> On 13 May 2018, at 21:53, John Clark <[email protected]> wrote: > > > > On Sat, May 12, 2018 at 4:21 AM, Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > > > I use computer for “universal Turing machine”. That notion assumes (and > is Turing-equivalent with (very) elementary arithmetic). > > A Turing Machine knows no theories
I have no clues why you say so. It is just false with the definition I have given of “knowing” (beweisbar and true). > and it operates under the laws of physics That is a confusion between a Turing machine and a physical implementation of a Turing machine. > not because it assume them but because it has no choice in the matter. > > >> Computers are made of matter that obeys the laws of physics, > > Physical computer. > > > A Turing Machine is a physical computer and a Turing Machine is the only type > of computer that there is; even a virtual computer needs a Turing machine > somewhere down the line. Only when we assume Aristotle’s metaphysics. But that begs the question. > > > But I do not assume [...] > > A Turing Machine doesn't give a damn what you do or do not assume, it just > keeps on cranking away according to the laws of laws of physics. The laws of physics he nothing to do with the laws of computability and computation. I suggest you read the original papers of the discoverers of the universal machine (reprinted for example in Martin Davis (ed) “The undecidable” by Dover. > > >>when the voltage on one of the inputs of the microchip is positive > physics orders it will do one thing and when the voltage is negative it will > order it to do something different. By picking A you are in effect saying you > have looked at the pattern of voltages physics told the microchip to have and > you have interpreted that pattern to to be a even number that is not the sum > two prime numbers, and you believe what physics is telling you even if the > axioms of Number Theory says such a number can not exist. > > > I have not assume physics anywhere, > > That's OK, physics doesn't assume you either. But you have said if the ZFC > axioms say one thing and the computer says the opposite then you'd believe > the computer and not the axioms, and that is what any sane man would do > because theories come and go but physics always tells the truth, Why would I believe a computer saying something? They can lie as much as the humans. What I said was only that if a computer find an even number not sum of two primes, I would believe the computer over a proof in ZF. The reason is that the negation of Goldbach conjecture is sigma_1, so if a computer can refute Goldbach, so can ZF. You were assuming implicitly that ZF is inconsistent. > > > so this does not make any sense. > > Then how can you make sense out of ANY post from ANYBODY on this list? How > can you reply to any post when its just a pattern of voltages on the > microchip inside your computer? Not at all. A post are ideas represented through a physical means, which is need n the physical reality. That has nothing to do with the idea that a primary physical reality as to be assumed in computability theory. > > > >>By picking A you are saying physics is more trustworthy than any set of > axioms could be, if there is a contradiction between the two it is the axioms > that need to give way not physical law because although physics can be > weird it has no self contradictions, but man made axioms can. > > > Physical theories can be contradictory. > > If two physical theories try to explain the same phenomena then they are > ALWAYS contradictory, otherwise they'd be the same theory, Of course not. QM, for example, came up with different theories, proved to be equivalent, but they are still different (cf Heisenberg versus Schoredinger, versus Feynmann), unless you identify a theory with all its theorem, in which case I can agree. > but at least one of those theories must be wrong and that's where experiment > comes in. Physics (not to be confused with physical theories) Physics is usually used for “physical theories”. It would help to use “the physical reality” instead of physics, which is the name of the science, not the reality. > is never contradictory and will always tell you the truth, I would even say > its the very definition of truth. The physical reality is not a theory. It does not tell anything. Unless you 1) assume that such a reality 2) identify that reality with the set of all propositions satisfied by that reality. But I prefer to avoid doing such identification, which in metaphysics can only be misleading. Then you identify “physics” with truth, which again is Aristotle main metaphysical assumption, andit has been shown not compatible with computationalism. > > > And physical reality is not an assumption available at the start. > > To hell with assumptions! If I walk across a bridge it won't stay intact if > I make one assumption and collapse if I make another assumption. > The bridge will either collapse or it won't. The bridge doesn't care what I > assume and neither do the laws of physics. Correct, but that applies to many dreams and video games, which are all implemented in virtue of the semi-computable number relations in arithmetic. > > > >> A real machine will NEVER operate contrary to the laws of physics, > > > In which theory. > > What in the world that mean?? In which theory what? In which metaphysical theory would you define what is a *real* machine. I think you keep begging the question. > > > You are using implicit metaphysical assumption. > > A collapsed or intact bridge is not metaphysical nor is it an assumption, > it is matter operating according to the laws of physics. A collapsed or intact bridge is not metaphysical, I agree. But we are not talking about that. We are talking about the metaphysical assumption that a bridge is primary physical. You dismiss the key nuance, illustrating that you assume some materialism or physicalism at the start. But then you have to explain how that primary matter makes “more real” some computations, and "less real” others. But it can be proved that this cannot be done, without violating the computationalist hypothesis. > > >> but a set of axioms will ALWAYS be inconsistent or incomplete or both. > > > If a theory is inconsistent, it is obviously complete. > > Yes, you're right, my error. If I'm working with inconsistent axioms then I > can prove all true mathematical statements therefore its complete, OK. > the only trouble is I can prove all false mathematical statements are true > too. In a lecture on logic Bertrand Russell said a false proposition implies > any proposition. A student challenged him on that and said ”In that case, > given that 1 = 0 prove that you are the Pope.” Without hesitation Russell > said ”Add 1 to both sides of the equation: then we have 2 = 1. The set > containing just me and the Pope has 2 members. But 2 = 1, so it has only 1 > member; therefore, I am the Pope.” > > > If a physical computer (assumed to have no bugs in it) can find an even > number not being the sum of two prime, then that number can be find by very > elementary arithmetic, > > And you already said, quite wisely, that if you had correctly used the ZFC > axioms to produce a proof the Goldbach Conjecture was true but then a > computer found a number that violated Goldbach you would place the blame on > the ZFC axioms and not on the laws of physics the computer operates under. > If a computer find an even number not sum of two primes, and that is verified by many other computers, I would blame ZF, or my derivation of Goldbach in ZF, as this would prove that ZF is inconsistent. If Goldbach if false, that would automatically be provable in all Turing-complete theories. Even by Robinson Arithmetic and all its extension (PA, ZF, …). > So like me you are saying it is physics and not axioms that is the ultimate > judge > > that decides what it true and what is not That is Aristotle theology. I am skeptical, and I ahem shown that it is incompatible with Digital Mechanism (aka indexical computationalism). 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.
