> On 10 May 2018, at 19:11, John Clark <[email protected]> wrote: > > On Thu, May 10, 2018 at 10:36 AM, Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > >> if you can not then the word "model" has no meaning. Unlike the > Continuum Hypothesis the Goldbach Conjecture is subject to the potential of > experimental falsification, if logicians eventually proved that it is true, > > > We don’t prove that something is true. We just prove it. That plays some > role. No sound machine can ever prove that whatever she proves is true. > > 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. > >
A. (Guessing that you mean axiom of number theory, not set theory, as you said above) > 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 all computers do get the same error, that would only provide more weight on A > 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. > How so? In A, no physical assumption is used. Only the axioms of Number Theory. If a computer get a different conclusion, I will believe that there is some bug in its relative (to me) implementation. If all computer gives that different conclusion, I will suspect an error in my proof. I guess you know that the universal dovetetailer emulate also the programs with bugs. I guess you know that Gödel’s second incompleteness theorem shows that if a machine or a theory is consistent, then the statement that the machine or the theory is inconsistent *is* consistent with the axiom of the theory: ~[]f -> <>[]f. (Not-provable(false) implies the consistency of (false is provable) Bruno > If you choose B then madness awaits because your brain also operates > according to those very same laws. > > > > 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.
