Conheço fibração em geometria. Como é em lógica? 2011/10/9 Valeria de Paiva <[email protected]>
> 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 <[email protected]>: > > 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 > > <[email protected]>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 <[email protected]> > >> Date: 2011/10/1 > >> Subject: [FOM] inconsistency of P > >> To: [email protected] > >> > >> > >> 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 > >> [email protected] > >> 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: [email protected] > >> Website: http://www.cle.unicamp.br/prof/carnielli > >> _______________________________________________ > >> Logica-l mailing list > >> [email protected] > >> http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l > >> > > _______________________________________________ > > Logica-l mailing list > > [email protected] > > 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 > [email protected] > http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l > -- fad ahhata alati, awienta Wilushati _______________________________________________ Logica-l mailing list [email protected] http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l
