oi Tony, >We can look back at Goedel's work as one early attempt of fibring of formal >systems. e', a gente sempre pode "look at anything as anything", mas qual 'e a sua evidencia de que isso 'e util? o que voce acha que ganha com essa interpretacao?
obrigada, valeria 2011/10/1 Tony Marmo <marmo.t...@gmail.com>: > Dear friends, > > We can look back at Goedel's work as one early attempt of fibring of formal > systems. Thus, the problem of determining the consistency and the > completeness of the system seems to be like the same problem for a given > logic L which is obtained by the fibring of two logics L* and L**. First > order arithmetics is thus the fibring of first order logic and Peano's > arithmetics, which yields the known results presented by Goedel. > > We have no a priori intuitive reason to assume that a certain fibring will > produce a consistent and complete system. This has to be checked as the > systems are combined. If in combining two systems one produces results like > those of Goedel's theorems, it must still be possible to investigate the > resulting system by investigating other features of the same, namely > checking whether it has different, new, unusual or unexpected properties. > > In sum, I don't expect to see novelties that can or will overshadow Goedel's > contributions, except in consequence of more advances in the field of > fibring. > > Em 1 de outubro de 2011 14:21, Walter Carnielli > <walter.carnie...@gmail.com>escreveu: > >> Caros colegas: >> >> como vimos, o Ed Nelson retirou seu "claim" sobre a inconsistência de >> P. >> Isso, contudo, não significa o fim das discussões, nem menos a >> garantia da consistência de P! >> >> Quero aqui parabenizar ao nosso colega Daniel Tausk do IME USP >> (http://www.ime.usp.br/~tausk/) >> pela excelente observação que convenceu o Nelson. Imagino que o >> Rodrigo Freire e outros coelgas da USP tenham participado >> ativamente da atmosfera de discussão que levou o Daniel a observar o >> erro na pretensa prova do Ed Nelson. >> >> E finalmente parabenizo o Ed Nelosn pela coragem em propor sua >> alegação, e pela humildade em reconhecer publicamente o erro. Acho >> que é assim que se faz ciência, e acho que esse tipo de atitude é >> que devemos ensinar aos nossos estudantes, e aprendermos nós >> mesmos. Ed Nelson merece uma homegagem. >> >> Abraços, >> >> Walter >> >> ---------- Forwarded message ---------- >> From: Edward Nelson <nel...@math.princeton.edu> >> Date: 2011/10/1 >> Subject: [FOM] inconsistency of P >> To: f...@cs.nyu.edu >> >> >> Terrence Tao, at >> http://golem.ph.utexas.edu/category/2011/09/ >> and independently Daniel Tausk (private communication) >> have found an irreparable error in my outline. >> In the Kritchman-Raz proof, there is a low complexity >> proof of K(\bar\xi)>\ell if we assume \mu=1, but the >> Chaitin machine may find a shorter proof of high >> complexity, with no control over how high. >> >> My thanks to Tao and Tausk for spotting this. >> I withdraw my claim. >> >> The consistency of P remains an open problem. >> >> Ed Nelson >> _______________________________________________ >> FOM mailing list >> f...@cs.nyu.edu >> http://www.cs.nyu.edu/mailman/listinfo/fom >> >> >> >> -- >> ----------------------------------------------- >> Prof. Dr. Walter Carnielli >> Director >> Centre for Logic, Epistemology and the History of Science – CLE >> State University of Campinas –UNICAMP >> 13083-859 Campinas -SP, Brazil >> Phone: (+55) (19) 3521-6517 >> Fax: (+55) (19) 3289-3269 >> Institutional e-mail: walter.carnie...@cle.unicamp.br >> Website: http://www.cle.unicamp.br/prof/carnielli >> _______________________________________________ >> Logica-l mailing list >> Logica-l@dimap.ufrn.br >> http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l >> > _______________________________________________ > Logica-l mailing list > Logica-l@dimap.ufrn.br > http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l > -- Valeria de Paiva http://www.cs.bham.ac.uk/~vdp/ http://valeriadepaiva.org/www/ _______________________________________________ Logica-l mailing list Logica-l@dimap.ufrn.br http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l
