Christopher Gauker

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.

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.

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.

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.).

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.

The network theory of conceptual development is the theory that conceptual developmentmay be represented as a process of constructing a network of linked nodes. The nodes of such a network represent concepts and the links between nodes represent relations between concepts. The structure of such a network is not determined by experience alone but must evolve in accordance with abstraction heuristics, which constrain the varieties of network between which experience must decide. This paper criticizes the network theory on the grounds that current proposals regarding these abstraction heuristics all fail, and further, that, given certain plausible assumptions, no viable account of these abstraction heuristics will be possible. Abstraction heuristics cannot be universal principles of rational thought because virtually no concept is intrinsically unsuitable for use in a true and useful representation of reality. Nor can they be species-specific natural conventions because in that case, it is argued, we would not be able even in principle to learn to understand the language of creatures who used different ones.

The key to an adequate account of presupposition projection is to accommodate the fact that the presuppositions of a sentence cannot always be read off the sentence but can often be identified only on the basis of prior utterances in the conversation in which the sentence is uttered. In addition, an account of presupposition requires a three-valued semantics of assertibility and deniability in a context. Presuppositions can be explicated as sentences that belong to the conversation and the assertibility of which ensures that the remaining assertibility and deniability conditions of the presupposition-bearing sentence are dual to one another. The prevailing approach to presuppositions, grounded in Heim’s context-change semantics, can be criticized both on philosophical grounds and for failing to accommodate the phenomena

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

Much discussed but still unresolved is whether a subject's internal physical structure is a sufficient condition for his beliefs and desires. The question has sometimes been expressed as a question about microstructurally identical Doppelgänger. Imagine two subjects who are identical right down to the ions traversing the synapses. Their senses are stimulated in all the same ways, their bodies execute the same motions, and identical physical events mediate between the sensory inputs and the behavioral outputs. Must they have the very same beliefs and desires? Let us call the thesis that they must, internalism. The internalist may hold that a physical similarity less complete than this will also guarantee identity in beliefs and desires, but certainly, he holds, perfect identity of internal physical histories will suffice.Internalism will be opposed by those who sense that the nature of mentality is closely tied to the nature of explanation in terms of mental states and that in explaining a subject's behavior we cannot abstract, even in principle, from the character of the environment in which the subject is embedded. This essay offers a partial articulation of this point of view and shows how it conflicts with internalism. A consequence of the view to be described is that our attributions of belief must reflect the probabilistic regularities in the subject's environment. As we shall see, this consequence conflicts with internalism in two ways. The first conflict turns on the fact that there is no limit on the possible variety of such regularities. The second conflict turns on the fact that two subjects might by chance have the same micro-structural history though different probabilistic regularities obtain in their respective environments.

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.

[Note 2015: Much of the content of these remarks has now been published in my paper "Presuppositions as Anaphoric Duality Enablers", Topoi.] 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.

A theory of reference may be either an analysis of reference or merely an account of the correct use of the verb "refer". If we define the validity of arguments in the standard way, in terms of assignments of individuals and sets to the nonlogical vocabulary of the language, then we will be committed to seeking an analysis of reference. Those who prefer a metalinguistic account, therefore, will desire an alternative to standard semantics. One alternative is the Quinean conception of logical validity as essentially a matter of logical form. Another alternative is Leblanc's truth-value semantics. But these prove to be either inadequate for purposes of metatheory or philosophically unsatisfactory. This paper shows how validity (i.e., semantic consequence) may be defined in a way that avoid the problems facing these other alternatives to standard semantics and also permits a metalinguistic account of reference. The validity of arguments is treated as a matter of logical form, but validity for forms is defined on analogy with the definition of semantic consequence in truth-value semantics. (A more radical kind of semantics without reference is the context logical approach represented in several of my other publications.)

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.

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.

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.

In order to capture our intuitions about the logical consistency of sentences and the logical validity of arguments, a semantics for a natural language has to allow for the fact that different occurrences of a single bare demonstrative, such as “this”, may refer to different objects. But it is not obvious how to formulate a semantic theory in order to achieve this result. This paper first criticizes several proposals: that we should formulate our semantics as a semantics for tokens, not expressions, Kaplan’s idea that syntax associates a demonstration with each occurrence of a demonstrative, Braun’s idea that a context may specify shifts in context across the evaluation of the expressions in a sentence; and Predelli’s idea that we should countenance different classes of contexts. Finally, a solution is proposed that allows that a natural language persists across the addition of basic lexical items but defines logical properties in terms of language stages. A surprising result is that we do not need to think of demonstratives as taking different referents in different situations

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.