On 9 June 2015 at 14:00, meekerdb <[email protected]> wrote: > On 6/8/2015 4:16 PM, LizR wrote: > > On 9 June 2015 at 05:31, meekerdb <[email protected]> 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 [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/d/optout.
