On Thursday, November 8, 2018 at 3:10:15 AM UTC-6, Bruno Marchal wrote: > > > On 5 Nov 2018, at 18:05, Philip Thrift <cloud...@gmail.com <javascript:>> > wrote: > > > > On Friday, November 2, 2018 at 3:47:58 AM UTC-5, Bruno Marchal wrote: >> >> >> On 1 Nov 2018, at 19:59, Philip Thrift <cloud...@gmail.com> wrote: >> >> >> >> On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote: >>> >>> >>> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift <cloud...@gmail.com> wrote: >>> >>> *> infinite time Turing machines are more powerful than ordinary Turing >>>> machines* >>> >>> >>> That is true, it is also true that if dragons existed they would be >>> dangerous and if I had some cream I could have strawberries and cream, if I >>> had some strawberries. >>> >>> *> How "real" you think this is depends on whether you are a Platonist >>>> or a fictionalist.* >>>> >>> >>> No, it depends on if you think logical contradictions can exist, if they >>> can then there is no point in reading any mathematical proof and logic is >>> no longer a useful tool for anything. >>> >>> John K Clark >>> >>> >>>> >> Of course logics are fiction too. (They're just languages after all.) >> >> >> >> There is a logical language, but that is different from a logical theory. >> It is important to distinguish the languages from the theories, and the >> theories from the models/interpretations. >> >> Bruno >> >> >> > > Logics correspond to type-theoretic programming languages. > > > ? > > That would restrict the meaning of logic to the logic obtained by the > Curry-Howard morphism. There is no compelling reason to do that. > > Bruno > > > I don't know. Even Hegel's logic is not immune:
https://ncatlab.org/nlab/show/Hegel%27s+%22Logic%22+as+Modal+Type+Theory *Hegel's "Logic" as Modal Type Theory* Abstract *While analytic philosophy famously rejected the speculative metaphysics of Hegel in favor of the analysis of concepts by means of mathematical logic, in particular predicate logic, recent developments in the foundations of mathematics via homotopy type theory offer a way to re-read Hegel as having useful formal meaning not in predicate logic, but in ‘modal type theory’. The essence of this suggestion has been made by Lawvere in 1991, which however remains largely unnoticed. Here we aim to give a transparent account of this perspective both philosophically as well as category-theoretically. We then further expand on Lawvere’s formalization of Hegel’s “Science of Logic” in terms of the categorical semantics given by cohesive higher toposes. We discuss how there is a useful formalization of a fair bit of modern fundamental physics, in fact of local gauge quantum field theory, to be found here.* - pt -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
