Exploring critical issues in the philosophy of logic and mathematics, this volume addresses topics such as reverse mathematics, the nature of proof, and the significance of Church's Thesis. It delves into the relationship between mathematics and theology, the concept of truth, and examines the philosophical landscape of logic and mathematics during interwar Poland. The diverse range of problems presented offers a comprehensive look at the intricate connections between these fields.
Focusing on the intersection of philosophy and mathematics, this book delves into the contributions of Polish logicians and mathematicians during the 1920s and 1930s, a pivotal era for Polish science. It explores whether advancements in logic and mathematics were paralleled by philosophical inquiry, analyzing the works and ideas of notable figures such as Waclaw Sierpinski and Alfred Tarski. Additionally, it provides context by examining the influence of earlier thinkers like Jan Sniadecki and Józef Maria Hoene-Wronski, enriching the understanding of this intellectual landscape.
Studies in the Philosophy of Mathematics and History of Logic
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, Gödel’s theorems and computer science, philosophy of mathematics in Polish mathematical and logical schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory.
"Recursive Functions and Metamathematics" explores completeness and decidability in theories through recursive functions. It covers Gödel's incompleteness theorems, their generalizations, and decidability theory, alongside historical and philosophical contexts. The book is self-contained, suitable for scholars and advanced students in logic and mathematics.