On Thursday, September 27, 2018 at 7:44:04 AM UTC-5, Bruno Marchal wrote: > > > On 26 Sep 2018, at 19:32, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > > I should add that in parallel to mathematical logic and computability > theory and even type theory there is the somewhat more practical subject of > programming language theory (*PLT*). > > Any entry point is OK. > > https://www.google.com/search?q=progamming+language+theory+books > https://en.wikipedia.org/wiki/Programming_language_theory > > > Some concepts from PLT (continuations, reflective monads, ...) can go back > into mathematica logic. > > > > No problem with this. I guess you appreciate topos theory and > intutionistic logic, but as I said to Bruce, machine’s theology, even > without oracle (but even more with oracle) is necessarily non constructive. > I am aware that some people, like the French logicians Jean-Yves Girard, > or Jean-Louis Krivine tried to extend the Curry-Howard isomorphism to > classical logic. If they succeed, PLT might have application in theology, > but a lot of works would have to be done before. > > If you follow the combinators thread, at some point I might talk about > typed combinators and constructive logics, but mainly to point out how much > non constructive theoretical computer needs to be. > > Bruno > > > > The debate of arithmetical realism (arithmeticalism) vs. material realism (materialism) is a continuation of the older immaterialism vs. materialism type debates: It will just evolve.
For materialists, arithmetic is genre of fiction - a useful one. Why does math describe what matter does? *Because matter has a programmatic nature*. But matter includes both informationality and experientiality, the latter seemingly missing from arithmetic. >From "The Universal Numbers. From Biology to Physics" there could be an approach for how experientiality could come from arithmetic. It could be interesting for PLT research (where modal logics are also used). - 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
