The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for ...

AN INVESTIGATION OF THE LAWS OF THOUGHT. CHAPTER I. NATURE AND DESIGN OF THIS WORK. . HPHE design of the following treatise is to investigate the ...

Bertrand Russell remains one of the greatest philosophers and most complex and controversial figures of the twentieth century. Here, in this frank, humorous and decidedly charming autobiography, Russell offers readers the story of his life – introducing the people, events and influences that shaped the man he was to become. Originally published in three volumes in the late 1960s, _Autobiography_ by Bertrand Russell is a revealing recollection of a truly extraordinary life written with the vivid freshness and clarity that has (...) made Bertrand Russell’s writings so distinctively his own. (shrink)

Appropriate for upper-level undergraduates and graduate students, this volume includes a variety of Boole's writings on logical subjects, along with papers on related questions of probability. His earlier work, The Mathematical Analysis of Logic, appears here, together with an account of the notes Boole made on his own interleaved copy. In addition, the appendices contain relevant papers by contemporaries with whom the author engaged in discussion, making it possible to trace interesting developments in Boolean reasoning-particularly in regard to his extended (...) treatment of the relation between formal logic and the theory of probabilities. 1952 ed. (shrink)

Logical psychologism is the position that logic is a special branch of psychology, that logical laws are descriptíons of experience to be arrived at through observation, and are a posteriori.The accepted arguments against logical psychologism are effective only when directed against this extreme version. However, the clauses in the above characterization are independent and ambiguous, and may be considered separately. This separation permits a reconsideration of less extreme attempts to tie logic to psychology, such as those defended by Mill and (...) Boole. It also provides the basis for a reexamination of the relationship between logic and psychology, and raises the possibility of a deeper investigation into the nature of logic itself. (shrink)

The great influence of Georg Cantor's theory of sets and transfinite arithmetic has led to a considerable interest in his life. It is well known that he had a remarkable and unusual personality, and that he suffered from attacks of mental illness; but the ‘popular’ account of his life is richer in falsehood and distortion than in factual content. This paper attempts to correct these misrepresentations by drawing on a wide variety of manuscript sources concerning Cantor's life and career, including (...) the texts of some important documents. An appendix describes the most important collection of missing manuscripts, whose location would help further the preparation of a biographical study of Cantor. (shrink)

This paper studies the possible influences on Boole's logic of the writings related to the controversy over the quantification of the predicate between the philosopher William Hamilton and the mathematician Augustus De Morgan. As Boole himself testified in the introduction to his book The mathematical analysis of logic , this controversy was the external agent that stimulated him into writing up his earlier thoughts about a new conception of logic. But in addition to the external role that was played by (...) the controversy, it seems that other kinds of influences on Boole of Hamilton's and De Morgan's ideas about logic, which were made explicit in writings related to the controversy, can also be traced. (shrink)

Mary Everest, Boole's wife, claimed after the death of her husband that his logic had a psychological, pedagogical, and religious origin and aim rather than the mathematico-logical ones assigned to it by critics and scientists. It is the purpose of this paper to examine the validity of such a claim. The first section consists of an exposition of the claim without discussing its truthfulness; the discussion is left for the sections 2?4, in which some arguments provided by the examination of (...) the inner consistency of Mary Everest's writings, Boole's own writings, and other sources, lead to the conclusion that there are sound reasons to accept Mary Everest's viewpoint. (shrink)

This paper is concerned with the influence that the set theory of Georg Cantor bore upon the mathematical logic of Bertrand Russell. In some respects the influence is positive, and stems directly from Cantor's writings or through intermediary figures such as Peano; but in various ways negative influence is evident, for Russell adopted alternative views about the form and foundations of set theory. After an opening biographical section, six sections compare and contrast their views on matters of common interest; irrational (...) numbers, infinitesimals, cardinal and ordinal numbers, the axiom of infinity, the paradoxes, and the axioms of choice. Two further sections compare the two men over more general questions: the role of logic and the philosophy of mathematics. In a final section I draw some conclusions. (shrink)

This paper deals with the influence exerted by Boole's own work on differential equations on his creation of algebraic logic. The main traits of Boole's methodology of logic, and the particular algorithms which he used in his 1847 The mathematical analysis of logic, are first pointed out. An examination of the mathematical papers which Boole wrote before the publication of the mentioned logical treatise shows that both the methodology leading to the production of his logic and the algorithms used in (...) its development were repeatedly used by him in his earlier work in analysis. (shrink)

/ Part INTRODUCTION Fuzziness is not a priori an obvious concept and demands some explanation. "Fuzziness" is what Black (NF) calls "vagueness" when ...