This volume presents the philosophical and heuristic framework Cantor developed and explores its lasting effect on modern mathematics. "Establishes a new plateau for historical comprehension of Cantor's monumental contribution to mathematics." --The American Mathematical Monthly.
This paper treats some of the issues raised by Putnam's discussion of, and claims for, quantum logic, specifically: that its proposal is a response to experimental difficulties; that it is a reasonable replacement for classical logic because its connectives retain their classical meanings, and because it can be derived as a logic of tests. We argue that the first claim is wrong (1), and that while conjunction and disjunction can be considered to retain their classical meanings, negation crucially does not. (...) The argument is conducted via a thorough analysis of how the meet, join and complementation operations are defined in the relevant logical structures, respectively Boolean- and ortholattices (3). Since Putnam wishes to reinstate a realist interpretation of quantum mechanics, we ask how quantum logic can be a logic of realism. We show that it certainly cannot be a logic of bivalence realism (i.e., of truth and falsity), although it is consistent with some form of ontological realism (4). Finally, we show that while a reasonable explication of the idealized notion of test yields interesting mathematical structure, it by no means yields the rich ortholattice structure which Putnam (following Finkelstein) seeks. (shrink)
The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...) Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic. (shrink)