Perspectives on the history of mathematical logic, edited by Thomas Drucker, Birkhäuser, Boston, Basel, and Berlin, 1991, xxiii + 195 pp. - John W. Dawson Jr. The reception of Gödel's incompleteness theorems. Pp. 84–100. (Reprinted from PSA 1984, Proceedings of the 1984 biennial meeting of the Philosophy of Science Association, volume two, edited by Peter D. Asquith and Philip Kitcher, Philosophy of Science Association, East Lansing, Mich., 1985, pp. 253–271.)

1992 ◽  
Vol 57 (4) ◽  
pp. 1487-1489
Author(s):  
Stewart Shapiro
Keyword(s):  
Mathematical Logic ◽  
Philosophy Of Science ◽  
Philip Kitcher ◽  
History Of ◽  
Incompleteness Theorems ◽  
Science Association ◽  
Gödel’S Incompleteness Theorems

Gödel's Incompleteness Theorems

1992 ◽  
Author(s):  
Raymond M. Smullyan
Keyword(s):  
Mathematical Logic ◽  
Number Theory ◽  
Continuum Theory ◽  
Kurt Gödel ◽  
The World ◽  
Computer Scientists ◽  
Incompleteness Theorems ◽  
The Axiom Of Choice ◽  
Gödel’S Incompleteness Theorems ◽  
The Continuum

Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.

Incompleteness, Mechanism, and Optimism

1998 ◽  
Vol 4 (3) ◽  
pp. 273-302 ◽  
Author(s):  
Stewart Shapiro
Keyword(s):  
Mathematical Logic ◽  
Turing Machine ◽  
Digital Computer ◽  
Human Mind ◽  
Indefinite Extensibility ◽  
Incompleteness Theorems ◽  
The Devil ◽  
Gödel’S Incompleteness Theorems ◽  
Gödel’S Theorem ◽  
Different Parts

§1. Overview. Philosophers and mathematicians have drawn lots of conclusions from Gödel's incompleteness theorems, and related results from mathematical logic. Languages, minds, and machines figure prominently in the discussion. Gödel's theorems surely tell us something about these important matters. But what?A descriptive title for this paper would be “Gödel, Lucas, Penrose, Turing, Feferman, Dummett, mechanism, optimism, reflection, and indefinite extensibility”. Adding “God and the Devil” would probably be redundant. Despite the breath-taking, whirlwind tour, I have the modest aim of forging connections between different parts of this literature and clearing up some confusions, together with the less modest aim of not introducing any more confusions.I propose to focus on three spheres within the literature on incompleteness. The first, and primary, one concerns arguments that Gödel's theorem refutes the mechanistic thesis that the human mind is, or can be accurately modeled as, a digital computer or a Turing machine. The most famous instance is the much reprinted J. R. Lucas [18]. To summarize, suppose that a mechanist provides plans for a machine, M, and claims that the output of M consists of all and only the arithmetic truths that a human (like Lucas), or the totality of human mathematicians, will ever or can ever know. We assume that the output of M is consistent.

scholarly journals International scientific associations of the History of Science and Technology: formation and development (part III)

2021 ◽  
Vol 29 (1) ◽  
pp. 113-122
Author(s):  
A. Lytvynko
Keyword(s):  
Philosophy Of Science ◽  
International Organizations ◽  
Science And Technology ◽  
International Federation ◽  
Human Sciences ◽  
International Council ◽  
Learned Societies ◽  
European Philosophy ◽  
History Of ◽  
Science Association

The activity of international organizations on the history and philosophy of science and technology is a remarkable phenomenon in the world scientific and sociocultural sphere. Such centers influence and contribute to the scientific communication of scientists from different countries and the comprehensive development of numerous aspects of the history and phylosiphy of science and technology, carry out scientific congresses. That is why the analysis of the acquired experience and the obtained results of these groups are important. The history of the formation and development, task, structure, background and directions of the activities of some international organizations in the field of history and philosophy of science and technology, including The European Philosophy of Science Association (EPSA), The International Society for the History of Philosophy of Science (HOPOS), The International Federation of Philosophical Societies (FISP) and The International council for philosophy and human sciences (ICPHS) have been shown. The European Philosophy of Science Association (EPSA) was established in 2007 to promote and advance the investigations and teaching the philosophy of science in Europe. EPSA edits the European Journal for Philosophy of Science (EJPS), which publishes articles in all areas of philosophy of science. The International Society for the History of Philosophy of Science (HOPOS) promotes serious, scholarly research on the history of the philosophy of science and gathers scholars who share an interest in promoting research on the history of the philosophy of science and related topics in the history of the natural and social sciences, logic, philosophy and mathematics. The scholarly journal HOPOS is published by University of Chicago Press. The International Federation of Philosophical Societies (FISP) is the highest nongovernmental world organization for philosophy, whose members-societies represent every country where there is significant academic philosophy. It was established in Amsterdam in 1948. FISP’s first seat was located at the the Sorbonne in Paris. FISP includes approximately one hundred members. It does not include individual members, but only «societies» in a broad sense, that is, philosophical institutions of different kinds, such as associations, societies, institutes, centres and academies at national, regional and international levels. The International council for philosophy and human sciences (ICPHS) is a non-governmental organisation within UNESCO, which federates hundreds of different learned societies in the field of philosophy, human sciences and related subjects. It was conceived as the intermediary between UNESCO on one hand, and learned societies and national academies on the other. Its aim was to extend UNESCO's action in the domain of humanistic studies.

Addendum to early history of the Association for Symbolic Logic

1963 ◽  
Vol 28 (4) ◽  
pp. 279-279
Author(s):  
C. J. Ducasse ◽  
Haskell B. Curry
Keyword(s):  
Philosophy Of Science ◽  
Early History ◽  
Symbolic Logic ◽  
History Of ◽  
Science Association

Since publication of our account of the early history of the Association for Symbolic Logic in the September 1962 issue of its Journal, the fact has been called to our attention that — because much of the correspondence at that time is no longer available and we had therefore to depend on our memory — we failed to mention an important item of that early history.This was a letter from Professor Paul Weiss to the Editor of Philosophy of Science, which appeared in the April, 1934, issue of that periodical. This letter, entitled “A Home for Logic,” called attention to the fact that papers on logic were scattered in heterogeneous periodicals, and suggested that the Philosophy of Science Association take under its wing the establishment of a Logical Association.

Robert M. Young's Mind, Brain and Adaptation revisited

2021 ◽  
pp. 1-17
Author(s):  
Christopher Lawrence
Keyword(s):  
Nineteenth Century ◽  
Philosophy Of Science ◽  
Experimental Psychology ◽  
Social Reform ◽  
Victorian Britain ◽  
Unique Character ◽  
Philosophy Department ◽  
History Of ◽  
Science Community ◽  
Scientific Ideas

Abstract Robert Maxwell Young's first book Mind, Brain and Adaptation in the Nineteenth Century (1970), written from 1960 to 1965, still merits reading as a study of the naturalization of mind and its relation to social thought in Victorian Britain. I examine the book from two perspectives that give the volume its unique character: first, Young's interest in psychology, which he considered should be used to inform humane professional practices and be the basis of social reform; second, new approaches to the history of scientific ideas. I trace Young's intellectual interests to the Yale Philosophy Department, the Cambridge Department of Experimental Psychology and a new history and philosophy of science community. Although Young changed his political outlook and historiography radically after 1965, he always remained faithful to ideas about thought and practice described in Mind, Brain.

The tenure of English judges

1913 ◽  
Vol 7 (2) ◽  
pp. 217-229 ◽  
Author(s):  
C. H. McIlwain
Keyword(s):  
Supreme Court ◽  
Political Science ◽  
Theory And Practice ◽  
The Political ◽  
The Supreme Court ◽  
History Of ◽  
The Subject ◽  
General Object ◽  
William Iii ◽  
Science Association

At the meeting of the Political Science Association last year, in the general discussion, on the subject of the recall, I was surprised and I must admit, a little shocked to hear our recall of judges compared to the English removal of judges on address of the houses of parliament.If we must compare unlike things, rather than place the recall beside the theory or the practice of the joint address, I should even prefer to compare it to a bill of attainder.In history, theory and practice the recall as we have it and the English removal by joint address have hardly anything in common, save the same general object.Though I may not (as I do not) believe in the recall of judges, this paper concerns itself not at all with that opinion, but only with the history and nature of the tenure of English judges, particularly as affected by the possibility of removal on address. I believe a study of that history will show that any attempt to force the address into a close resemblance to the recall, whether for the purpose of furthering or of discrediting the latter, is utterly misleading.In the history of the tenure of English judges the act of 12 and 13 William III, subsequently known as the Act of Settlement, is the greatest landmark. The history of the tenure naturally divides into two parts at the year 1711. In dealing with both parts, for the sake of brevity, I shall confine myself strictly to the judges who compose what since 1873 has been known as the supreme court of judicature.

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