Wittgenstein Finitism and the Foundations of Mathematics

Author: Mathieu Marion
Publisher: Oxford University Press
ISBN: 9780198235163
Format: PDF, ePub
Download Now
Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking from the 1920s through to the 1950s, in the context of themathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. He shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy,and also that it can do much to illuminate current debates about the foundations of mathematics.

The Oxford Handbook of Philosophy of Mathematics and Logic

Author: Stewart Shapiro
Publisher: Oxford University Press
ISBN: 0198033990
Format: PDF, ePub, Docs
Download Now
Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

Category Mistakes

Author: Ofra Magidor
Publisher: OUP Oxford
ISBN: 0191662844
Format: PDF, ePub, Mobi
Download Now
Category mistakes are sentences such as 'Green ideas sleep furiously', 'Saturday is in bed', and 'The theory of relativity is eating breakfast'. Such sentences strike most speakers as highly infelicitous but it is a challenge to explain precisely why they are so. Ofra Magidor addresses this challenge, while providing a comprehensive discussion of the various treatments of category mistakes in both philosophy of language and linguistics. The phenomenon of category mistakes is particularly interesting to both these fields because a plausible case can be (and has been) made for explaining it in terms of syntax, semantics, and pragmatics—making it a fruitful case for exploring the relations between and nature of these three fundamental realms of language. Category Mistakes follows this division. After an introduction which explains the aims and motivations for the project and provides a brief historical survey of the (modern) treatment of category mistakes in each of philosophy, linguistics, and computer science, Magidor discusses four approaches in turn: first, the syntactic approach, which maintains that category mistakes are syntactically ill-formed; then two semantic approaches, though ones that appeal to different semantic facets: the meaninglessness view, which maintains that category mistakes are meaningless, and the MBT view, according to which category mistakes are meaningful but truth-valueless; and finally the pragmatic approach, according to which category mistakes are syntactically well-formed, meaningful, truth-valued but nevertheless pragmatically inappropriate. Magidor argues that the first three approaches ought to be rejected, and in the final chapter addresses the main challenge by developing and defending a particular version of the pragmatic approach: a presuppositional account of category mistakes.

The Philosophy of Mathematics Today

Author: Matthias Schirn
Publisher: Oxford University Press
ISBN: 9780199262625
Format: PDF, Docs
Download Now
The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come.

Social Constructivism as a Philosophy of Mathematics

Author: Paul Ernest
Publisher: SUNY Press
ISBN: 9780791435878
Format: PDF, Kindle
Download Now
Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.

The Autonomy of Mathematical Knowledge

Author: Curtis Franks
Publisher: Cambridge University Press
ISBN: 0521514371
Format: PDF, Mobi
Download Now
This study reconstructs, analyses and re-evaluates the programme of influential mathematical thinker David Hilbert, presenting it in a new light.

Groups and Geometry

Author: P. M. Neumann
Publisher: Oxford University Press on Demand
ISBN: 9780198534518
Format: PDF, Docs
Download Now
Available for the first time in published form, Groups and Geometry presents the Oxford Mathematical Institute notes for undergraduates and first year postgraduates. The content is guided by the Oxford syllabus but includes much more material than is included on the syllabus. This book is about the measurement of symmetry: covering groups and geometry with the symbiotic relationship between the two more than justifying the union. A number of exercises are included in this sylish text to help the reader gain a full understanding of this branch of mathematics.

The Adventure of Reason

Author: Paolo Mancosu
Publisher: Oxford University Press
ISBN: 0199546533
Format: PDF
Download Now
Paolo Mancosu presents an innovative set of studies of logic and the foundations of mathematics in the first half of the 20th century. He sheds new light on important topics such as the relationship between phenomenology and the exact sciences, the nature of truth and logical consequence, and the nature of mathematical intuition.