The present volume is intended as an all-round introduction to constructivism. Here constructivism is to be understood in the wide sense, and covers in particular Brouwer's intuitionism, Bishop's constructivism and A.A. Markov's constructive recursive mathematics. The ending "-ism" has ideological overtones: "constructive mathematics is the (only) right mathematics"; we hasten, however, to declare that we do not subscribe to this ideology, and that we do not intend to present our material on such a basis.

Following the speech act theory, we take hypotheses and assertions as linguistic acts with different illocutionary forces. We assume that a hypothesis is justified if there is at least a scintilla of evidence for the truth of its propositional content, while an assertion is justified when there is conclusive evidence that its propositional content is true. Here we extend the logical treatment for assertions given by Dalla Pozza and Garola by outlining a pragmatic logic for assertions and hypotheses. On the (...) basis of this extension we analyse the standard logical opposition relations for assertions and hypotheses. We formulate a pragmatic square of oppositions for assertions and a hexagon of oppositions for hypotheses. Finally, we give a mixed hexagon of oppositions to point out the opposition relations for assertions and hypotheses. (shrink)

1 INTRODUCTION Above the other titles he might justly have claimed, Charles S. Peirce prized the title 'logician'. He expressed in several places his ...

Charles Sanders Peirce has been characterized as the greatest American philosophic genius. He is the creator of pragmatism and one of the founders of modern logic. James, Royce, Schroder, and Dewey have acknowledged their great indebtedness to him. A laboratory scientist, he made notable contributions to geodesy, astronomy, psychology, induction, probability, and scientific method. He introduced into modern philosophy the doctrine of scholastic realism, developed the concepts of chance, continuity, and objective law, and showed the philosophical significance of the theory (...) of signs and mathematical logic. The present series is the first published edition of his systematic works. (shrink)

The following two articles comprise two sets of Charles Peirce’s manuscripts, “Recent Developments of Existential Graphs and their Consequences for Logic” (MS 498, MS 499, MS 490 & S-36, 1906) and “Assurance through Reasoning” (MS 669 & MS 670, 1911), written for the National Academy of Sciences meetings in 1906 and 1911. The papers are deposited at Houghton Library, Harvard University. Only some parts of MS 470 have been published before, and in somewhat defective form. Although “Assurance” follows “Recent Developments” (...) chronologically, given the expository style of the former it is recommended to be read before “Recent Developments”. As the title indicates, in the latter Peirce goes on to describe his latest discoveries concerning the method and the logic of existential graphs. The transcription reproduces all significant deletions that appear in the original sheets. Editorial comments and additions are given in brackets. [Alt.:] means the beginning of an alternative sequence. [Del. (shrink)

The theory of existential graphs, which Peirce ultimately divided into four quadrants , is a rich method of analysis in the philosophy of logic. Its $$\upbeta $$ β -part boasts a diagrammatic theory of quantification, which by 1902 Peirce had used in the logical analysis of natural-language expressions such as complex donkey-type anaphora, quantificational patterns describing new mathematical concepts, and cognitive information processing. In the $$\upbeta $$ β -quadrant, he came close to inventing independence-friendly logic, the idea of which he (...) found indispensable in fulfilling the tasks –. (shrink)

The ideas of the German philosopher and mathematician Gottlob Frege lie at the root of the analytical movement in philosophy. Frege and Other Philosophers comprises all of Professor Dummett's published and previously unpublished essays on Frege, with the exception of those included in his Truth and Other Enigmas. In some of these essays he explores the relation of Frege's ideas to those of his predecessors and contemporaries. In others he considers critically some interpretations of Frege, and develops the argument for (...) a sound understanding of Frege's thought which he first delineated in The Interpretation of Frege's Philosophy. Several of the essays illustrate his contention that Frege's work remains the best starting point for the investigation of problems concerning truth, meaning, thought, and language, which are still among the most contentious issues in modern analytical philosophy. Any discussion of Frege's ideas is therefore also an exploration of fundamental and as yet unresolved issues of philosophy. (shrink)

Examines Frege's theory of judgement, according to which a judgement is, paradigmatically, the assertion that a particular object falls under a given concept. Throughout the book the aim is to both state Frege's views clearly and concisely, and to defend, modify or reject these where appropriate.

Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea (...) constitutes the fundamental motive of philosophy of notation both in algebraic and graphical logic. We explain how in his algebras and graphs Peirce arrived at a unifying notation for logical constants that represent both truth-function and scope. Finally, we show that Shin’s argument for multiple readings of Alpha graphs is circular. (shrink)

Following the speech act theory, we take hypotheses and assertions as linguistic acts with different illocutionary forces. We assume that a hypothesis is justified if there is at least a scintilla of evidence for the truth of its propositional content, while an assertion is justified when there is conclusive evidence that its propositional content is true. Here we extend the logical treatment for assertions given by Dalla Pozza and Garola (1995, Erkenntnis, 43, 81–109) by outlining a pragmatic logic for assertions (...) and hypotheses. On the basis of this extension we analyse the standard logical opposition relations for assertions and hypotheses. We formulate a pragmatic square of oppositions for assertions and a hexagon of oppositions for hypotheses. Finally, we give a mixed hexagon of oppositions to point out the opposition relations for assertions and hypotheses. (shrink)

The ideas of the German philosopher and mathematician Gottlob Frege lie at the root of the analytic movement in philosophy; Michael Dummett is his leading modern critical interpreter and one of today's most eminent philosophers. This volume collects together fifteen of Dummett's classic essays on Frege and related subjects.