The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, (...) and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. (shrink)

The product/process distinction with regards to “argument” has a longstanding history and foundational role in argumentation theory. I shall argue that, regardless of one’s chosen ontology of arguments, arguments are not the product of some process of arguing. Hence, appeal to the distinction is distorting the very organizational foundations of argumentation theory and should be abandoned.

The problem addressed is that of finding a sound characterization of ambiguity. Two kinds of characterizations are distinguished: tests and definitions. Various definitions of ambiguity are critically examined and contrasted with definitions of generality and indeterminacy, concepts with which ambiguity is sometimes confused. One definition of ambiguity is defended as being more theoretically adequate than others which have been suggested by both philosophers and linguists. It is also shown how this definition of ambiguity obviates a problem thought to be posed (...) by ambiguity for truth theoretical semantics. In addition, the best known test for ambiguity, namely the test by contradiction, is set out, its limitations discussed, and its connection with ambiguity's definition explained. The test is contrasted with a test for vagueness first proposed by Peirce and a test for generality propounded by Margalit. (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)

Noam Chomsky's book on syntactic structures is a serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction ...

Lexical Semantics is about the meaning of words. Although obviously a central concern of linguistics, the semantic behaviour of words has been unduly neglected in the current literature, which has tended to emphasize sentential semantics and its relation to formal systems of logic. In this textbook D. A. Cruse establishes in a principled and disciplined way the descriptive and generalizable facts about lexical relations that any formal theory of semantics will have to encompass. Among the topics covered in depth are (...) idiomaticity, lexical ambiguity, synonymy, hierarchical relations such as hyponymy and meronymy, and various types of oppositeness. Syntagmatic relations are also treated in some detail. The discussions are richly illustrated by examples drawn almost entirely from English. Although a familiarity with traditional grammar is assumed, readers with no technical linguistic background will find the exposition always accessible. All readers with an interest in semantics will find in this original text not only essential background but a stimulating new perspective on the field. (shrink)

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

In this book two of the leading figures in argumentation theory present a view of argumentation as a means of resolving differences of opinion by testing the acceptability of the disputed positions. Their model of a 'critical discussion' serves as a theoretical tool for analysing, evaluating and producing argumentative discourse. They develop a method for the reconstruction of argumentative discourse that takes into account all aspects that are relevant to a critical assessment. They also propose a practical code of behaviour (...) for discussants who want to resolve their differences in a reasonable way. This is a major contribution to the study of argumentation and will be of particular value to professionals and graduate students in speech communication, informal logic, rhetoric, critical thinking, linguistics, and philosophy. (shrink)

This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...

A Theory of Argument is an advanced textbook intended for students in philosophy, communications studies and linguistics who have completed at least one course in argumentation theory, information logic, critical thinking or formal logic. Containing nearly 400 exercises, Mark Vorobej develops a novel approach to argument interpretation and evaluation. One of the key themes of the book is that we cannot succeed in distinguishing good argument from bad arguments until we learn to listen carefully to others. Part I develops a (...) relativistic account of argument cogency that allows for rational disagreement. Part II offers a comprehensive and rigorous account of argument diagramming. Hybrid arguments are contrasted with linked and convergent arguments, and a novel technique is introduced for graphically recording disagreements with authorial claims. (shrink)

David Hitchcock, in his recent “Informal Logic and the Concept of Argument”, defends a recursive definition of ‘argument.’ I present and discuss several problems that arise for his definition. I argue that refining Hitchcock’s definition in order to resolve these problems reveals a crucial, but minimally explicated, relation that was, at best, playing an obscured role in the original definition or, at worst, completely absent from the original definition.

A certain metaphysical thesis about meaning that we'll call Informational Role Semantics (IRS) is accepted practically universally in linguistics, philosophy and the cognitive sciences: the meaning (or content, or `sense') of a linguistic expression1 is constituted, at least in part, by at least some of its inferential relations. This idea is hard to state precisely, both because notions like metaphysical constitution are moot and, more importantly, because different versions of IRS take different views on whether there are constituents of meaning (...) other than inferential role, and on which of the inferences an expression occurs in are meaning constitutive. Some of these issues will presently concern us; but for now it will do just to gesture towards such familiar claims as that: it's part and parcel of dog meaning dog2 that the inference from x is a dog to x is an animal is valid; it's part and parcel of boil meaning boil that the inference from x boiled y to y boiled is valid; it's part and parcel of kill meaning kill that the inference from x killed y to y died is valid; and so on. (See Cruse, Ch. 1 and passim.) IRS brings in its train a constellation of ancillary doctrines. Presumably, for example, if an inference is constitutive of the meaning of a word, then learning the word involves learning that the inference holds. If dog means dog because dog ---> animal is valid, then knowing that dog ---> animal is valid is part and parcel of knowing what the word dog means; and, similarly, learning that x boiled y ---> y boiled is part and parcel of learning what boil means, and so forth. IRS constrains grammatical theories. The semantic lexicon of a language is supposed to make explicit whatever one has to know to understand the lexical expressions of the language, so IRS implies that meaning constitutive inferences are part of the semantic lexical entries for items that have them. Lexical entries are thus typically complex objects (`bundles of inferences') according to standard interpretations of IRS.. (shrink)