The twentieth century has witnessed a striking transformation in the understanding of the theories of mathematical physics. There has emerged clearly the idea that physical theories are significantly characterized by their abstract mathematical structure. This is in opposition to the tradi- tional opinion that one should look to the specific applications of a theory in orrter to understand it. One might with reason now espouse the view that to understand the deeper character of a theory one must know its abstract structure and understand the significance of that structure, while to understand...

XIV The stability of a philosophical construction will depend not only upon the solidity of the blocks, of the pillars and architraves that make it up, but also upon the way in which all these parts are connected. Of course, it will not be possible to argue for every single part of a philosophical building: to do so would mean to embark in a virtually endless enterprise. Accordingly, some of the parts of a philosophical building will have to be taken from the literature on the subject as 'ready made' or 'semi-finished' elements, while others will be argued for in the course of building. This...

InSeptember2000theArcheCentrelauncheda ve-yearresearchprojecten- tled the Logical and Metaphysical Foundations of Classical Mathematics. Its goal was to study the prospects, philosophical and technical, for abstractionist foundations for the classical mathematical theories of the natural, real and complex numbers and standard set theory. Funding was provided by the then Arts and Humanities Research Board (now the Arts and Humanities Research Council) for the appointment of full-time postdoctoral research fellows and PhD students to collaborate with more senior colleagues in the project, and...

Focuses on the points of intersection between analytic philosophy and the philosophy of the exact sciences. This title deals with the connections between knowledge in mathematics and the exact sciences, on the one hand, and the conceptual foundations of knowledge in general.

Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilbert's program of consistency proofs; he explores "implicit definition" (a generalization of definition by abstraction) and indicates how this...

Graham Solomon, to whom this collection is dedicated, went into hospital for antibiotic treatment of pneumonia in Oc- ber, 2001. Three days later, on Nov. 1, he died of a massive stroke, at the age of 44. Solomon was well liked by those who got the chance to know him--it was a revelation to ?nd out, when helping to sort out his a?airs after his death, how many "friends" he had whom he had actually never met, as his email included correspondence with philosophers around the world running sometimes to hundreds of messages. He was well respected in the philosophical community more broadly. He...

JeffandImetwhenIwasagraduatestudentattheUniversityofMinnesotaandhewas a post doctoral fellow, first in the Chemistry Department, and then in the Center for Philosophy of Science. Later we were colleagues atWestern Ontario. Our friendship and collaboration owe a great deal to both these institutions. In the mid-1960s the Center enjoyed great success under Feigl's directorship. The history of the Center has been only very partially documented. Feyerabend's recollections, reportedinhisAutobiography, andsomeyearsearlierinhisremarksfor Feigl's Festschrift, possess an immediacy that makes them...

Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant's theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Godel, Poincare, Weyl and Bohr thought that intuition was an indispensable element in...

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 (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank...