> On 13 Nov 2018, at 15:38, John Clark <[email protected]> wrote: > > On Mon, Nov 12, 2018 at 9:35 PM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > >> You've got it backwards, physics can simulate a Turing Machine but a > >> Turing Machine can't simulate anything or do anything at all without the > >> help of matter that obeys the laws of physics. > > > That is plainly false. If u is a universal machine/number, phi_u(x, y) > > emulate the number/machine x on the input y. > > So you say, but I see precisely ZERO evidence that "phi_u(x, y)" can emulate > a machine or emulate anything a or in fact do anything at all because > "phi_u(x, y)" never changes, not in time and not in space. You wrote > "phi_u(x, y)" in the above about 11 hours ago thousands of miles from me, > but here I am looking at "phi_u(x, y)" and "phi_u(x, y)" is still just > "phi_u(x, y)” .
Your confusion here is equivalent with confusing a far away galaxy with the telescope, or confusing a physical universe with a book on the physical universe. The emulation is in the meaning of “phi_u(x,y)”, not in the string of symbols referring to that meaning. > > >>A mathematical model is a description of something written in the language > >>of mathematics, like most descriptions it is not complete, > > > You are using “model” in the sense of the physicist, and logicians call > > that a theory, which can be seen indeed as a (incomplete) theory. But a > > model, in the logician sense is complete [...] > > Then logicians are talking about something that is self contradictory because > nothing mathematical or logical can be both complete and consistent. No mathematical and effective (sigma_1, checkable) theory can be complete. A model is complete by definition: it is what we intend to talk about. > > > [...] by definition. > > You have a tendency to use those 2 words as if they were the final mark of > authority, but the words "by definition" does not cause things to suddenly > spring into existence, that utterance is no more magical than "abracadabra". > Hogwarts Castle is a school for wizards BY DEFINITION, there is absolutely no > doubt about it, but do you think it would be worth your time to go looking > for it? But some existence can follow from definition, even, imprecise one. To prove that a computable function exist, just one example is enough, using a simple example. To prove that something is NOT computable, needs a precise mathematical definition. That is why we need Church, Turing, … Then, if you are OK that 2+2=4 and similar are true independently of you and me, computations and their many realisation all exists, in a provable way, in the arithmetical reality/model. > > > It is usually infinite, > > Yet another reason to suspect it does not exist. Indeed. Infinity exist only in the phenomenology. Just look ate the TOE I gave. None assumes infinity. I assume 0, s(0), s(s(0)), … only. > > > A model is a model of a theory. > > So I guess a model of a theory is a model of a model of a theory, and a model > of a model of a theory is a model of a model of a model of a theory, and a > model of…. You might decide one day to study a bit of mathematical logic. The notion of model applies to a theory, only, or to a machine, in a related sense. (In infinitary logic, where we allow alphabet with arbitrary cardinality, some models can be see as theory, but that has no uses in our context. Bruno > > John K Clark > > > > > -- > 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 post to this group, send email to [email protected] > <mailto:[email protected]>. > 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
