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 ...

Michael Dummett is a leading contemporary philosopher whose work on the logic and metaphysics of language has had a lasting influence on how these subjects are conceived and discussed. This volume contains some of the most provocative and widely discussed essays published in the last fifteen years, together with a number of unpublished or inaccessible writings. Essays included are: "What is a Theory of Meaning?," "What do I Know When I Know a Language?," "What Does the Appeal to Use (...) Do for the Theory of Meaning?," "Language and Truth," "Truth and Meaning," "Language and Communication," "The Source of the Concept of Truth," "Mood, Force, and Convention," "Frege and Husserl on Reference," "Realism," "Existence," "Does Quantification Involve Identity?," "Could there be Unicorns?," "Causal Loops," "Common Sense and Physics," "Testimony and Memory," "What is Mathematics About?," "Wittgenstein on Necessity: Some Reflections," and "Realism and Anti-Realism." Serving well as a companion to Dummett's other collections, the essays in this volume are not forbiddingly technical or specialized, and have relevance to many areas of analytic philosophy. (shrink)

In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

Editorial NoteThis paper was read by Michael Dummett at Leiden University on September 26, 1992 at the invitation by Göran Sundholm to address the topic mentioned in the title. Dummett’s lecture was part of a workshop, Meaning Theory and Intuitionism, with 12 invited speakers over three days. After the workshop, Dummett gave a copy of the manuscript to Sundholm together with permission to publish it. At the time, nothing came of the publication plans, nor did Dummett publish it in any (...) other form. The text has remained virtually unknown, and apart from a lecture of Per Martin-Löf, also at Leiden, on the same topic, it has received no scholarly attention. We are indebted to Dummett’s literary executor, Professor Ian Rumfitt, of All Souls College, Oxford, who after nearly three decades confirmed the earlier permission to publish.Göran SundholmAnsten Klev. (shrink)

A collection of all but two of the author's philosophical essays and lectures originally published or presented before August 1976.

While it is relatively clear what the subject matter of empirical sciences is, puzzles persist about the proper subject matter of mathematics. The logicists took mathematics to be concerned solely with deductive arguments. Their programme attempted to combine three incompatible claims: that mathematics is a body of truths, that it is non‐empirical, and that it employs proofs obeying the rules of classical logic. By giving up the third contention, it becomes possible to salvage the logicist programme and to explain (...) better mathematical practice, including the fact of its application in empirical disciplines. (shrink)

[An Anti-Realist Perspective on Language, Thought, Logic and the History of Analytic Philosophy. .].

The short fragment of Frege's Nachlass which bears the above title, given to it by the editors, is in fact a sequence of connected comments by him on the Introduction to Lotze's Logik, or, more exactly, a response by him to that Introduction. It is thus very probably the earliest piece of writing from Frege's pen on the philosophy of logic surviving to us, and, when it is read in this light, the motivation for its author's puzzling selection of (...) remarks and the turns of phrase he employs become intelligible. We see here an early attempt by Frege to attain clarity about a topic that was to preoccupy him throughout his entire philosophical career, the nature of thoughts. (shrink)

Frege held that logical objects are objective but not wirklich, and that psychologism follows from the mistake of believing whatever is not wirklich to be subjective. It has been suggested that Frege's use of the terms ?objective? and ?wirklich? is in line with that found in Lotze's Logic; from this it has been inferred that Frege's doctrines have been misinterpreted as being ontological in character, but that they really belong to epistemology. In fact, Lotze held that something may be (...) the same for all thinkers, and yet may exist only in thought, not independently of it. For Frege, by contrast, there is nothing intermediate between the content of a single consciousness and what exists independently of being thought at all. This crucial disagreement underlies the divergence between Frege's realism and Lotze's idealism. (shrink)

Radical conventionalism treats every necessary truth as a linguistic convention, akin to the statement ’There are seven days in a week’. Wittgenstein's endorsement of this view was a result of his belief that nothing can explain the fact of the acceptance of necessary truths. There could not be necessary truths being a consequence of human nature, which have not yet been recognized, or those which would never be recognized as such. This view stands in contrast to moderate conventionalism, which is (...) powerless to explain the necessity of logical consequence. (shrink)

We present nested sequent systems for propositional Gödel-Dummett logic and its first-order extensions with non-constant and constant domains, built atop nested calculi for intuitionistic logics. To obtain nested systems for these Gödel-Dummett logics, we introduce a new structural rule, called the linearity rule, which (bottom-up) operates by linearising branching structure in a given nested sequent. In addition, an interesting feature of our calculi is the inclusion of reachability rules, which are special logical rules that operate by propagating data and/or (...) checking if data exists along certain paths within a nested sequent. Such rules require us to generalise our nested sequents to include signatures (i.e. finite collections of variables) in the first-order cases, thus giving rise to a generalisation of the usual nested sequent formalism. Our calculi exhibit favourable properties, admitting the height-preserving invertibility of every logical rule and the (height-preserving) admissibility of a large collection of structural and reachability rules. We prove all of our systems sound and cut-free complete, and show that syntactic cut-elimination obtains for the intuitionistic systems. We conclude the paper by discussing possible extensions and modifications, putting forth an array of structural rules that could be used to provide a sizable class of intermediate logics with cut-free nested sequent systems. (shrink)

In this article the contemporary debate between realism and anti-realism in analytical philosophy is analyzed and discussed. It is claimed that the nature of the reference relation which holds between language and the world is central in this discussion which has both logical, semantical, and epistemological aspects. In a firstpart, A Tarski's (semantic) theory of truth is explained and it is shown how, amongst several theories of truth, Tarski's may be called a realist one. However, a Tarski-style semantics need not (...) lead to a realist theory of Truth and Reference, as is shown in a subsequent part. Here, H Putnam's views on these matters are discussed. It is shown how Putnam in the course of his intellectual history has changed his view from a realist to an anti-realist position. Putnam'sarguments show the importance of logical and metalogical issues in the debate. In a final part, Putnam's views are criticized and it is shown how a line of argument, analogous to Putnam's, may lead to a realist theory of meaning and reference. (shrink)

David Bell argued in his book Husserl that Frege's notion of reference was realist, whereas Husserl's notion of reference in Logical Investigations was non‐realist. The suitable notion of reference should reconcile between extensional and intensional modes of speaking of the object. According to Husserl, intentional objects do not form an ontological category: to speak of them is to adopt the material mode of saying what, in the formal mode, relates to a singular term standing in an intensional context. Thus, Husserl's (...) solution closely resembles Frege's, and both are essentially realist ones. (shrink)

Attention is drawn to the fact that what is alternatively known as Dummett logic, Gödel logic, or Gödel-Dummett logic, was actually introduced by Skolem already in 1913. A related work of 1919 introduces implicative lattices, or Heyting algebras in today's terminology.

We enrich intuitionistic logic with a lax modal operator and define a corresponding intensional enrichment of Kripke models M = (W, , V) by a function T giving an effort measure T(w, u) {} for each -related pair (w, u). We show that embodies the abstraction involved in passing from true up to bounded effort to true outright. We then introduce a refined notion of intensional validity M |= p : and present a corresponding intensional calculus iLC-h which gives (...) a natural extension by lax modality of the well-known G: odel/Dummett logic LC of (finite) linear Kripke models. Our main results are that for finite linear intensional models L the intensional theory iTh(L) = {p : | L |= p : } characterises L and that iLC-h generates complete information about iTh(L).Our paper thus shows that the quantitative intensional information contained in the effort measure T can be abstracted away by the use of and completely recovered by a suitable semantic interpretation of proofs. (shrink)

ABSTRACT In ‘The philosophical basis of intuitionistic logic’, Michael Dummett discusses two routes towards accepting intuitionistic rather than classical logic in number theory, one meaning-theoretical and the other ontological. He concludes that the former route is open, but the latter is closed. I reconstruct Dummett's argument against the ontological route and argue that it fails. Call a procedure ‘investigative’ if that in virtue of which a true proposition stating its outcome is true exists prior to the execution of (...) that procedure; and ‘generative’ if the existence of that in virtue of which a true proposition stating its outcome is true is brought about by the execution of that procedure. The problem with Dummett's argument then is that a particular step in it, while correct for investigative procedures, is not correct for generative ones. But it is the latter that the ontological route is concerned with. (shrink)

The main goal of the paper is to suggest some analytic proof systems for LC and its finite-valued counterparts which are suitable for proof-search. This goal is achieved through following the general Rasiowa-Sikorski methodology for constructing analytic proof systems for semantically-defined logics. All the systems presented here are terminating, contraction-free, and based on invertible rules, which have a local character and at most two premises.

I begin this paper by orienting Michael Dummett’s work in relation to what Adrian Moore identifies as the central concern of metaphysics: making sense of things. The metaphysical issue that most exercises Dummett is the adjudication between a realist and an antirealist conception of reality, and he believes that it is by careful attention to theories of meaning that we can come to see difficulties for a realist metaphysics. Fregean realism gives way to Dummettian antirealism. But Moore is not convinced. (...) While Dummett connects truth with our capacity to know, Moore challenges Dummett to say more about this capacity. Moore accuses Dummett of attempting, with his theory of meaning, to identify limits to our sense-making. As well as running into trouble with (what he identifies as) the limit argument, Moore believes that there may also be a lurking conservatism in Dummett’s work insofar as it can be accused of making no provision for radical conceptual innovation in metaphysics. I attempt to defend Dummett against both criticisms. (shrink)

In this exciting new collection, a distinguished international group of philosophers contribute new essays on central issues in philosophy of language and logic, in honor of Michael Dummett, one of the most influential philosophers of the late twentieth century. The essays are focused on areas particularly associated with Professor Dummett. Five are contributions to the philosophy of language, addressing in particular the nature of truth and meaning and the relation between language and thought. Two contributors discuss time, in particular (...) the reality of the past. The last four essays focus on Frege and the philosophy of mathematics. The volume represents some of the best work in contemporary analytical philosophy. (shrink)

The aim of this paper is to provide a decision procedure for Dummett's logic LC, such that with any given formula will be associated either a proof in a sequent calculus equivalent to LC or a finite linear Kripke countermodel.