Philosophy's Loss of Logic to Mathematics

Description

This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century. Front Matter ....Pages i-xii Introduction (Woosuk Park)....Pages 1-6 Front Matter ....Pages 7-7 Frege’s Distinction Between “Falling Under” and “Subordination” (Woosuk Park)....Pages 9-30 Scotus, Frege, and Bergmann (Woosuk Park)....Pages 31-45 On Cocchiarella’s Retroactive Theory of Reference (Woosuk Park)....Pages 47-56 Front Matter ....Pages 57-57 Zermelo and the Axiomatic Method (Woosuk Park)....Pages 59-86 Friedman on Implicit Definition: In Search of the Hilbertian Heritage in Philosophy of Science (Woosuk Park)....Pages 87-102 Between Bernays and Carnap (Woosuk Park)....Pages 103-120 Front Matter ....Pages 121-121 Patterson on Tarski’s Definition of Logical Consequence (Woosuk Park)....Pages 123-144 On the Motivations of Gödel’s Ontological Proof (Woosuk Park)....Pages 145-154 Front Matter ....Pages 155-155 Ontological Regress of Maddy’s Mathematical Naturalism (Woosuk Park)....Pages 157-187 What if Haecceity Is not a Property? (Woosuk Park)....Pages 189-206 Biancani on Scientiae Mediae (Woosuk Park)....Pages 207-221 Back Matter ....Pages 223-230