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 <javascript:>> > 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.
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