communication. Philosophers and linguists standardly conceive of language as basically a means by which speakers convey the content of (...) their thoughts to others. The question is whether that is a correct picture of linguistic communication. This is a question about the relation between thought and language because this standard picture of communication gives propositional thought a certain priority over language. If, as I intend to show, there are reasons to doubt the standard picture, then we cannot expect to make much progress with the more superficial questions without thinking about the nature of linguistic communication. (shrink)
Millikan proposes that there are mapping functions through which spoken sentences represent reality. Such mappings seem to depend on thoughts that words express and on concepts as components of such thoughts, but such concepts would conflict with Millikan's other claims about concepts and language.
Feature-based theories of concept formation face two dilemmas. First, for many natural concepts, it is hard to see how the concepts of the features could be developmentally more basic. Second, concept formation must be guided by “abstraction heuristics,” but these can be neither universal principles of rational thought nor natural conventions.
For many purposes in pragmatics one needs to appeal to a context of utterance conceived as a set of sentences or propositions. The context of utterance in this sense is often defined as the set of assumptions that the speaker supposes he or she shares with the hearer. I argue by stages that this is a mistake. First, if contexts must be defined in terms of shared assumptions, then it would be preferable to define the context as the set of (...) assumptionsthat the interlocutors really do share. Second, not all shared assumptions belong to the context, because not all are relevant. Third, hearers need not accept every member of the context, because some presuppositions are informative. Finally, presupposition coordination problems show that contexts may have contents that even the speaker does not accept. Contexts, we may conclude, are mind-transcendent. In one sense of the term a "presupposition" is an interlocutor's take on this mind-transcendent context. (shrink)
The proposition expressed by an utterance of a quantified sentence depends on a domain of discourse somehow determined by the context. How does the context of utterance determine the content of the domain of discourse? Many philosophers would approach this question from the point of view of an expressive theory of linguistic communication, according to which the primary function of language is to enable speakers to convey the propositional contents of their thoughts to hearers. This paper argues that (...) from this point of view there is no persuasive treatment of the determinants of the domain of discourse. The argument focuses on an abnormal case in which the domain the speaker has in mind is not evident to the hearer. In this way the question concerning the determinants of the domain of discourse is used to challenge the expressive theory of communication. (shrink)
The rule of universal instantiation appears to be subject to counterexamples, although the rule of existential generalization is not subject to the same doubts. This paper is a survey of ways of responding to this problem, both conservative and revisionist. The conclusion drawn is that logical validity should be defined in terms of assertibility in a context rather than in terms of truth on an interpretation. Contexts are here defined, not in terms of the attitudes of the interlocutors, but in (...) terms of the goals of conversation, and assertibility is explained in terms of cooperation. (shrink)
Kripke's puzzle about rule-following is a form of the traditional problem of the nature of linguistic meaning. A skeptical solution explains not what meaning is but the role that talk of meaning plays in the linguistic community. Contrary to what some have claimed, the skeptical approach is not self-refuting. However, Kripke's own skeptical solution is inadequate. He has not adequately explained the conditions under which we are justified in attributing meanings or the utility of the practice of attributing meanings. An (...) alternative skeptical solution may be founded on a nonepistemic conception of assertibility. Roughly, a sentence is assertible if it facilitates cooperation. The function of meaning-talk is to resolve certain sorts of conflicts in assertion. Attributions of meaning to persons outside the community may be a proper expression of a practice whose reason for being lies entirely within the community. -/- . (shrink)