> On 29 Feb 2020, at 03:04, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 2/28/2020 12:04 AM, Bruno Marchal wrote: >>> On 27 Feb 2020, at 18:28, 'Brent Meeker' via Everything List >>> <[email protected]> wrote: >>> >>> >>> >>> On 2/27/2020 4:11 AM, Bruno Marchal wrote: >>>>> On 26 Feb 2020, at 21:36, 'Brent Meeker' via Everything List >>>>> <[email protected]> wrote: >>>>> >>>>> >>>>> >>>>> On 2/26/2020 2:48 AM, Bruno Marchal wrote: >>>>>>> Being sure of that sentence is true, "Dr Watson was a friend of >>>>>>> Sherlock Holmes." doesn't mean the things named in the sentence exist. >>>>>> It certainly means that Watson and Homes exist, in some sense. The >>>>>> question is “is that sense interesting with respect to our goal of >>>>>> explaining "everything” (matter and consciousness) in a coherent way? >>>>> They exist in exactly the same way arithmetic and Turing machines exist. >>>> Really? >>>> >>>> The difference is that arithmetic is used by all physicists, >>>> mathematicians, economists, and that if you are mistaken about their >>>> relations, your rocket might blow up, or miss the moon. >>>> >>>> But if you are wrong about Watson or Holmes, you might just get a bad note >>>> at your English literature course. >>> None of those people use all of arithmetic. >> They use a part of it, which suppose it consistent, and that is global. >> Nobody use “all” of arithmetic, it is a highly non computable set, and >> nobody can use that (as opposed of making theories which put some light on >> it). >> > But they don't use the part of it you need to derive Goedel's theorem and > Loeb's theorem etc.
? I think they use it. You have already incompleteness in Robison Arithmetic, and Löb’s theorem needs the induction axioms, which are used all the time, like when believing that x + y = y + x for all natural numbers. That was the point of Gödel: his incompleteness theorem is provable by the theories he was concerned about. Incompleteness arrives very quickly, indeed, in very elementary arithmetic (“very” = no induction axioms, and “elementary” = axiomatisable in first order logic). Bruno > > Brent > > -- > 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 view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/a49c0c00-cc27-c757-5b06-f8b7e639d085%40verizon.net. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/89671112-5428-499B-AB92-A9F14DE9CE54%40ulb.ac.be.
