On 9 June 2015 at 14:00, meekerdb <meeke...@verizon.net> wrote: > On 6/8/2015 4:16 PM, LizR wrote: > > On 9 June 2015 at 05:31, meekerdb <meeke...@verizon.net> wrote: > >> On 6/8/2015 1:03 AM, Bruno Marchal wrote: >> >> or that maths exists independently of mathematicians. >> >> That even just arithmetical truth is independent of mathematician. This >> is important because everyone agree with any axiomatic of the numbers, but >> that is not the case for analysis, real numbers, etc. >> >> Everyone agrees on ZFC in the same sense. So does that make set theory >> and its consequences real? >> >> Reality isn't defined by what everyone agrees on. > > > Tell it to Bruno, I was just following him. >
If it was then the religious majority throughout history would have been right. > What makes ZFC (or whatever) real, or not, is whether it kicks back. > > Mathematics doesn't kick back - except metaphorically. > Are you claiming an alien in another galaxy wouldn't find that arithmetic works? I'm not making any metaphysical claims about the status of maths, merely saying that most mathematicians would, I think, agree that two people working independently can make the same mathematical discovery by different routes, and that some maths has real-world applications, and that when it does, it works. (But I'm not sure how much kicking back you need from something, maybe being independently discoverable and working isn't enough?) > Is it something that was invented, and could equally well have been > invented differently, or was it discovered as a result of following a chain > of logical reasoning from certain axioms? > > I'd say ZFC and arithmetic were both invented and then an axiomatization > was invented for each of them. I'm not sure what "invented differently" > means?...getting to the same axiomatization by a different historical > path? Or inventing something similar, but not identical, as ZF is > different from ZFC. > > It means that two people starting from the same axioms and using the same system of logic came up with two different results (and neither made a mistake). If within a given system A always leads to B, then it's reasonable to say B is discovered - like, for example, a certain endgame in chess leading to a particular set of possible conclusions. But if within a system A can lead to B, C, D etc then it's reasonable to say it's invented, like a competition to finish (within the grammatical system of English) a poem that begins "And now the end is near..." -- 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.
