Logic, the tradition has it, is normative for reasoning. But is that really so? And if so, in what sense is logic normative for reasoning? As Gilbert Harman has reminded us, devising a logic and devising a theory of reasoning are two separate enterprises. Hence, logic's normative authority cannot reside in the fact that principles of logic just are norms of reasoning. Once we cease to identify the two, we are left with a gap. To bridge the gap one would (...) need to produce what John MacFarlane has appropriately called a bridge principle, i.e. a general principle articulating a substantive and systematic link between logical entailment and norms of reasoning. This is Harman's skeptical challenge. In this paper I argue that Harman's skeptical challenge can be met. I show how candidate bridge principles can be systematically generated and evaluated against a set of well‐motivated desiderata. Moreover, I argue that bridge principles advanced by MacFarlane himself and others, for all their merit, fail to address the problem originally set forth by Harman and so do not meet the skeptical challenge. Finally, I develop a bridge principle that meets Harman's requirements as well as being substantive. (shrink)

Some writers object to logical pluralism on the grounds that logic is normative. The rough idea is that the relation of logical consequence has consequences for what we ought to think and h...

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.

Dialetheism is the view that some contradictions are true. This is a view which runs against orthodoxy in logic and metaphysics since Aristotle, and has implications for many of the core notions of philosophy. Doubt Truth to Be a Liar explores these implications for truth, rationality, negation, and the nature of logic, and develops further the defense of dialetheism first mounted in Priest's In Contradiction, a second edition of which is also available.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Available for the first time in 20 years, here is the Rudolf Carnap's famous principle of tolerance by which everyone is free to mix and match the rules of ...

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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)

We are logical pluralists who hold that the right logic is dependent on the domain of investigation; different logics for different mathematical theories. The purpose of this article is to explore the ramifications for our pluralism concerning normativity. Is there any normative role for logic, once we give up its universality? We discuss Florian Steingerger’s “Frege and Carnap on the Normativity of Logic” as a source for possible types of normativity, and then turn to our own proposal, which postulates that (...) various logics are constitutive for thought within particular practices, but none are constitutive for thought as such. (shrink)

This is a paper about the constituents of arguments. It argues that several different kinds of truth-bearer may be taken to compose arguments, but that none of the obvious candidates—sentences, propositions, sentence/truth-value pairs etc.—make sense of logic as it is actually practiced. The paper goes on to argue that by answering the question in different ways, we can generate different logics, thus ensuring a kind of logical pluralism that is different from that of J. Beall and Greg Restall.

The paper argues for two theses: a) there are certain truths which are analytic; b) these are true by convention. Much of the paper deals with quine's arguments against these claims. The paper starts by accepting quine's network theory of belief and arguing that this presupposes a certain concept of rule following. This may be used to define analyticity. The paper then discusses the conventional nature of rule following and argues that this implies the conventional truth of analytic truths. Quine's (...) arguments against truth by convention are then disarmed. Finally, The paper shows that the account of analyticity given gives rise to a modal logic in the order of s4, Disarming another argument against conventionalism. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

Logical Pluralists maintain that there is more than one genuine/true logical consequence relation. This paper seeks to understand what the position could amount to and some of the challenges faced by its formulation and defence. I consider in detail Beall and Restall’s Logical Pluralism—which seeks to accommodate radically different logics by stressing the way that they each fit a general form, the Generalised Tarski Thesis (GTT)—arguing against the claim that different instances of GTT are admissible precisifications of logical consequence. I (...) then consider what it is to endorse a logic within a pluralist framework and criticise the options Beall and Restall entertain. A case study involving many-valued logics is examined. I next turn to issues of the applications of different logics and questions of which logic a pluralist should use in particular contexts. A dilemma regarding the applicability of admissible logics is tackled and it is argued that application is a red herring in relation to both understanding and defending a plausible form of logical pluralism. In the final section, I consider other ways to be and not to be a logical pluralist by examining analogous positions in debates over religious pluralism: this, I maintain, illustrates further limitations and challenges for a very general logical pluralism. Certain less wide-ranging pluralist positions are more plausible in both cases, I suggest, but assessment of those positions needs to be undertaken on a case-by-case basis. (shrink)

Preface 1 Introduction: The Persistence of the Attitudes 2 Individualism and Supervenience 3 Meaning Holism 4 Meaning and the World Order Epilogue Creation Myth Appendix Why There Still Has to be a Language of Thought Notes References Author Index.

There are quite a few theses about logic that are in one way or another pluralist: they hold (i) that there is no uniquely correct logic, and (ii) that because of this, some or all debates about logic are illusory, or need to be somehow reconceived as not straightforwardly factual. Pluralist theses differ markedly over the reasons offered for there being no uniquely correct logic. Some such theses are more interesting than others, because they more radically affect how we are (...) initially inclined to understand debates about logic. Can one find a pluralist thesis that is high on the interest scale, and also true? (shrink)

According to the logical pluralism of Beall and Restall, there are several distinct relations of logical consequence. Some critics argue that logical pluralism suffers from what I call the collapse problem: that despite its intention to articulate a radically pluralistic doctrine about logic, the view unintentionally collapses into logical monism. In this paper, I propose a contextualist resolution of the collapse problem. This clarifies the mechanism responsible for a plurality of logics and handles the motivating data better than the original (...) view. It is a major improvement that should be embraced by all logical pluralists. (shrink)

I. Recent years have witnessed a great resurgence of interest in the writings of the later Wittgenstein, especially with those passages roughly, Philosophical Investigations p)I 38 — 242 and Remarks on the Foundations of mathematics, section VI that are concerned with the topic of rules. Much of the credit for all this excitement, unparalleled since the heyday of Wittgenstein scholarship in the early IIJ6os, must go to Saul Kripke's I4rittgenstein on Rules and Private Language. It is easy to explain why. (...) To begin with, the dialectic Kripke uncovered from Wittgenstein's.. (shrink)

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)

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)

Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

Normativism in the theory of meaning and content is the view that linguistic meaning and/or intentional content are essentially normative. As both normativity and its essentiality to meaning/content can be interpreted in a number of different ways, there is now a whole family of views laying claim to the slogan “meaning/content is normative”. In this essay, we discuss a number of central normativist theses, and we begin by identifying different versions of meaning normativism, presenting the arguments that have been put (...) forth for and against them. (shrink)

Logical pluralism is the claim that different accounts of validity can be equally correct. Beall and Restall have recently defended this position. Validity is a matter of truth-preservation over cases, they say: the conclusion should be true in every case in which the premises are true. Each logic specifies a class of cases, but differs over which cases should be considered. I show that this account of logic is incoherent. Validity indeed is truth-preservation, provided this is properly understood. Once understood, (...) there is one true logic, relevance logic. The source of Beall and Restall’s error is a recent habit of using a classical metalanguage to analyse non-classical logics generally, including relevance logic. (shrink)

In my thesis, I address the question ʽWhat normative status does logic have?', to argue that logical normativity is of a weak sort, and that its constraining power is similar to that of recommendations. The thesis first discusses the notion of logical validity and logical formality, then asks whether logic is a priori and whether it can provide a priori norms for thinking. Subsequently, the issue of the bridge principles linking formal logic to informal reasoning is addressed, jointly with a (...) brief discussion of the deontic operators included in the bridge principles. Then, the thesis addresses three criticisms of the normative role of logic with respect to rational reasoning. The first criticism is discussed in the fourth chapter; it starts from the consideration of the cognitive limitations of human agents and discusses a model of rationality that takes those limitations into account. The second criticism is analyzed in the fifth chapter; it is motivated by the empirical studies in the psychology of reasoning, and discusses human reasoning from a descriptive point of view, lending support to the model of rationality presented in the fourth chapter. The third criticism, presented in the sixth and final chapter, addresses the normative role of logic from an a priori point of view, showing how the epistemic paradoxes are crucial for determining what normative import logic has on rational reasoning. The final chapter defends the main thesis that logic has a weak import on our reasoning, which resembles a recommendation rather than an obligation. (shrink)