By Palle Yourgrau
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Extra info for A World Without Time: The Forgotten Legacy Of Godel And Einstein
Not content with this, Frege employed this new mathematized logic-which for him was not a mere calculating device, but a proper science, with its own content and subject matter-as itself a foundation for mathematics, in particular for arithmetic, or number theory. rege's, a field that came to be known as metamathematics, since it involved the mathematical study of mathematical systems themselves. (Hilbert had been introduced to the idea of metamathematics-and more generally to the notion of a metalanguage-by the Dutch mathematician L.
Since the direction of maximum entropy has been held to account for the "direction of time" and for the existence of irreversible physical processes like breaking an egg, Boltzmann's contribution was enormous. It was certainly not lost on the young Einstein, who embraced probability eagerly, and it later paved the way for the use of proba- Vienna: Logical Circles o I 37 bilistic methods in quantum mechanics (which an older Einstein found far less palatable). Again in opposition to Mach, Boltzmann was a firm believer in the importance of mathematical methods in the physical sciences, pointing the way to the future of physics, while Mach faced toward the past.
Frege's work gave birth, then, to two new subfields of mathematics: mathematical logic and axiomatic set theory. G6del's mathematical advisor, Hans Hahn, kept abreast of all these new developments in mathematical logic and set theory. Indeed, he directed a seminar devoted to the classic of modern mathematical logic, Principia Mathematica, by Bertrand Russell and Albert North Whitehead. G6del did not participate in that seminar, but he did attend one given by the philosopher Moritz Schlick on Bertrand Russell's later work, Introduction to Mathematical Philosophy (written while Russell was in jail in England for his protests against British participation in World War I).
A World Without Time: The Forgotten Legacy Of Godel And Einstein by Palle Yourgrau