In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 8 Feb., 23:05, Virgil <vir...@ligriv.com> wrote: > > In article > > <43d2d64e-7641-4f96-bbe6-59fe20991...@e11g2000vbv.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 8 Feb., 12:13, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote: > > > > WM <mueck...@rz.fh-augsburg.de> writes: > > > > > On 7 Feb., 20:17, William Hughes <wpihug...@gmail.com> wrote: > > > > ... > > > > >> In classical set theory the accessible numbers are listable > > > > > > >> Note from the Wikipedia quote > > > > > > >> > Constructively it is consistent to assert the > > > > >> > subcountability of some uncountable collections > > > > > > > Of course, the intuitionists accepted this nonsense, perhaps forced by > > > > > the matheologians. > > > > > > What a joker! > > > > > > You tell us that you do not know Brouwer's opinion on this question, > > > > but here you are telling us what intuitionists accept. > > > > > I know Brouwer's opinion very well But I do not discuss with you about > > > that opinionb because you turn every word in my mouth. > > > > That words seem to turn in WM's mouth does not man that anyone other > > than WM himself is responsible for such turnings. > > > > > > WM is inconsistent. > > > > > > As for intuitionists being "forced" into taking up a > > > > position inconsistent with classical mathematics by classical > > > > mathematicians ... > > > > a classic absurdity. > > > > > No. Hilbert fired Brouwer from his most prestigious position with the > > > Annalen. > > > > How would that force Brouwer into taking up a position INCONSISTENT with > > classical mathematics? > > Vice versa. Brouwer had a position inconsistent with Hilbert's > mathematics. Therefore he was fired.
Once he was fired, what further force could Hilbert, or anyone else, exert on him, to make him change his mind? > > > > > Could an intelligent man or woman who observes that all levels of the > > > Binary Tree are crossed by a finite number of distinct paths really > > > believe that there are uncountably many, where uncountable means much > > > more than infinitely many? > > > > While each "level" individually may be only finitely crossed, it is > > wrong, or at least deliberately misleading, to say that all of > > infinitely many of them are collectively only "finitely crossed". > > It is simple to prove it in mathematics. Every term of the sequence > 2^n is finite. And there is no infinite level.
Every f 2^n is exceeded by most others so there cannot be a last member, which requires more than any finite number of finite levels.
What term or terms does WM want to use for "more than any finite number finite levels"? > > > > And uncountable does not mean more that infinitely many, but only more > > that countably many. Infinite includes both countable and uncountable. > > That is purest nonsense .
It beats hell out of WM's grossly impure and mathematically incoherent nonsense. --