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This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the “algebraic” approach to math...
Arno Bohm and Ilya Prigogine's Brussels-Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's...
Hilbert's machine is a supertask machine inspired by Hilbert's Hotel whose functioning leads to a contradiction that compromises the Axiom of Infinity.
I examine Frege’s explanation of how Hilbert ought to have presented his proofs of the independence of the axioms of geometry: in terms of mappings between (what we would call) fully interpreted state...
Only recently, David Hilbert's program to axiomatize the sciences according to the pattern of geometry has left the shade of his formalist program in the foundations of mathematics. This relative negl...
Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbe...
Only recently, David Hilbert's program to axiomatize the sciences according to the pattern of geometry has left the shade of his formalist program in the foundations of mathematics. This relative negl...

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