Download or read book Proofs and Refutations written by Imre Lakatos and published by Cambridge University Press. This book was released on 1976 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Download or read book Formal Proofs and Refutations written by Jesse Alama and published by . This book was released on 2009 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proofs and Refutations written by Imre Lakatos and published by Cambridge University Press. This book was released on 2015-10-08 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.
Download or read book Proofs and Refutations written by Imre Lakatos and published by . This book was released on 1964 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proofs and Refutations written by Imre Lakatos and published by . This book was released on 1987 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proof and Disproof in Formal Logic written by Richard Bornat and published by Oxford University Press on Demand. This book was released on 2005 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. This book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses - natural deduction - is very simple and shows how large mathematical universes can be built on small foundations. Aimed at undergraduates and graduates in computerscience, logic, mathematics, and philosophy, the text includes reference to...
Download or read book Proofs and Refutations the Logic of Mathematical Discovery written by Imre Lakatos and published by . This book was released on 1979 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book 18 Unconventional Essays on the Nature of Mathematics written by Reuben Hersh and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines
Download or read book Investigating Notions of Proof written by Keir Finlow-Bates and published by Lulu.com. This book was released on 2009-10 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although proof is seen by most mathematicians as lying at the heart of mathematics, it is rarely explicitly taught at any point in the mathematics curriculum. This is compounded by the fact that within the mathematics and education communities there is no clear definition of or consensus on what actually constitutes proof. In this book a fallibilist approach based on the work of Imre Lakatos is adopted, and proof and proving are set within the context of a form of social knowledge in order to gain insight into the proof-activities of degree level mathematics students.
Download or read book Protocols Strands and Logic written by Daniel Dougherty and published by Springer Nature. This book was released on 2021-11-18 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift was published in honor of Joshua Guttman on the occasion of his 66.66 birthday. The impact of his work is reflected in the 23 contributions enclosed in this volume. Joshua’s most influential and enduring contribution to the field has been the development of the strand space formalism for analyzing cryptographic protocols. It is one of several “symbolic approaches” to security protocol analysis in which the underlying details of cryptographic primitives are abstracted away, allowing a focus on potential flaws in the communication patterns between participants. His attention to the underlying logic of strand spaces has also allowed him to merge domain-specific reasoning about protocols with general purpose, first-order logical theories. The identification of clear principles in a domain paves the way to automated reasoning, and Joshua has been a leader in the development and distribution of several tools for security analysis.
Download or read book Five Proofs of the Existence of God written by Edward Feser and published by Ignatius Press. This book was released on 2017-08-25 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed, updated exposition and defense of five of the historically most important (but in recent years largely neglected) philosophical proofs of God’s existence: the Aristotelian, the Neo-Platonic, the Augustinian, the Thomistic, and the Rationalist. It also offers a thorough treatment of each of the key divine attributes—unity, simplicity, eternity, omnipotence, omniscience, perfect goodness, and so forth—showing that they must be possessed by the God whose existence is demonstrated by the proofs. Finally, it answers at length all of the objections that have been leveled against these proofs. This work provides as ambitious and complete a defense of traditional natural theology as is currently in print. Its aim is to vindicate the view of the greatest philosophers of the past— thinkers like Aristotle, Plotinus, Augustine, Aquinas, Leibniz, and many others— that the existence of God can be established with certainty by way of purely rational arguments. It thereby serves as a refutation both of atheism and of the fideism that gives aid and comfort to atheism.
Download or read book Logic for Computer Science written by Jean H. Gallier and published by Courier Dover Publications. This book was released on 2015-06-18 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.
Download or read book Proof in Mathematics Education written by David A. Reid and published by BRILL. This book was released on 2010-01-01 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research on teaching and learning proof and proving has expanded in recent decades. This reflects the growth of mathematics education research in general, but also an increased emphasis on proof in mathematics education.
Download or read book Logical Foundations of Mathematics and Computational Complexity written by Pavel Pudlák and published by Springer Science & Business Media. This book was released on 2013-04-22 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.
Download or read book Trust written by Adriano Fabris and published by Springer Nature. This book was released on 2020-04-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents cutting-edge concepts on the question of trust. Written by leading experts, it investigates a paradoxical feature of contemporary society: while information and communication technologies, on the one hand, and scientific discourses, on the other, can promote more informed participation in public and democratic life, they have also led to a dramatic decline in our communicative and cooperative skills. The book analyzes the notion of trust from an interdisciplinary perspective by combining the normative (continental) and empirical (Anglo-American) approaches and by considering the political, epistemological, and historical transformations in the interpersonal relationships sparked by new technologies. Using trust as a model, it then investigates and clarifies the new types of participation that are made possible by scientific and technological advances.
Download or read book Justification Logic written by Sergei Artemov and published by Cambridge University Press. This book was released on 2019-05-02 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops a new logic paradigm which emphasizes evidence tracking, including theory, connections to other fields, and sample applications.
Download or read book New Perspectives on Mathematical Practices written by Bart Van Kerkhove and published by World Scientific. This book was released on 2009 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.
