On 9 June 2015 at 11:26, Bruce Kellett <bhkell...@optusnet.com.au> wrote:
> LizR wrote: > >> Reality isn't defined by what everyone agrees on. What makes ZFC (or >> whatever) real, or not, is whether it kicks back. 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? >> > > Why do not those same arguments apply equally to arithmetic? What axioms > led to arithmetic? Could one have chosen different axioms? > > The arguments do apply. The point is that once the axioms are chosen, the results that follow are not a matter of choice. Arithmetical truths appear to take the form "if A, then (necessarily) B". However, some of the elementary axioms (or even perhaps axions! :-) do appear to be demonstrated by nature - certain numerical quantities are (apparently) conserved in fundamental particle interactions, quantum fluctuations can only occur in ways that balance energy budgets, etc. So one could say that for anyone of a materialist persuasion, the assumptions of elementary arithmetic aren't unreasonable, at least (Bruno often mentions that comp only assumes some very simple arithmetical axioms - the existence of numbers and the correctness of addition and multiplication, I think) So if you choose Peano arithmetic, then such-and-such follows, while if you choose modular arithmetic, something else follows. The "kicking back" part is simply the fact that the same result always follows from a given set of assumptions. To put it a bit more dramatically, an alien being in a different galaxy, or even in another universe, would still get the same results. Nature is telling us that given A, we always get B. -- 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.
