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- Richard L. Tieszen (2005). Phenomenology, Logic, and the Philosophy of Mathematics. Cambridge University Press.Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this book is divided into three parts. Part I, Reason, Science, and Mathematics contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay oN phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, Penelope Maddy and Roger Penrose. Part III deals with elementary, constructive areas of mathematics. These are areas of mathematics that are closer to their origins in simple cognitive activities and in everyday experience. This part of the book contains essays on intuitionism, Hermann Weyl, the notion of constructive proof, Poincare; and Frege.Reading list | Discuss | Edit | Categorize |My bibliography
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This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...
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| | Other links: dx.doi.org | Scholar | At my library | More options ... Chihara here develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. He utilizes this system in the analysis of the nature of mathematics, and discusses many recent works in the philosophy of mathematics from the viewpoint of the constructibility theory developed. This innovative analysis will appeal to mathematicians and philosophers of logic, mathematics, and science.
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| | Scholar | At my library | More options ... Translator's introduction -- Fundamental questions of geometry -- The decidability requirement -- The origin of the concept of number -- Implicit definition and the proper grounding of mathematics -- Rigid bodies in geometry -- Prelude to geometry : the essential ideas -- Physical and mathematical geometry -- Natural geometry -- The concept of the differential -- Reflections on the proper grounding of mathematics I -- Concepts and proofs in mathematics -- Dimension and space in mathematics -- Reflections on the proper grounding of mathematics II -- The axiomatic method in modern mathematics.
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| | Scholar | At my library | More options ... This paper contains answers to the following Five questions, posed by the editors are answered: (1) Why were you initially drawn to the foundations of mathematics and/or the philosophy of mathematics? (2) What example(s) from your work (or the work of others) illustrates the use of mathematics for philosophy? (3) What is the proper role of philosophy of mathematics in relation to logic, foundations of mathematics, the traditional core areas of mathematics, and science? (4) What do you consider the most neglected topics and/or contributions in late 20th century philosophy of mathematics? (5) What are the most important open problems in the philosophy of mathematics and what are the prospects for progress?
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| | Other links: mally.stanford.edu | Scholar | At my library | More options ... This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.
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| | Scholar | At my library | More options ... The relation between Wittgenstein's philosophy of mathematics and mathematical Intuitionism has raised a considerable debate. My attempt is to analyse if there is a commitment in Wittgenstein to themes characteristic of the intuitionist movement in Mathematics and if that commitment is one important strain that runs through his Remarks on the foundations of mathematics. The intuitionistic themes to analyse in his philosophy of mathematics are: firstly, his attacks on the unrestricted use of the Law of Excluded Middle; secondly, his distrust of non-constructive proofs; and thirdly, his impatience with the idea that mathematics stands in need of a foundation. These elements are Fogelin's starting point for the systematic reconstruction of Wittgenstein's conception of mathematics.
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| | Other links: tandfonline.com dx.doi.org | Scholar | At my library | More options ... '' FROM THE INTRODUCTION Among the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics.
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| | Scholar | At my library | More options ... Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert’s metamathematics. Part III focuses on the philosophy of mathematics. Each chapter has extensive supplementary notes; a detailed appendix charts modern developments.
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| | Scholar | At my library | More options ... The paper discusses Husserl's phenomenology of mathematics in his Formal and Transcendental Logic (1929). In it Husserl seeks to provide descriptive foundations for mathematics. As sciences and mathematics are normative activities Husserl's attempt is also to describe the norms at work in these disciplines. The description shows that mathematics can be given in several different ways. The phenomenologist's task is to examine whether a given part of mathematics is genuine according to the norms that pertain to the approach in question. The paper will then examine the intuitionistic, formalistic, and structural features of Husserl's philosophy of mathematics.
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| | Other links: philmat.oxfordjournals.org dx.doi.org | Scholar | At my library | More options ... Discussion of Richard L. Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics
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