On 3/17/2013 2:28 PM, WM wrote: > On 17 Mrz., 19:49, Virgil <vir...@ligriv.com> wrote: > >>> Zermelo created the axiom of choice because it was obvious to him that >>> is is correct, i.e., that his choice can be done, at least in >>> principle. Then he went on and "proved" from this axiom the well- >>> ordering theorem. If he had known that the axiom of choice can be >>> disproved by proving that at most countably many choiced can be >>> executed, even in principle, why should he have used it? >> >> Standard mathematics does not accept any such claimed disproof as valid! >> >> Acceptance or rejection of the axiom of choice remains optional in > > matheology just like the AMS.
Yes... the AMS
So, when Brouwer was complaining about the use of mutual exclusion, it had been in the context of Hilbert's program before the Goedel incompleteness theorem.
The reason for presenting such examples had been that mutual exclusion was viewed as implying the solvability of every mathematical problem.
At least, this is the account in an introduction I read this evening.
You turn to an outdated strategy directed to a situation that no longer exists rather than do the hard work of grounding your claims. You do this to say that just because you do not believe a particular axiom, that axiom should be compared with nonsense. Yet, there is an established criterion for demonstrating that the axiom you do not believe is, in fact, in error. You say that you do not need to respect this criterion. Nor, do you elucidate an alternate criterion that others might consider. Yet, you say that meaningful discourse requires agreement between parties.
Perhaps you are doing this in a way with which Brouwer would have agreed. It will take more research on my part to determine this. But, your record with regard to these kind of things is rather paltry.