Vagueness provides the first comprehensive examination of a topic of increasing importance in metaphysics and the philosophy of logic and language. Timothy Williamson traces the history of this philosophical problem from discussions of the heap paradox in classical Greece to modern formal approaches such as fuzzy logic. He illustrates the problems with views which have taken the position that standard logic and formal semantics do not apply to vague language, and defends the controversial realistic view that vagueness is a kind (...) of ignorance--that there really is a grain of sand whose removal turns a heap into a non-heap, but we cannot know which one it is. (shrink)

Most of our knowledge is inexact, and known by us to be so. An example of such known inexactness will be described in some detail. The description seems to entail a contradiction. However, the paradoxical reasoning rests on an assumption. It will be suggested that the description is correct and this assumption false. Its failure will be explained by means of a picture of inexact knowledge in which the notion of a margin for error is central. This picture suggests diagnoses (...) of other paradoxical arguments: Surprise Examinations, backwards inductions about Iterated Prisoner's Dilemma, and the Heap. (shrink)

In virtue of its form [‘I am here’] must be true on any occasion on which [it is] asserted, and yet the proposition it expresses on each occasion [is] contingent. Intuitively, [‘I am here now’] is deeply, and in some sense universally, true. One need only understand the meaning of [it] to know that it cannot be uttered falsely. The sentence ‘I am here’ has the peculiar property that whenever I utter it, it is bound to be true. Even if (...) I am lost and do not know where I am, I can bravely say ‘I am here’, and know that I am expressing a truth. (shrink)

Demonstratives seem to have posed a severe difficulty for Frege’s philosophy of language, to which his doctrine of incommunicable senses was a reaction. In “The Thought,” Frege briefly discusses sentences containing such demonstratives as “today,” “here,” and “yesterday,” and then turns to certain questions that he says are raised by the occurrence of “I” in sentences (T, 24-26). He is led to say that, when one thinks about oneself, one grasps thoughts that others cannot grasp, that cannot be communicated. However, (...) nothing could be more out of the spirit of Frege’s account of sense and thought than an incommunicable, private thought. In the first part of the paper, I explain the problem demonstratives pose for Frege, and explore three ways he might have dealt with it. I argue that none of these ways provides Frege with a solution to his problem consistent with his philosophy of language. The first two are plausible as solutions, but contradict his identification of the sense expressed by a sentence with a thought. The third preserves the identification, but is implausible. In the second part, I suggest that Frege was led to his doctrine of incommunicable senses as a result of some appreciation of the difficulties his account of demonstratives faces, for these come quickly to the surface when we think about “I.” I argue that incommunicable senses won’t help. I end by trying to identify the central problem with Frege’s approach, and sketching an alternative. (shrink)

In natural language we rarely use relation-words with more than three argument places. This paper studies one systematic device, rooted in natural language, by which relations of greater adicity can be expressed. It is based on a higher-order relation between 1-place, 2-place, and 4-place relations (and so on) of which the relation between the positive and comparative degrees of a predicate is a special case. Two formal languages are presented in this connection, one of which represents the language of communication (...) and the other the contextual information against which the first language is interpreted. A semantical theory is described, which treats the two languages in an interdependent way. Logical consequence is non-compact. Connections with issues about vagueness are made. (shrink)

In 'You and She*' (ANALYSIS 51.3, June 1991) C.J.F. Williams notes the importance of reflexive pronouns in attributions of propositional attitudes, and claims to improve upon an earlier account of Hector-Neri Castaneda's in [1]. However, to the extent which his remarks are accurate, they reveal nothing that Castaneda hasn't already said, while insofar as they are new, they obliterate distinctions vital to Castaneda's theory. Castaneda called these pronouns quasi-indicators and noted that they function as linguistic devices used for attributing indexical (...) reference to others. For example, in hearing Arthur say 'I am wise' we would report his claim in English with, (1) Arthur thinks that he himself is wise. where 'he himself' is a quasi-indicator used to attribute to Arthur reference to himself qua self -- an expression that Castaneda abbreviated with 'he*.' Note that (1) is quite different from, (2) Arthur thinks that I am wise for 'I', functioning here as an indexical term, represents only the speaker's reference. Nor can (1) be identified with, (3) Arthur thinks that Arthur is wise. for this fails to represent the indexical character of Arthur's thought. Thus, (3) falls short of the informational content of (1). Moreover, as Williams, echoing Castaneda, points out, Arthur might not know that he himself is Arthur, or that he is named 'Arthur.' Hence, (3) might be false even if (1) is true. Williams observes that 'she' can also be used in oratio obliqua to report an indexical 1 usage, e.g., in (4) Arthur told Mary that she ought to talk to Shirley Makepeace's.. (shrink)

Indexicality is a feature of predicates and predicate components (verbs, adjectives, adverbs and the like) as well as of referring expressions. With classic referring indexicals such as 'I' or 'that' a distinctive rule takes us from token and context to some item present in the content which is the semantic correlate of the token. Predicates and predicate components may function in an analogous fashion. For example 'thus' is an indexical adverb which latches onto some manner of performance present in its (...) context. 'John sang thus', said while indicating someone singing discordantly, claims that John sang discordantly. The phenomenon of predicatival indexicality is widespread in English and is expressed in a variety of idioms. Indexical predication plays important epistemological and psychological roles and the notion may have other interesting philosophical applications. (shrink)

Definite descriptions, I shall argue, have two possible functions. 1] They are used to refer to what a speaker wishes to talk about, but they are also used quite differently. Moreover, a definite description occurring in one and the same sentence may, on different occasions of its use, function in either way. The failure to deal with this duality of function obscures the genuine referring use of definite descriptions. The best known theories of definite descriptions, those of Russell and Strawson, (...) I shall suggest, are both guilty of this. Before discussing this distinction in use, I will mention some features of these theories to which it is especially relevant. (shrink)

There are at least four varieties of quotation, including pure, direct, indirect and mixed. A theory of quotation, we argue, should give a unified account of these varieties of quotation. Mixed quotes such as 'Alice said that life is 'difficult to understand'', in which an utterance is directly and indirectly quoted concurrently, is an often overlooked variety of quotation. We show that the leading theories of pure, direct, and indirect quotation are unable to account for mixed quotation and therefore unable (...) to provide a unified theory. In the second half of the paper we develop a unified theory of quotation based on Davidson's demonstrative theory. 'Language is the instrument it is because the same expression, with semantic features (meaning) unchanged, can serve countless purposes.' (Davidson 1968). (shrink)

This textbook based on syntactic theory draws on Chomsky's minimalist programme.

The author resolves a conflict between Frege's view that the cognitive significance of coreferential names may be distinct and Kaplan's view that since coreferential names have the same "character", they have the same cognitive significance. A distinction is drawn between an expression's "character" and its "cognitive character". The former yields the denotation of an expression relative to a context (and individual); the latter yields the abstract sense of an expression relative to a context (and individual). Though coreferential names have the (...) same character, they may have distinct cognitive characters. Propositions involving these abstract senses play an important role in explaining de dicto belief contexts. (shrink)