> On 23 Oct 2018, at 19:40, Philip Thrift <cloudver...@gmail.com> wrote: > > > > On Tuesday, October 23, 2018 at 11:23:22 AM UTC-5, Bruno Marchal wrote: > > > On 23 Oct 2018, at 04:30, Brent Meeker <meek...@verizon.net <javascript:>> > > wrote: > > > > > > > > On 10/22/2018 6:54 AM, Bruno Marchal wrote: > >> The mathematical reality has noting to do with languages, except that > >> languages are needed if machine/people want to share the results of their > >> exploration. > > > > So how do you prove theorems without a language? > > Of course, proving a theorem requires a theory, and a language. I was saying > (see the quote) that the *arithmetical reality* does not require a language. > > The arithmetical reality does not require a language more than dinosaurs > needed the word “dinosaur” to exist. The prime character of 17 does not need > a mathematician to assert it, or to think about. > > To prove a theorem requires a theory, which requires a language. We can only > ope that our theory is in relation with truth, but the truth of 17 is prime, > assuming it true, does not need a proof to be true. A proof is neither > necessary, nor sufficient. The arithmetical reality is independent of the > big-bang. It is more plausible than an event like the big-bang requires some > part of the arithmetical reality. > > Bruno > > > > People have debated (written books on) arithmetical or mathematical realism > vs. fictionalism (and everything in between) until the cows come home (count > them!), but here is something I found recently: > > https://twitter.com/philipthrift/status/1053537641420021761 > > It's about the Sumerian goddess Nisaba who turned out to be the goddess of > both writing and counting/arithmetic. > > (There was no mathematics before writing.)
I think remembering that neurophysiologist have found very separate region in the brain for words treatment and numbers treatment. Some people can become aphasic and still compute easily, and vice versa. Don’t hesitate to verify this. But words can be Turing universal, like with Post Production systems, or with any programming languages at some level. Words, numbers, combinators, game-of-life pattern , all you need is to fix one Turing universal system, and then we use it to make N into a combinatory algebra, but that is just steps toward addressing the" border of the universal mind introspecting itself", needed to formulate the mind-body problem, in particular the measure problem, in arithmetic. The “problem” is that if we can ascribe a mind to a 3p describable thing, the 1p cannot do that, and is determined by an infinity of computations (sigma_1 sentences). That leads to a first person, and a first person plural, indeterminacy, from which physics is a part. The solution exists at the propositional level, where we get an entire" theology”. I have mentioned the reference. It includes the logic of the observable, so we can compare, and up to now, it fits, thanks to Quantum logic. You cited very good papers, but most of what I say need only Boolos 1979. The Russian and Georgian have solved most complex unsolved conjectures from Boolos 1979. See Boolos 1993. But the simpler Forever Undecided is a nice introduction to the logic G. Artemov+Becklemishev paper is quite interesting, a bit advanced. Now, when you say that there was no mathematics before writing, I am not sure. I think the incas have developed ways to compute (notably the position of the star in the sky) before writing. I think that arithmetic precede thought which precedes languages, and I can identify machines, words, numbers, finitely-describale-thing, as opposed to the meaning which are usually infinite, but will belong to the machines/numbers mind. There was no physics before writing, also; but there was a physical reality and a mathematical reality before human writing, and before humans, although this is metaphorical, as the arithmetical reality is out of time and space. It is a category error to ask if 2+2=4 is true now or yesterday. Bruno > > - 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 > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.
