On Friday, February 28, 2020 at 7:56:23 AM UTC-6, Bruno Marchal wrote: > > > On 28 Feb 2020, at 13:05, Philip Thrift <cloud...@gmail.com <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 <cloud...@gmail.com> 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/ > > > Take arithmetic (encoded in the Peano axioms): > > *Peano axioms of natural numbers in Agda* > 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. > 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/ > > @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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/6b49ae77-2429-496d-a464-67588eb77445%40googlegroups.com.
