Fixing Frege (eBook)

John P. Burgess (Autor)

eBook Download: PDF

2018
Princeton University Press (Verlag)
978-0-691-18706-8 (ISBN)

Infos

The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been proposed, each a consistent theory permitting the development of a significant portion of mathematics. This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured.

Autor

John P. Burgess is Professor of Philosophy at Princeton University. He is the author of numerous articles on mathematical and philosophical logic and philosophy of mathematics and coauthor of A Subject with No Object.

Produkt-Details

• Erscheint lt. Verlag: 5.6.2018
• Reihe/Serie: Princeton Monographs in Philosophy
• Reihe/Serie: Princeton Monographs in Philosophy
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Philosophie
• Schlagworte: Ackermann function • Addition • Arbitrarily large • arithmetic • associative property • Axiom • Axiom of constructibility • Axiom of extensionality • axiom of infinity • Axiom of reducibility • Begriffsschrift • Burali-Forti paradox • Cantor's paradox • Cantor's Theorem • cardinal number • Church–Turing thesis • Classical Logic • classical mathematics • commutative property • complex number • Comprehension (logic) • conservative extension • consistency • Continuum Hypothesis • Contradiction • Degeneracy (mathematics) • Denotation • empty set • Entscheidungsproblem • Equation • Equinumerosity • existential quantification • exponentiation • extensionality • First-Order Logic • Gödel's Incompleteness Theorems • Gottlob Frege • Higher-Order Logic • Hilbert's program • Hume's principle • I0 • Inaccessible cardinal • Integer • Interpretability • Introduction to Mathematical Philosophy • Intuitionism • Large cardinal • Limitation of size • Logic • Logical biconditional • Logical conjunction • Logical connective • Logical disjunction • Mathematical Induction • Mathematics • Metatheorem • model Theory • Natural number • Natural proof • Negation • Non-Euclidean geometry • Null set • Parameter • Peano axioms • Permutation • philosophy of mathematics • Point at infinity • Power set • Predicate (mathematical logic) • Primitive Recursive Function • Propositional function • Quantifier (linguistics) • Quantifier (logic) • Quantity • Rational number • real number • Recursively enumerable set • Reinhardt cardinal • reverse mathematics • Robinson Arithmetic • Russell's paradox • satisfiability • scientific notation • second-order logic • set theory • soundness • Special case • Subset • Successor function • Theorem • theory • transfinite • Transfinite number • Transitive relation • Transitive set • Universal set • Upper and lower bounds • Variable (mathematics) • Well-order • Zermelo–Fraenkel set theory
• ISBN-10: 0-691-18706-1 / 0691187061
• ISBN-13: 978-0-691-18706-8 / 9780691187068