On Fri, May 11, 2018 at 12:18 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
> >> If you started with the basic axioms of number theory and proved the >> Goldbach Conjecture is true, and you were convinced you had not made an >> error in the proof, and then the next day a computer found a huge even >> number that was NOT the sum of 2 primes, would you: > > A) Conclude that there must be something wrong with the basic axioms of >> set theory. >> >> Or >> >> B) Conclude that computers can’t be trusted because for some unknown >> reason all computers always make an error when making that particular >> calculation. >> If its A then you are tacitly giving the laws of physics the right to >> determine truth from falsehood because those laws determine how the machine >> operates. If you choose B then madness awaits because your brain also >> operates according to those very same laws. > > *How so? * I'm surprised I have to spell this out. > *> In A, no physical assumption is used. Only the axioms of Number > Theory.* A computer needs to know nothing about number theory and it assumes nothing. Computers are made of matter that obeys the laws of physics, 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. 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 althoughphysics can be weird it has no self contradictions, but man made axioms can. > > > *I guess you know that Gödel’s second incompleteness theorem shows that if > a machine or a theory is consistent,* > A real machine will NEVER operate contrary to the laws of physics, but a set of axioms will ALWAYS be inconsistent or incomplete or both. It could be that the the current axioms of number theory are not strong enough to prove or disprove Goldbach, so if the laws of physics ever tell us, by way of a computer, that there is a even number that is not the sum of 2 primes then it would be wise to add the negation of Goldbach as a new axiom because physics is the ultimate arbiter about what is true and what is not . 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
