Proofs and Refutations
Title | Proofs and Refutations PDF eBook |
Author | Imre Lakatos |
Publisher | Cambridge University Press |
Pages | 190 |
Release | 1976 |
Genre | Mathematics |
ISBN | 9780521290388 |
Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Proofs and Refutations
Title | Proofs and Refutations PDF eBook |
Author | Imre Lakatos |
Publisher | Cambridge University Press |
Pages | 190 |
Release | 1976-01-01 |
Genre | Science |
ISBN | 1107268109 |
Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.
Proofs and Refutations
Title | Proofs and Refutations PDF eBook |
Author | Imre Lakatos |
Publisher | Cambridge University Press |
Pages | 197 |
Release | 2015-10-15 |
Genre | Mathematics |
ISBN | 1107113466 |
This influential book discusses the nature of mathematical discovery, development, methodology and practice, forming Imre Lakatos's theory of 'proofs and refutations'.
Conjectures and Refutations
Title | Conjectures and Refutations PDF eBook |
Author | Karl Raimund Popper |
Publisher | Psychology Press |
Pages | 614 |
Release | 2002 |
Genre | Knowledge, Theory of |
ISBN | 9780415285940 |
Conjectures and Refutations is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.
Charles S. Peirce's Mathematical Logic and Philosophy
Title | Charles S. Peirce's Mathematical Logic and Philosophy PDF eBook |
Author | Alan J. Iliff |
Publisher | |
Pages | 170 |
Release | 2018-03-31 |
Genre | Mathematics |
ISBN | 9781942795995 |
Charles S. Peirce is generally regarded today as one of the most out-standing philosophers in American history, and especially as the inventor of pragmatism. Nevertheless, he also discovered several of the most important concepts of twentieth-century mathematical logic, including thequantifiers, the interpretation of first-order logic by means of relations, and the concept of logical consequence. There is very little general knowledge of Peirce's influence on the development of mathematical logic andalmost total ignorance of the details of that influence. The main technical results of this book establish that Peirce laid down the main elements of a framework for the model-theoretic line of development in mathematical logic.
For and Against Method
Title | For and Against Method PDF eBook |
Author | Imre Lakatos |
Publisher | University of Chicago Press |
Pages | 465 |
Release | 2010-05-27 |
Genre | Science |
ISBN | 0226467031 |
The work that helped to determine Paul Feyerabend's fame and notoriety, Against Method, stemmed from Imre Lakatos's challenge: "In 1970 Imre cornered me at a party. 'Paul,' he said, 'you have such strange ideas. Why don't you write them down? I shall write a reply, we publish the whole thing and I promise you—we shall have a lot of fun.' " Although Lakatos died before he could write his reply, For and Against Method reconstructs his original counter-arguments from lectures and correspondence previously unpublished in English, allowing us to enjoy the "fun" two of this century's most eminent philosophers had, matching their wits and ideas on the subject of the scientific method. For and Against Method opens with an imaginary dialogue between Lakatos and Feyerabend, which Matteo Motterlini has constructed, based on their published works, to synthesize their positions and arguments. Part one presents the transcripts of the last lectures on method that Lakatos delivered. Part two, Feyerabend's response, consists of a previously published essay on anarchism, which began the attack on Lakatos's position that Feyerabend later continued in Against Method. The third and longest section consists of the correspondence Lakatos and Feyerabend exchanged on method and many other issues and ideas, as well as the events of their daily lives, between 1968 and Lakatos's death in 1974. The delight Lakatos and Feyerabend took in philosophical debate, and the relish with which they sparred, come to life again in For and Against Method, making it essential and lively reading for anyone interested in these two fascinating and controversial thinkers and their immense contributions to philosophy of science. "The writings in this volume are of considerable intellectual importance, and will be of great interest to anyone concerned with the development of the philosophical views of Lakatos and Feyerabend, or indeed with the development of philosophy of science in general during this crucial period."—Donald Gillies, British Journal for the Philosophy of Science (on the Italian edition) "A stimulating exchange of letters between two philosophical entertainers."—Tariq Ali, The Independent Imre Lakatos (1922-1974) was professor of logic at the London School of Economics. He was the author of Proofs and Refutations and the two-volume Philosophical Papers. Paul Feyerabend (1924-1994) was educated in Europe and held numerous teaching posts throughout his career. Among his books are Against Method; Science in a Free Society; Farewell to Reason; and Killing Time: The Autobiography of Paul Feyerabend, the last published by the University of Chicago Press.
A First Course in Mathematical Logic and Set Theory
Title | A First Course in Mathematical Logic and Set Theory PDF eBook |
Author | Michael L. O'Leary |
Publisher | John Wiley & Sons |
Pages | 464 |
Release | 2015-09-14 |
Genre | Mathematics |
ISBN | 1118548019 |
A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.