On Wed, Apr 29, 2015 at 10:56 AM, John Clark <johnkcl...@gmail.com> wrote:
> On Wed, Apr 29, 2015 Jason Resch <jasonre...@gmail.com> wrote: > > >> Maybe all true statements exist is some sort of abstract Platonic >>> world, but even if they do I'm not sure that would be very important >>> because all false statements would exist in that very same world, >>> >> >> >We're not talking of the existence of statements, but the existence of >> truths. >> > > Truths are not the only thing that exists, falsehoods exist too and there > are many more falsehoods than truths because there are many ways to be > wrong but only one way to be right. And Godel proved that there is no > mathematical procedure that can put all the truths in one set and all the > falsehoods in another. You can find mathematical procedures that allow you > to put some truths in the true set and you can find mathematical procedures > that allow you to put some falsehoods in the false set, but Turing proved > that in general there is no way to know if any given statement has such a > procedure or not, all you can do is keep trying and you might be trying > forever. Even mathematics doesn't know if some statements are true or not, > so if there is a Platonic world that contains only true statements and no > false ones the separation must have been done by something other than > mathematics and therefore mathematics can not be fundamental. > > >> > If program P is a brain emulation of John Clark then you might even say >> that facts about John's thoughts and (perhaps even conscious perceptions) >> are mathematical facts, existing as a consequence of self-existant >> arithmetical truth. >> > > Arithmetical truth remains arithmetical truth even when I'm under > anesthesia, so why doesn't my consciousness exist when I'm under > anesthesia? > Your consciousness always exists in all the places it exists. In past and future points in time, in other branches of the wave function, etc. Just because the you-here-now isn't aware of them in the you-elsewhere doesn't mean the you-elsewhere's consciousness has stopped or is not existing. > > > I agree there is an analogy between discovering and inventing when it >> comes to computations and mathematical truth. Given Godel, I think the only >> consistent view is that mathematical truth (which includes computation) is >> discovered. >> > > It could be that parts of the language of mathematics are discovered and > other parts are invented, just as a scientific paper can be written in the > language of English but so can a Harry Potter novel. I'm not saying that is > the case I'm just saying maybe. > > >> > Physics might be necessary for humans to discover and talk about >> mathematical concepts, >> > > And physics is required to make the concept of "explanation" be > meaningful, and perhaps for "meaningful" to be meaningful too. > > >> > but physics can't make the 9th Mersenne Prime "2305843009213693951" and >> not some other number. >> > > Integers involve counting and the 9th Mersenne Prime is an integer, but if > physics did not exist and there was nothing to count not even ONE thing, > and there was nothing around to do any counting even if there were > something to count, would the very idea of number mean anything? > > > computationalism can explain all possible observations since all >> possible computations exist assuming arithmetical realism. >> > > We're far from having solved all the problems in physics so it's very > premature to say that mathematics can explain, much less create, all of it. > I said it can explain all possible observations, since all possible computations exist in arithmetic, and by computationalism, all possible observations (conscious states) can be produced by the appropriate computation. Jason > Let me make it clear that I'm playing devil's advocate here, maybe > mathematics really is fundamental but what I object to is the dogmatic > assertion that we already know for certain that it is. > > > Since you can say 2 + 2 = 4, and always has > > > Actually 2 + 2 = 5 for extremely large values of 2. :>) > > 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 everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
