On Tue, Jan 21, 2014 at 6:02 PM, meekerdb <[email protected]> wrote:
> On 1/21/2014 3:30 PM, Jason Resch wrote: > > > > > On Tue, Jan 21, 2014 at 3:30 PM, meekerdb <[email protected]> wrote: > >> On 1/21/2014 8:13 AM, Jason Resch wrote: >> >> Why would you want to do that? It seems like an unnecessary extra >> axiom that doesn't have any purpose or utility. >> >> >> It prevents the paradoxes of undeciability, Cantor diagonalization, and >> it corresponds more directly with how we actually use arithmetic. >> >> >> I'm not sure it helps. What you may gain from avoiding paradoxes makes >> many of our accepted proofs false. E.g. Euclids proof of infinite primes. >> Or Euler's identity. Most of math would be ruined. A circle's circumference >> would not even be pi*diameter. >> >> Would this biggest number be different for different beings in >> different universes? What is it contingent on? >> >> >> You're taking an Platonic view that there really is an arithmetic and >> whether there's a biggest number is an empirical question. I'm saying it's >> an invention. We invented an system in which you can always add 1 because >> that was convenient; you don't have to think about whether you can or not. >> > > So to use this same line of reasoning, would you say there is no > definite (a priori) fact of the matter of whether or not a given program > terminates, unless we actually build a machine executing that program and > observe it terminate? > > > That's kind of mixing categories since 'program' (to you) means something > in Platonia and there you don't need a machine to run it. > You're right, it is mixing categories, yet for some reason I still think the question "would this machine halt on its own, if given enough resources to run forever" is a meaningful question, which has a definite answer, even if we don't (or can't) determine it. > In the physical world there is no question, all programs running on a > machine terminate, for one reason or another. Non-terminating programs are > the result of over idealization. > > > > If that is the case, when is it determined (for us) that a certain > program terminates? Is it when the first being anywhere in any universe > tests it, when someone in our universe tests it, when someone in our past > light cone tests it, when you test it yourself or read about someone who > did? Would it ever be possible for two beings in two different universes to > find different results regarding the same program? If not, then what > enforces this agreement? > > >> But if it leads to paradoxes or absurdities we should just modify our >> invention keeping the good part and avoiding the paradoxes if we can. >> Peano's arithmetic will still be there in Platonia and sqrt(2) will be >> irrational there. But the diagonal of a unit square may depend on how we >> measure it or what it's made of. >> > > Does this instrumentalist approach prevents one from having a theory of > reality? > > > Who said it's instrumentalist? Just because it considers a finite model > of reality? > No, it was just your comment "the diagonal of a unit square may depend on how we measure it" that made me think you were implying there is no reality except what we can measure. Jason > When Bruno proposes to base things on arithmetic and leave analysis and > set theory alone, does that make him an instrumentalist? > > 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]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- 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 http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
