Studies in the Philosophy of Logic and Mathematics
The volume consists of thirteen papers devoted to various problems of the philosophy of logic and mathematics. They can be divided into two groups. The first group contains papers devoted to some general problems of the philosophy of mathematics whereas the second group – papers devoted to the history of logic in Poland and to the work of Polish logicians and mathematicians in the philosophy of mathematics and logic.
The first group is opened by the chapter “On the philosophical meaning of reverse mathematics” in which philosophical consequences of this research project in the foundations of mathematics are discussed. In particular, we are interested in its implications for Hilbert’s program. The chapter “On the distinction proof–truth in mathematics” is devoted to some historical, philosophical and logical considerations connected with the distinction between proof and truth in mathematics. The crucial role of Gödel’s incompleteness theorems as well as of the undefinability of truth vs. definability of provability and the role of finitary vs. infinitary methods are stressed. The problem of the need of extending the available methods by new rules of inference and new axioms is also considered. The problem of a proof in mathematics is discussed also in the chapter “Some historical, philosophical and methodological remarks on proof in mathematics”. It is devoted to historical and philosophical as well as methodological considerations on the role and meaning of proof in mathematics. In particular, the following problems are discussed: the role of informal proofs in mathematical research practice,...
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