On Mon, May 14, 2018 at 7:01 PM, Russell Standish <[email protected]> wrote:
> > * > How do you establish that the proof has no error? Why are we > supposing that the ZFC axiom correctly describes the mathematical system? > How do you establish that the computers haven't made an error?* It seems to me you're trying very hard to understand my question. In arithmetic if ZFC or any set of axioms says that a number with certain mathematical traits can not exist but a computer finds a number with exactly those mathematical traits then both of them can't be correct, and in that situation I simply don't believe you'd take the part of the axioms because you are not insane. > > It really underscores Chaitin's point that at some level of > complexity, mathematics becomes an empirical subject, perhaps not all > that different from physics. > Yes mathematics can be empirical, and that means regardless of how beautiful your axioms are if the experimental evidence conflicts with them then those axioms then they have to be junked because experimental evidence outranks everything. The mathematical counterpart to a test tube is a computer and the fundamental operating system of any computer is the laws of physics. So physics can exercise veto power even in pure mathematics. 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]. 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.
