On Wed, 27 May 2009 01:04:52 -0700 (PDT), WM <firstname.lastname@example.org> wrote:
>On 26 Mai, 21:49, Virgil <virg...@nowhere.com> wrote: > >> > If we define: >> >> > 1 is a natural number >> > and >> > with n also n+1 is a natural number >> > and >> > N is the smallest set that satisfies both conditions >> >> > then N is uniquely specified. >> > Of course there can be different models for N and there can be >> > different names for the elements of N. But that does not matter. The >> > natural numbers do not enter mathematics because someone "defines" >> > them, names them, or makes models of them, but because the natural >> > numbers are simply existing and mathematics is built upon them. > >> But according to WM, no such thing as N can exist. >> So WM wold throw out the naturals on which so much is built. > >The question is not whether the complete set of all naturals exists. >That question alrady is nearly as ridiculous as any affirmative >answer. > >The question is whether we could inform someone who does not yet know, >what we understand by the sequence of natural numbers.
Sorry, I can't follow any of this, because I don't already know what you mean by the words "question", "is", "whether", "we". "could", "inform", "someone", "who", "does", "not", "yet", and "understand".
>In order to answer this question, we need not wait until SETI gets >contact. We can answer it in every first class of every elementary >school. Of course we can inform any child with average intelligence >what we understand by this sequence 1, 2, 3, ... > >Only logicians seem to see problems where no problems are. (As some >kind of compensation they see no problems where problems are.) > >Of course this sequence 1, 2, 3, ... is uniquely defined, because it >is possible to inform any intelligent being about it. There is no the >slightest difference between the idea of N and the idea of a sonata or >pi. > >Regards, WM > >On 26 Mai, 23:09, Virgil <virg...@nowhere.com> wrote: >> In article >> <b54a16b3-914d-47eb-bd89-967cc10d2...@u10g2000vbd.googlegroups.com>, >> >> >> >> >> >> WM <mueck...@rz.fh-augsburg.de> wrote: >> > On 25 Mai, 17:40, WM <mueck...@rz.fh-augsburg.de> wrote: >> > > ... classical logic was abstracted from the mathematics of finite sets >> > > and their subsets .... Forgetful of this limited origin, one >> > > afterwards mistook that logic for something above and prior to all >> > > mathematics, and finally applied it, without justification, to the >> > > mathematics of infinite sets. [H. Weyl]. >> >> > > One example is this. For infinite sets with a linear ordering ³=<² the >> > > implication >> > > En Am: m =< n ==> Am En m =< n (1) >> > > is held correct, but not the equivalence >> > > En Am: m =< n <==> Am En m =< n (2) >> > > For any finite set with linear ordering however, (2) is true. The >> > > reason is that all elements of a finite set are subject to >> > > investigation. Therefore, if in ³completed², i.e., ³actual² infinity, >> > > as used in set theory, all elements are available, then also (2) >> > > should be used. (2) can only be false, if potentially infinite sets >> > > are considered, i.e., non-static sets which are never complete but >> > > allow that elements can be added. >> >> But non-static sets do not exist in any mathematical set theory. > >They do not exist in what is commonly called ste theory and what is >eternally false mathematics. > >Regards, WM
David C. Ullrich
"Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to." (John Jones, "My talk about Godel to the post-grads." in sci.logic.)