By Gregory J. Chaitin

"Il filo conduttore di tutti questi saggi è dato dalla nozione di complessità, definita in modo assai specifico come l. a. misura dell'informazione contenuta in una proposizione matematica. Chaitin mostra che los angeles stessa matematica ha infinita complessità, ciò che tra le altre cose comporta l. a. sua inesauribilità; presa come oggetto finito, los angeles mente umana è incapace già solo di creare quel Sacro Graal caro ai fisici, una "teoria del tutto" contenente tutte le possibili verità matematiche. Il dato che emerge con l. a. stessa inesauribilità della matematica è l. a. più specialty conferma possibile del fatto che l. a. pratica della matematica è più come una scienza fisica, che un semplice esercizio di logica. Le idee che troverete qui, rappresentano il nucleo stesso della filosofia della matematica e meritano los angeles più ampia viewers possibile. l. a. ricerca di Greg Chaitin sarà ricordata affianco a quelle di Godel, di Turing, di von Neumann e di altre semidivinità presenti nel Pantheon della matematica, le cui idee hanno cambiato los angeles nostra prospettiva su ciò che è e ciò che non è. I saggi presentati in questo quantity rappresentano una essenza distillata di questa ricerca." (John Casti).

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Journal of Symbolic Logic, 58(4):1426–1450, December 1993. 15. H. Rott. Change, Choice and Inference: A Study of Belief Revision and Non-monotonic Reasoning. Oxford University Press, Oxford, 2001. 16. A. Rubinstein and Y. Salant. A model of choice from lists. Theoretical Economics, 45:3–17, 2006. 17. K. Sen. Choice functions and revealed preference. The Review of Economic Studies, 38(3):307–317, July 1971. 18. K. Sen. Social choice theory: A re-examination. Econometrica, 45(1):53–88, January 1977.

This lack of a justification component has, perhaps, contributed to a certain gap between epistemic logic and mainstream epistemology [28, 29]. We would like to think that Justification Logic is a step towards filling this void. Justification Logic had been anticipated in [25] (as the logic of explicit mathematical proofs) and in [54] (in epistemology), developed in [2, 3, 36, 42] and other papers (as the Logic of Proofs), and then in [4, 6, 7, 9, 14, 22, 23, 27, 33, 35, 45, 48, 50, 56] and other papers in a broader epistemic context.

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