On Sat, Dec 15, 2018 at 1:09 AM Brent Meeker <[email protected]> wrote:
> > > On 12/14/2018 7:31 PM, Jason Resch wrote: > > On Fri, Dec 14, 2018 at 8:43 PM Brent Meeker <[email protected]> wrote: > >> Yes, you create a whole theology around not all truths are provable. But >> you ignore that what is false is also provable. Provable is only relative >> to axioms. >> >> > 1. Do you agree a Turing machine will either halt or not? > > 2. Do you agree that no finite set of axioms has the power to prove > whether or not any given Turing machine will halt or not? > > > 3. What does this tell us about the relationship between truth, proofs, > and axioms? > > > What do you think it tells us. Does it tell us that a false axiom will > not allow proof of a false proposition? > It tells us mathematical truth is objective and doesn't come from axioms. Axioms are like physical theories, we can test them and refute them if they lead to predictions that are demonstrably false. E.g., if they predict a Turing machine will not halt, but it does, then we can reject that axiom as an incorrect theory of mathematical truth. Similarly, we might find axioms that allow us to prove more things than some weaker set of axioms, thereby building a better theory, but we have no mechanical way of doing this. In that way it is like doing science, and requires trial and error, comparing our theories with our observations, etc. Jason -- 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.
