On 9 June 2015 at 11:26, Bruce Kellett <[email protected]> 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 [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.
