> On 28 Feb 2020, at 19:32, Philip Thrift <[email protected]> wrote: > > > > On Friday, February 28, 2020 at 7:56:23 AM UTC-6, Bruno Marchal wrote: > >> On 28 Feb 2020, at 13:05, Philip Thrift <[email protected] <javascript:>> >> wrote: >> >> >> >> On Friday, February 28, 2020 at 2:01:22 AM UTC-6, Bruno Marchal wrote: >> >>> On 27 Feb 2020, at 13:17, Philip Thrift <[email protected] <>> wrote: >>> >>> >>> >>> On Wednesday, February 26, 2020 at 6:54:36 PM UTC-6, Alan Grayson wrote: >>> >>> >>> On Wednesday, February 26, 2020 at 1:36:49 PM UTC-7, Brent 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. >>> >>> Brent >>> >>> Are the integers, and by extension arithmetic, fictitious? AG >>> >>> >>> Arithmetic (or algebra, or geometry) is a language (or collection/family of >>> languages to be picky) - expressed formally as a list of axioms and >>> theorems produced from that list of axioms - so as a language it is itself >>> not fiction, just as when you walk into the fiction section of a library, >>> you see books written in English, and English as a language is itself not >>> fictitious. >>> >>> But numbers - the entities or subjects of arithmetic - are fictitious. >> >> >> That seems to me to be a confusion between language and theories, and their >> semantics. You did not comment on my superhero triangle, which illustrates >> that the arithmetical reality is not fiction. >> >> You *can* call that fiction, but then the point will be that the physical >> reality emerges from that fiction, and the word “fiction” will lose its >> common meaning, and mislead people. The point is that for all I and j, >> phi_i(j) converges or does not converges. If it was fiction, we could decide >> which is the case, but then elementary arithmetic becomes inconsistent. >> >> Bruno >> >> >> >> >> Semantics is very much the thing (the elephant in the room) of >> languages/theory - certainly from the perspective of programming language >> theory. >> >> Real computing is computing voided of Platonism. >> >> >> >> >> https://codicalist.wordpress.com/2018/09/30/real-computationalism/ >> <https://codicalist.wordpress.com/2018/09/30/real-computationalism/> >> >> >> Take arithmetic (encoded in the Peano axioms): >> >> Peano axioms of natural numbers in Agda >> https://gist.github.com/IKEGAMIDaisuke/1211203 >> <https://gist.github.com/IKEGAMIDaisuke/1211203> >> >> >> What is its ultimate semantics? > > The standard model of arithmetic, which refers to what we have learned in > school. > > > > So much for the mathematical educational system. It has become an orthodox, > fundamentalist divinity school.
Have you heard of parents taking their kids out of school after they taught that 2 + 2 = 4? I am not sure what you are saying here, nor below. If you can elaborate? Bruno > > > Nobody can define this, but everybody has a good idea of what it is. Then, > with Mechanism and Traski theorem, we understand why we cannot define it. > > > > > >> As one sees theorems being proven and produced on the computer screen, it is >> the result of movement of elections in computer circuits and pixels. > > But this concerns the proof. It is not a semantic. If it is proved in a > complete theory, like RA or PA or any first order arithmetic, the semantical > part will means “true in all models of the the theory”. That implies “trie in > the standard model”, but the reciprocal is not true. In fact the standard > model (semantic) eludes all effective theories of arithmetic. > > > What is taught in schools though: > > Operational semantics is a category of formal programming language > <https://en.wikipedia.org/wiki/Semantics_(computer_science)>semantics > <https://en.wikipedia.org/wiki/Semantics_(computer_science)> in which certain > desired properties of a program, such as correctness, safety or security, are > verified <https://en.wikipedia.org/wiki/Formal_verification> by constructing > proofs from logical statements about its execution and procedures, rather > than by attaching mathematical meanings to its terms (denotational semantics > <https://en.wikipedia.org/wiki/Denotational_semantics>). > > > (Wikipedia) > > > >> >> What is its semantics in the human brain of the person watching the computer >> screen of the Agda program "doing its thing" with the Peano axioms and >> proving theorems? >> >> One could leave that answer to neuroscientists about what the human brain >> does with looking at proof of arithmetic on a computer screen (or in a >> printed book for that matter). > > Not sure if the neuroscientist will help here. > > >> >> Only Platonists jump to a belief that there is a ghostly world of abstract >> entities called "numbers" that exists outside of matter (whether that matter >> is your brain or your computer). > > We don’t need this either. We need only to believe that 2+3 = 5, or that > phi_i(j) converges or not converges. The philosophy and metaphysics come > after. > If not, it is like studying the working of my brain to convince myself that I > understand correctly that 2+2=4. That does not work, because my brain study > is based on my belief that 2+2=4. > You could aswel say that Einstein’s theory is circular, because you want to > explain 2+2=4 with Matter, but Einstein’s theory use the numbers, and assumes > they do what they need to give sense to, say, E= mc^2. > > At some point, people have to put *all* the hypothesis on the table, so that > it is clear what is assumed, and what is derived. > > Bruno > > > > That "2_2=4" works in Einstein's theory - and it its numerical relativity > implementations - is a matter of mathematical pulp fictionalism. > > https://codicalist.wordpress.com/2018/08/26/mathematical-pulp-fictionalism/ > <https://codicalist.wordpress.com/2018/08/26/mathematical-pulp-fictionalism/> > > @philipthrift > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/6b49ae77-2429-496d-a464-67588eb77445%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/6b49ae77-2429-496d-a464-67588eb77445%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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/7FC19C1A-3DFB-4F26-843C-8FE29D9DEE36%40ulb.ac.be.
