Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Godel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse...

The book is a collection of the author's selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the history of logic and mathematics. They address such issues...

Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Godel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse...

The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert's program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Godel's theorems and computer science, philosophy of mathematics in Polish mathematical and...

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s.It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent thedevelopment of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing both works of Polish logicians and mathematicians who have a philosophical temperament...