Matthias Baaz;, Christos H. Papadimitriou;, Hilary W. Putnam;, Dana S. Scott;, Charles L. HarperJr. (Editors). Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. xxiii + 515 pp., illus., tables, bibl., index. Cambridge: Cambridge University Press, 2011. $99 (cloth).

Isis ◽  
2012 ◽  
Vol 103 (2) ◽  
pp. 383-384
Author(s):  
Paolo Mancosu
Keyword(s):  
Foundations Of Mathematics ◽  
Cambridge University ◽  
Kurt Gödel

scholarly journals Observações sobre a meta final do modo de fazer filosofia de Ludwig Wittgenstein

2019 ◽  
Vol 22 (3) ◽  
pp. 411-438
Author(s):  
Gustavo Augusto Fonseca
Keyword(s):  
Ludwig Wittgenstein ◽  
Basic Concept ◽  
Foundations Of Mathematics ◽  
Newtonian Physics ◽  
Alan Turing ◽  
Kurt Gödel ◽  
Perfect Model ◽  
Proposal A ◽  
Heinrich Hertz

In The Principles of Mechanics, physicist Heinrich Hertz argues that instead of replying to the question “what is force?” like physicists and philosophers had been doing unsuccessfully, Newtonian physics should be reformulated without considering “force” a basic concept. Decades after Hertz’s book, Ludwig Wittgenstein considered the physicist’s proposal a perfect model for how philosophical problems should be solved, to the point that he made it the foundation of his way of doing philosophy. This article addresses Wittgenstein’s way of doing philosophy, while it also proposes the reason why he failed in solving the philosophical problems — as did Hertz in his project on reformulating Newtonian physics without considering the concept “force”. And to illustrate Wittgenstein’s failure, it examines his disputes with mathematicians Kurt Gödel and Alan Turing on the foundations of mathematics.

Prologue

2017 ◽  
Author(s):  
Jan von Plato
Keyword(s):  
Information Society ◽  
Formal Languages ◽  
Foundations Of Mathematics ◽  
Direct Path ◽  
John Von Neumann ◽  
Von Neumann ◽  
Alan Turing ◽  
Kurt Gödel

It may sound paradoxical, but if around 1930 Kurt Gödel had not thought very deeply about the foundations of mathematics, there would be no information society in the form in which we have it today. Gödel’s solitary work was the single most important factor in the development of precise theories of formal languages, ones that through the coding he invented could be handled by a machine. Likewise, his work led to precise notions of algorithmic computability from which a direct path led to the first theoretical ideas of a computer, in the work of Alan Turing in 1936 and John von Neumann some years later....

Ernest Schimmerling. Covering properties of core models. Sets and proofs. (Leeds, 1997), London Mathematical Society Lecture Note Series 258. Cambridge University Press, Cambridge, 1999, pp. 281–299. - Peter Koepke. An introduction to extenders and core models for extender sequences. Logic Colloquium '87 (Granada, 1987), Studies in Logic and the Foundations of Mathematics 129. North-Holland, Amsterdam, 1989, pp. 137–182. - William J. Mitchell. The core model up to a Woodin cardinal. Logic, methodology and philosophy of science, IX (Uppsala, 1991), Studies in Logic and the Foundations of Mathematics 134, North-Holland, Amsterdam, 1994, pp. 157–175. - Benedikt Löwe and John R. Steel. An introduction to core model theory. Sets and proofs (Leeds, 1997), London Mathematical Society Lecture Note Series 258, Cambridge University Press, Cambridge, 1999, pp. 103–157. - John R. Steel. Inner models with many Woodin cardinals. Annals of Pure and Applied Logic, vol. 65 no. 2 (1993), pp. 185–209. - Ernest Schimmerling. Combinatorial principles in the core model for one Woodin cardinal. Annals of Pure and Applied Logic, vol. 74 no. 2 (1995), pp. 153–201. - Philip D. Welch. Some remarks on the maximality of inner models. Logic Colloquium '98 (Prague, 1998), Lecture Notes in Logic 13, Association of Symbolic Logic, Urbana, Illinois, 2000, pp. 516–540.

2004 ◽  
Vol 10 (4) ◽  
pp. 583-588
Author(s):  
Martin Zeman
Keyword(s):  
London Mathematical Society ◽  
Lecture Note ◽  
Mathematical Society ◽  
Core Model ◽  
Foundations Of Mathematics ◽  
Cambridge University ◽  
Applied Logic ◽  
The Core ◽  
Lecture Note Series ◽  
Woodin Cardinal
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