> On 15 Dec 2018, at 22:28, Brent Meeker <[email protected]> wrote: > > > > On 12/15/2018 7:43 AM, Jason Resch wrote: >> >> >> On Sat, Dec 15, 2018 at 1:09 AM Brent Meeker <[email protected] >> <mailto:[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] >>> <mailto:[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. > > Fine, except you've had to quailfy it as "mathematical truth", meaning that > it is relative to the axioms defining the Turning machine. Remember a Turing > machine isn't a real device.
Assuming a conventionalist or fictionalist philosophy of mathematics. With mechanism, it is the physical reality PRIMARINESS which is fiction. Bruno > > Brent > > -- > 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.
