This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that...
This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approac...
The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–VII of Plato’s Republic and Aristotle’s Prior and Posterior Analytics, to Kant’s Critique of Pure Reason and Mill’s A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers by Bertrand Russell (Logic and Knowledge. Essays, 1901–1950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge.
This book does not...
The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–...
This book presents Gödel’s incompleteness theorems and the other limitative results which are most significant for the philosophy of mathematics. Results are stated in the form most relevant for use in the philosophy of mathematics. An appendix considers their implications for Hilbert’s Program for the foundations of mathematics. The text is self-contained, all notions being explained in full detail, but of course previous exposure to the very first rudiments of mathematical logic will help.
This book presents Gödel’s incompleteness theorems and the other limitative results which are most significant for the philosophy of mathematics...
