Sets, numbers, and systems (Singer mathematics program)

Suppes, Patrick

Reference

L.W. Singer Co

Introduction to Logic (University Series in Undergraduate Mathematics)

Introduction to Logic.

Van Nostrand Reinhold Company

This well-organized book was designed to introduce students to a way of thinking that encourages precision and accuracy. As the text for a course in modern logic, it familiarizes readers with a complete theory of logical inference and its specific applications to mathematics and the empirical sciences. Part I deals with formal principles of inference and definition, including a detailed attempt to relate the formal theory of inference to the standard informal proofs common throughout mathematics. An in-depth exploration of elementary intuitive set theory constitutes Part II, with separate chapters on sets, relations, and functions. The final section deals with the set-theoretical foundations of the axiomatic method and contains, in both the discussion and exercises, numerous examples of axiomatically formulated theories. Topics range from the theory of groups and the algebra of the real numbers to elementary probability theory, classical particle mechanics, and the theory of measurement of sensation intensities. Ideally suited for undergraduate courses, this text requires no background in mathematics or philosophy.

Introduction to Logic (Dover Books on Mathematics)

Politics & Social Sciences

Philosophy

Dover Publications

From the Foreword is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or unhabited. Again there are some who, without regarding it as infinite, yet think that no number has been named which is great enough to exceed its multitude. And it is clear that they who hold this view, if they imagined a mass made up of sand in other respects as large as the mass of the earth, including in it all the seas and the hollows of the earth filled up to a height equal to that of the highest mountains, would be many times further still from recognizing that any number could be expressed which exceeded the multitude of the sand so taken. But I will try to show you by means of geometrical proofs, which you will be able to follow, that, of the numbers named by me and given in the work which I sent to Zeuxippus, some exceed not only the number of the mass of sand equal in magnitude to the earth filled up in the way described, but also that of a mass equal in magnitude to the universe.

Foundations of Measurement

Science & Math

Luce, R. Duncan

Tversky, Amos

Krantz, David H.

Mathematics

Dover Pubns

This is an important collection of essays on dealing with the foundations of probability that will be of value to philosophers of science, mathematicians, statisticians, psychologists and educationalists. The collection falls into three parts: Part I comprises five essays on the axiomatic foundations of probability. Part II contains seven articles on probabilistic causality and quantum mechanics, with an emphasis on the existence of hidden variables. The third part consists of a single extended essay applying probabilistic theories of learning to practical questions of education: it incorporates extensive data analysis.

Foundations of Probability with Applications: Selected Papers 1974–1995 (Cambridge Studies in Probability, Induction and Decision Theory)

Zanotti, Mario

Cambridge University Press

This book should be of interest to undergraduates taking introductory courses in logic.

Introduction to Logic

D. Van Nostrand Co.

The author argues for replacing logical empiricism with probabilistic empiricism. Patrick Suppes is (was) Lucie Stern Professor of Philosophy at Stanford University

Probabilistic metaphysics

Blackwell

Probabilistic Metaphysics

Blackwell Pub.

The thirty-one papers collected in this volume represent most of the arti cles that I have published in the philosophy of science and related founda tional areas of science since 1970. The present volume is a natural succes sor to Studies in the Methodology and Foundations of Science, a collection of my articles published in 1969 by Reidel (now a part of Kluwer). The articles are arranged under five main headings. Part I contains six articles on general methodology. The topics range from formal methods to the plurality of science. Part II contains six articles on causality and explanation. The emphasis is almost entirely on probabilistic approaches. Part III contains six articles on probability and measurement. The impor tance of representation theorems for both probability and measurement is stressed. Part IV contains five articles on the foundations of physics. The first three articles are concerned with action at a distance and space and time, the last two with quantum mechanics. Part V contains eight articles on the foundations of psychology. This is the longest part and the articles reflect my continuing strong interest in the nature of learning and perception. Within each part the articles are arranged chronologically. I turn now to a more detailed overview of the content. The first article of Part I concerns the role of formal methods in the philosophy of science. Here I discuss what is the new role for formal methods now that the imperialism of logical positivism has disappeared.

Models and Methods in the Philosophy of Science: Selected Essays (Synthese Library, 226)

Springer

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