On 28 Mai, 20:39, Virgil <virg...@nowhere.com> wrote: > but the laws of logic are derived from thoughts of an ideal > world and such thoughts are not obtained solely reality, but from > largely from an unreal vision of the ideal.
The result is in due shape. > > There > > > is no model of a complete linear set in reality that makes [*] false > > and [**] true. But there are many models showing that [*] is true > > whenever [**] is true. > > And many models for which "ExAy P(x,y) ==> AyEx P(x,y)" is false.
Not linear models. And no others!
> > Then WM better confine his attentions to areas in which no limiting > processes are wanted and no infinite sets are wanted, which excludes him > from all calculus.
Either Cantor?s diagonal proof shows that the limit of all omega indices can be reached by defining b_n =/= a_n for every n. Then my binary tree proof shows that the limit of all omega levels can be reached by showing that the number of distinct lines is countable at every level n. Then all reals are countable. (Only a very confused mind could consider the possibility that paths of the infinite tree and decimal expansions of real numbers might represent different mathematical objects).
Or the limit of the paths in the binary tree does not yield all real numbers. Then Cantors diagonal proof does not establish complete real number either, and the proof is void.
> > > > > This had already been recognized by the late Alexander Zenkin, one of > > the brave scientists who dared to condemn this hypocritical behaviour > > Scientists may mess with physics to their hearts content, but as > scientists, have no business messing with pure mathematics.
Mathematics is science done by scientists. Matheology is what you may have in mind. And in fact : That has as much to do with science as has astrology to with astronomy.
> > So if anyone introduced any "false logic", it would be physicists rather > than mathematicians.
I should refrain from calling what you and your ilk do : matheology. It could be understood by lurkers as if your hobby was based upon logic.
