The continuum hypothesis : independence and truth-value

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Philosophy, 1974.MIT Humanities Library copy: issued in two vols.Leaf number 84 used twice. Also issued as a two-volume set.Includes bibliographical references (leaves 217-258).by Thomas S. Weston.Ph.D

Adapting to Computer Science

Although I am not an engineer who adapted himself to computer science but a mathematician who did so, I am familiar enough with the development, concepts, and activities of this new discipline to venture an opinion of what must be adapted to in it. Computer and Information Science is known as Informatics on the European continent. It was born as a distinct discipline barely a generation ago. As a fresh young discipline, it is an effervescent mixture of formal theory, empirical applications, and pragmatic design. Mathematics was just such an effervescent mixture in western culture from the renaissance to the middle of the twentieth century. It was then that the dynamic effect of high speed, electronic, general purpose computers accelerated the generalization of the meaning of the word computation This caused the early computer science to recruit not only mathematicians but also philosophers (especially logicians), linguists, psychologists, even economists, as well as physicists, and a variety of engineers. Thus we are, perforce, discussing the changes and adaptations of individuals to disciplines, and especially of people in one discipline to another. As we all know, the very word discipline indicates that there is an initial special effort by an individual to force himself or herself to change. The change involves adaptation of one\u27s perceptions to a special way of viewing certain aspects of the - world, and also one\u27s behavior in order to produce special results. For example we are familiar with the enormous prosthetic devices that physicists have added to their natural sensors and perceptors in order to perceive minute particles and to smash atoms in order to do so (at, we might add, enormous expense, and enormous stretching of computational activity). We are also familiar with the enormously intricate prosthetic devices mathematicians added to their computational effectors, the general symbol manipulators, called computers

A personal account of Turing’s imprint on the development of computer science

The rst part of the XX century saw the development of the digital computer and the eld of computer science. In the present paper, we sketch our vision of that period and of the role that Alan Turing and some of his contemporary peers played in that development.Preprin

Neuere Entwicklungen der deklarativen KI-Programmierung : proceedings

The field of declarative AI programming is briefly characterized. Its recent developments in Germany are reflected by a workshop as part of the scientific congress KI-93 at the Berlin Humboldt University. Three tutorials introduce to the state of the art in deductive databases, the programming language Gödel, and the evolution of knowledge bases. Eleven contributed papers treat knowledge revision/program transformation, types, constraints, and type-constraint combinations

From mathematics in logic to logic in mathematics : Boole and Frege

This project proceeds from the premise that the historical and logical value of Boole's logical calculus and its connection with Frege's logic remain to be recognised. It begins by discussing Gillies' application of Kuhn's concepts to the history oflogic and proposing the use of the concept of research programme as a methodological tool in the historiography oflogic. Then it analyses'the development of mathematical logic from Boole to Frege in terms of overlapping research programmes whilst discussing especially Boole's logical calculus. Two streams of development run through the project: 1. A discussion and appraisal of Boole's research programme in the context of logical debates and the emergence of symbolical algebra in Britain in the nineteenth century, including the improvements which Venn brings to logic as algebra, and the axiomatisation of 'Boolean algebras', which is due to Huntington and Sheffer. 2. An investigation of the particularity of the Fregean research programme, including an analysis ofthe extent to which certain elements of Begriffsschrift are new; and an account of Frege's discussion of Boole which focuses on the domain common to the two formal languages and shows the logical connection between Boole's logical calculus and Frege's. As a result, it is shown that the progress made in mathematical logic stemmed from two continuous and overlapping research programmes: Boole's introduction ofmathematics in logic and Frege's introduction oflogic in mathematics. In particular, Boole is regarded as the grandfather of metamathematics, and Lowenheim's theorem ofl915 is seen as a revival of his research programme