Foreword

2020 ◽  
pp. 277-278
Author(s):  
Crispin Wright
Keyword(s):  
Intuitionistic Logic ◽  
Philosophy Of Mathematics ◽  
Sorites Paradox ◽  
Philosophy Of Logic ◽  
Metaphysical Possibility ◽  
Crispin Wright

This chapter is divided into four parts, corresponding to the partitioning of the essays in the volume. Part I, on neo-Fregeanism in the philosophy of mathematics develops replies to Demopolous, Heck, Rosen and Yablo, Boolos and Edwards; Part II, on vagueness, intuitionistic logic and the Sorites Paradox develops replies to Rumfitt and Schiffer; Part III, on revisionism in the philosophy of logic develops replies to Shieh and Tennant; and Part IV, on the epistemology of metaphysical possibility develops a reply to Hale. In each section, Crispin Wright offers an overview of the relevant area and outlines and refines his views on the relevant topics. Inter alia, he offers detailed replies to each of the ten contributed essays in the volume.

Logic, Language, and Mathematics

2020 ◽  
Keyword(s):  
Philosophy Of Mathematics ◽  
Sorites Paradox ◽  
Metaphysical Possibility ◽  
Unpublished Paper ◽  
Crispin Wright ◽  
Mathematics Section ◽  
Language And Mathematics ◽  
And Mathematics ◽  
Logical Revisionism ◽  
George Boolos

This Festschrift volume contains a series of specially commissioned papers by leading philosophers on themes from the philosophy of Crispin Wright and a previously unpublished paper by George Boolos, together with a substantial set of replies by Wright. Section I consists of five essays on Wright’s Neo-Fregean approach in the philosophy of mathematics, Section II consists of two essays on Wright’s work on vagueness, intuitionism and the Sorites Paradox, Section III contains two essays on logical revisionism, and Section IV consists of a single essay on the epistemology of metaphysical possibility. The volume also contains a full bibliography of Wright’s philosophical publications.

The Oxford Handbook of Philosophy of Mathematics and Logic

2009 ◽  
Keyword(s):  
Philosophy Of Mathematics ◽  
Philosophy Of Logic ◽  
Scholarly Work ◽  
Contemporary Philosophy ◽  
Philosophical System ◽  
A Priority ◽  
Correct Reasoning

The Oxford Handbook of Philosophy of Math and Logic is a reference about the philosophy of mathematics and the philosophy of logic. Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge-gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines, giving the reader an overview of the major problems, positions, and battle lines. The twenty-six articles are by established experts in the field, and these articles contain both exposition and criticism as well as substantial development of their own positions.

Intuitionism and the Sorites Paradox

2021 ◽  
pp. 393-422
Author(s):  
Crispin Wright
Keyword(s):  
Subject Matter ◽  
Classical Logic ◽  
Proof Theory ◽  
Philosophy Of Mathematics ◽  
Sorites Paradox ◽  
Major Premise ◽  
Stable Boundary

This chapter revisits and further develops all the principle themes and concepts of the preceding chapters. Epistemicism about vagueness postulates a realm of distinctions drawn by basic vague concepts that transcend our capacity to know them. Its treatment of their subject matter is thus broadly comparable to the Platonist philosophy of mathematics. An intuitionist philosophy of vagueness, as do many philosophies of the semantics and metaphysics of vague expressions, finds this idea merely superstitious and rejects it. The vagueness-intuitionist, however, credits the epistemicist with a crucial insight: that vagueness is indeed a cognitive, rather than a semantic, phenomenon—something that is not a consequence of some kind of indeterminacy, or open-endedness in the semantics of vague expressions but rather resides in our brute inability to bring, for example, yellow and orange right up against one another, so to speak, so as to mark a sharp and stable boundary. A solution to the Sorites paradox is developed that is consonant with this basic idea but, by motivating a background logic that observes (broadly) intuitionistic restrictions on the proof theory for negation, allows us to treat the paradoxical reasoning as a simple reductio of its major premise, without the unwelcome implication, sustained by classical logic, of sharp cut-offs.

Wittgenstein on Philosophy of Logic and Mathematics

2009 ◽  
Author(s):  
Juliet Floyd
Keyword(s):  
Ludwig Wittgenstein ◽  
Philosophy Of Mathematics ◽  
Vienna Circle ◽  
Short Review ◽  
Significant Part ◽  
Foundations Of Mathematics ◽  
Philosophy Of Logic ◽  
And Mathematics

Ludwig Wittgenstein (1889–1951) wrote as much on the philosophy of mathematics and logic as he did on any other topic, leaving at his death thousands of pages of manuscripts, typescripts, notebooks, and correspondence containing remarks on (among others) Brouwer, Cantor, Dedekind, Frege, Hilbert, Poincaré, Skolem, Ramsey, Russell, Gödel, and Turing. He published in his lifetime only a short review (1913) and the Tractatus Logico-Philosophicus (1921), a work whose impact on subsequent analytic philosophy's preoccupation with characterizing the nature of logic was formative. Wittgenstein's reactions to the empiricistic reception of his early work in the Vienna Circle and in work of Russell and Ramsey led to further efforts to clarify and adapt his perspective, stimulated in significant part by developments in the foundations of mathematics of the 1920s and 1930s; these never issued in a second work, though he drafted and redrafted writings more or less continuously for the rest of his life.

On Being in a Quandary

2021 ◽  
pp. 209-260
Author(s):  
Crispin Wright
Keyword(s):  
Intuitionistic Logic ◽  
Subject Matter ◽  
Classical Logic ◽  
The Other ◽  
Sorites Paradox ◽  
Metaphysical Realism ◽  
Specific Kind ◽  
Epistemic Conception ◽  
Broad Form

This chapter addresses three problems: the problem of formulating a coherent relativism, the Sorites paradox, and a seldom noticed difficulty in the best intuitionistic case for the revision of classical logic. A response to the latter is proposed which, generalized, contributes towards the solution of the other two. The key to this response is a generalized conception of indeterminacy as a specific kind of intellectual bafflement—Quandary. Intuitionistic revisions of classical logic are merited wherever a subject matter is conceived both as liable to generate Quandary and as subject to a broad form of evidential constraint. So motivated, the distinctions enshrined in intuitionistic logic provide both for a satisfying resolution of the Sorites paradox and a coherent outlet for relativistic views about, for example, matters of taste and morals. An important corollary of the discussion is that an epistemic conception of vagueness can be prised apart from the strong metaphysical realism with which its principal supporters have associated it, and acknowledged to harbour an independent insight.

scholarly journals Vagueness and Intuitionistic Logic

2020 ◽  
pp. 135-153
Author(s):  
Ian Rumfitt
Keyword(s):  
Intuitionistic Logic ◽  
Classical Logic ◽  
Affirmative Answer ◽  
Vague Predicate ◽  
Vague Term ◽  
Crispin Wright

This chapter considers the question: should we employ intuitionistic logic, not classical logic, when reasoning with vague concepts? In his commentary on Michael Dummett’s “Wang’s Paradox,” Crispin Wright presents an apparently powerful argument in favour of an affirmative answer to this question. This chapter advocates a less conclusive answer than Wright’s. It is argued that intuitionistic logic may be the strongest logic we are entitled to use in reasoning with any vague predicate, but there may also be common and central families of vague term where we are entitled to use classical logic.

The philosophy of logic

2012 ◽  
Vol 18 (4) ◽  
pp. 481-504 ◽  
Author(s):  
Penelope Maddy
Keyword(s):  
Subject Matter ◽  
Philosophy Of Mathematics ◽  
Philosophy Of Logic ◽  
Starting Point ◽  
The Subject ◽  
The Way

AbstractThis talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic—what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics—Logicism, Intuitionism, Formalism, Realism—and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam are among the philosophers considered along the way.

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