The philosophical interest of verbal disputes is twofold. First, they play a key role in philosophical method. Many philosophical disagreements are at least partly verbal, and almost every philosophical dispute has been diagnosed as verbal at some point. Here we can see the diagnosis of verbal disputes as a tool for philosophical progress. Second, they are interesting as a subject matter for first-order philosophy. Reflection on the existence and nature of verbal disputes can reveal something about the nature of concepts, (...) language, and meaning. In this article I first characterize verbal disputes, spell out a method for isolating and resolving them, and draw out conclusions for philosophical methodology. I then use the framework to draw out consequences in first-order philosophy. In particular, I argue that the analysis of verbal disputes can be used to support the existence of a distinctive sort of primitive concept and that it can be used to reconstruct a version of an analytic/synthetic distinction, where both are characterized in dialectical terms alone. (shrink)

In this paper, I distinguish different kinds of pluralism about logical consequence. In particular, I distinguish the pluralism about logic arising from Carnap’s Principle of Tolerance from a pluralism which maintains that there are different, equally “good” logical consequence relations on the one language. I will argue that this second form of pluralism does more justice to the contemporary state of logical theory and practice than does Carnap’s more moderate pluralism.

Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...) we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism. (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 ...

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

Mark Wilson presents a highly original and broad-ranging investigation of the way we get to grips with the world conceptually, and the way that philosophical problems commonly arise from this. He combines traditional philosophical concerns about human conceptual thinking with illuminating data derived from a large variety of fields including physics and applied mathematics, cognitive psychology, and linguistics. Wandering Significance offers abundant new insights and perspectives for philosophers of language, mind, and science, and will also reward the interest of psychologists, (...) linguists, and anyone curious about the mysterious ways in which useful language obtains its practical applicability. (shrink)

With his customary incisiveness, W. V. Quine presents logic as the product of two factors, truth and grammar--but argues against the doctrine that the logical truths are true because of grammar or language. Rather, in presenting a general theory of grammar and discussing the boundaries and possible extensions of logic, Quine argues that logic is not a mere matter of words.

Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. Stewart Shapiro explores various such views. He argues that the question of meaning shift is itself context-sensitive and interest-relative.

W.V. Quine’s article “Two Dogmas of Empiricism” is one of the most influential works in 20thcentury philosophy. The article is cast most explicitly as an argument against logical empiricists such as Carnap, arguing against the analytic/synthetic distinction that they appeal to along with their verificationism. But the article has been read much more broadly as an attack on the notion..

The relation between linguistics and logic has been discussed in a, recent paper by Bar-Hillel} where it is argued that a disregard for workin logical syntax and semantics has caused linguists to limit themselves too narrowly in their inquiries, and to fall into several errors. In particular, Bar-Hillel asserts, they have attempted to derive relations of synonymy and so-called ‘rules of transfOI`1'Il8.tiOH,, such as the active—pussive relation, from distributional studies alone, and they have hesitated to rely on considerations of meaning (...) in linguistic analysis. No one can quarrel with the suggestion that linguists interest themselves in meaning or transformation rules, but the relevance of logical syntax and semsmticsz (at least as we now know them) to this study is very dubious. I think that a closer investigation of the assumptions and concems of logical syntax and semantics will show that the hope of applying the results which have been achieved in these fields to the solution of linguistic problems is illusory. (shrink)

This chapter contains sections titled: Abstract Introduction Defining Terms: Relativism, Pluralism, Tolerance What Is Logic? One Route to Pluralism: Logic ‐ as ‐ Model The Boundary Between Logical and Non ‐ Logical Terminology Vagueness Relativity to Structure References.

Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.

The logician's central concern is with the validity of argument. A logical theory ought, therefore, to provide a general criterion of validity. This book sets out to find such a criterion, and to describe the philosophical basis and the formal theory of a logic in which the premises of a valid argument are relevant to its conclusion. The notion of relevance required for this theory is obtained by an analysis of the grounds for asserting a formula in a proof.

This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles and natural language conditionals. The book ends by examining various applications of relevant logic and (...) presenting some interesting open problems. It will be of interest to a range of readers including advanced students of logic, philosophical and mathematical logicians, and computer scientists. (shrink)

With his customary incisiveness, W. V. Quine presents logic as the product of two factors, truth and grammar-but argues against the doctrine that the logical truths are true because of grammar or language. Rather, in presenting a general theory of grammar and discussing the boundaries and possible extensions of logic, Quine argues that logic is not a mere matter of words.

This is the first elementary book to employ the concept of infinitesimals.

Rudolf Carnap’s logical pluralism is often held to be one in which corresponding connectives in different logics have different meanings. This paper presents an alternative view of Carnap’s position, in which connectives can and do share their meaning in some contexts. This re-interpretation depends crucially on extending Carnap’s linguistic framework system to include meta-linguistic frameworks, those frameworks which we use to talk about linguistic frameworks. I provide an example that shows how this is possible, and give some textual evidence that (...) Carnap would agree with this interpretation. Additionally, I show how this interpretation puts the Carnapian position much more in line with the position given in Shapiro than had been thought before. (shrink)

Quine correctly argues that Carnap's distinction between internal and external questions rests on a distinction between analytic and synthetic, which Quine rejects. I argue that Quine needs something like Carnap's distinction to enable him to explain the obviousness of elementary mathematics, while at the same time continuing to maintain as he does that the ultimate ground for holding mathematics to be a body of truths lies in the contribution that mathematics makes to our overall scientific theory of the world. Quine's (...) arguments against the analytic/synthetic distinction, even if fully accepted, still leave room for a notion of pragmatic analyticity sufficient for the indicated purpose. (shrink)

Classical logic has been attacked by adherents of rival, anti-realist logical systems: Ian Rumfitt comes to its defence. He considers the nature of logic, and how to arbitrate between different logics. He argues that classical logic may dispense with the principle of bivalence, and may thus be liberated from the dead hand of classical semantics.

A remarkable development in twentieth-century mathematics is smooth infinitesimal analysis ('SIA'), introducing nilsquare and nilpotent infinitesimals, recovering the bulk of scientifically applicable classical analysis ('CA') without resort to the method of limits. Formally, however, unlike Robinsonian 'nonstandard analysis', SIA conflicts with CA, deriving, e.g., 'not every quantity is either = 0 or not = 0.' Internally, consistency is maintained by using intuitionistic logic (without the law of excluded middle). This paper examines problems of interpretation resulting from this 'change of logic', (...) arguing that standard arguments based on 'smoothness' requirements are question-begging. Instead, it is suggested that recent philosophical work on the logic of vagueness is relevant, especially in the context of a Hilbertian structuralist view of mathematical axioms (as implicitly defining structures of interest). The relevance of both topos models for SIA and modal-structuralism as appled to this theory is clarified, sustaining this remarkable instance of mathematical pluralism. (shrink)