On 5/4/2013 12:13 PM, WM wrote: > On 4 Mai, 18:30, Dan <dan.ms.ch...@gmail.com> wrote: >>>> Either they're both relevant to Cantor's argument, or they're both >>>> irrelevant . >> >>> Cantor's argument is a single-eyed look into the infinite. >>> Forall n : d_n =/= a_nn is considered important. >>> Forall n : (d_n) is in the list, is not considered important. >> >> Why should it be considered important under the definition of >> equality? If they have at least one different digit , THEY'RE >> DIFFERENT. > > But there always only finitely many with at least one different digit > whereas there are always infinitely many with none different digit. > >> Every finite digit appears in the list at least once , but NEVER DO >> ALL OF THEM APPEAR AT ONCE , IN THE SAME NUMBER. > > Stop shouting. In order to support your "never", you should be able to > prove it. But you are not. You can look at a finite domain only, since > every line n is at a finite place and is followed by infinitely many > more lines. > >> >> THIS IS REQUIRED TO DISPROVE CANTOR : >> exists n , forall m , a_nm = d_m > > Of course, in a list that contains all rationals, this is easily > proved. > A simpler case is the list: > > 0.0 > 0.1 > 0.11 > 0.111 > ... > > with the substitution 0 --> 1. > > For all a_nn at finite places n (and others cannot be substituted at > all) we have all (d_1, ..., d_n) as an entry in the list. > > Your assertion that in your anti-diagonal there are more than all > digits that are already covered by the list is simply nonsense. > > And the proposal of ZeitGeist, that all digits 1 at possible finite > indices are in the list but distributed over several lines and not in > a single line, can be shouted loudly in a mad house, probably even > there raising objections, but not in mathematics.. > > My list is constructed such that all possible squences of digits 1 are > already in the list. No longer sequence is possible (otherwise it > would be in the list) and a shorter sequence cannot support Cantor's > claim. > > Simple as that. > >> And would you stop it with the countable language already? > > A language is man-made. Men cannot make uncountable language. And they > could not convey information by uncountable language. > > So if there was an "uncountable language", it was not a language (by > the way like finished infinity is not unfinished and therefore is no > infinity). > >> I find again ,sadly , that in this one circumstance , what cannot be >> said must be passed down in silence. > > In particular an uncountable language would force you to silence > because it is no language. Similarly: > An "infinitely complicated law" means no law at all. [§ 125] > > If you are interested in some more quotes by Wittgenstein, here you > are: > > It isn't just impossible "for us men" to run through the natural > numbers one by one; it's impossible, it means nothing. [?] you can?t > talk about all numbers, because there's no such thing as all numbers. > [§ 124] > > There's no such thing as "all numbers" simply because there are > infinitely many. [§ 126] > > Generality in mathematics is a direction, an arrow pointing along the > series generated by an operation. And you can even say that the arrow > points to infinity; but does that mean that there is something - > infinity - at which it points, as at a thing? Construed in that way, > it must of course lead to endless nonsense. [§ 142] > > If I were to say "If we were acquainted with an infinite extension, > then it would be all right to talk of an actual infinite", that would > really be like saying, "If there were a sense of abracadabra then it > would be all right to talk about abracadabraic sense perception". [§ > 144] > > Set theory is wrong because it apparently presupposes a symbolism > which doesn't exist instead of one that does exist (is alone > possible). It builds on a fictitious symbolism, therefore on nonsense. > [§ 174] > > [L. Wittgenstein: "Philosophical Remarks"] > > Regards, WM >
With all due respect, at what point did Wittgenstein produce a mathematics that could reconcile Berkeley and Newton?
The answer to that question illustrates the ultimate failure of mere criticism.