Proofs and Refutations

Proofs and Refutations
Author: Imre Lakatos
Publisher: Cambridge University Press
Total Pages: 190
Release: 1976
Genre: Mathematics
ISBN: 9780521290388

Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.

Proof and Disproof in Formal Logic

Proof and Disproof in Formal Logic
Author: Richard Bornat
Publisher: Oxford University Press on Demand
Total Pages: 243
Release: 2005
Genre: Mathematics
ISBN: 0198530277

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...

Five Proofs of the Existence of God

Five Proofs of the Existence of God
Author: Edward Feser
Publisher: Ignatius Press
Total Pages: 338
Release: 2017-08-25
Genre: Philosophy
ISBN: 1681497808

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.

Logic for Computer Science

Logic for Computer Science
Author: Jean H. Gallier
Publisher: Courier Dover Publications
Total Pages: 532
Release: 2015-06-18
Genre: Mathematics
ISBN: 0486780821

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.

Justification Logic

Justification Logic
Author: Sergei Artemov
Publisher: Cambridge University Press
Total Pages: 271
Release: 2019-05-02
Genre: Mathematics
ISBN: 1108424910

Develops a new logic paradigm which emphasizes evidence tracking, including theory, connections to other fields, and sample applications.

Proof in Mathematics Education

Proof in Mathematics Education
Author: David A. Reid
Publisher: BRILL
Total Pages: 265
Release: 2010-01-01
Genre: Education
ISBN: 946091246X

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.

Handbook of Proof Theory

Handbook of Proof Theory
Author: S.R. Buss
Publisher: Elsevier
Total Pages: 823
Release: 1998-07-09
Genre: Mathematics
ISBN: 0080533183

This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

Imre Lakatos and the Guises of Reason

Imre Lakatos and the Guises of Reason
Author: John Kadvany
Publisher: Duke University Press
Total Pages: 400
Release: 2001-04-09
Genre: Biography & Autobiography
ISBN: 9780822326496

DIVAn exploration of the philosophy of science and mathematics of Hungarian emigre, Imre Lakatos, demonstrating its contemporary relevance./div

Lakatos

Lakatos
Author: Brendan Larvor
Publisher: Psychology Press
Total Pages: 142
Release: 1998
Genre: Mathematics
ISBN: 0415142768

Lakatos: An Introduction provides a thorough overview of both Lakatos's thought and his place in twentieth century philosophy. It is an essential and insightful read for students and anyone interested in the philosophy of science.