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/ > > > 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 [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.
