Am Mittwoch, 4. Dezember 2013 15:47:46 UTC+1 schrieb fom: > On 12/4/2013 7:56 AM, WM wrote: > > > Am Mittwoch, 4. Dezember 2013 10:13:59 UTC+1 schrieb Zeit Geist: > > > > > >> Remember, before we write a Proof, we must first formalize the statement. This allows to understand clearly what the Natural Language statement actually means. > > > > > > No. Every formal particle has to be defined in normal language. Every composition of formal particles can be defined in normal language too. The language does not matter at all. But normal language often exhibits nonsensical approaches in formal language like the confusion of all and every. > > >> > > > > > > ... > > > > > >> Now, please tell me whose Methods the Quantifier Confusion resides in? > > > > > > > > > For every n in |N: The FIS d_1, d_2, ..., d_n is in the remaining part of the (rationals-complete) list > > > You agree. > > > > > > d_1, d_2, d_3, ... is in the remaining part of the list. > > > You do not agree. > > > > > > That means that d has the power to deviate from all entries of the list that none of the strings d_1, d_2, ..., d_n has. You see? > > > > > > So you have "proved" that d contains more than all d_n, (which is the same as to contain more than all strings d_1, ..., d_n). You don't call the difference d_oo, but you "proved" that it exists. > > > > > > > > > The quantifier confusion is this: > > > "For every natural index there is a larger one" > > > has been inverted to > > > "there is an index oo larger than every natural". > > > > > > > But, there is no quantifier confusion here. > > > > For every index, there is a larger index.
That is true in the list of all FIS too d_1 d_1, d_2 d_1, d_2, d_3 ... > All these FIS however, are not capable of distinguishing themselves from all rationals. That requires more: A good portion of faith. And a completed infinity for that np larger index is possible. Obviously the largest index has been applied. An index which is not present in any rational number. > > > Your statement speaks to what may be put under > > the scope of quantification. Cantor seems to have > > recognized fairly early that no transfinite notion > > could correspond with absolute infinity. It may > > have been his involvement with religious scholarship > > that helped him to avoid Russell's paradox directly.
He did not avoid it. He knew fairly early, in the 1890s, that the set of all sets is impossible. Unfortunately he did not recognize that the set of all natural numbers that are followed by infinitely many natural numbers is impossible too. (I.e., the set of all numbers that is not all numbers.)
The usual reply of matheologians, on the question how they know that they have all numbers without having the last one, is: There is no last natural number. But I im interested to see their escape with respect to the fact that no digit d_i ad no FIS is sufficient to accomplish a distinction of d from all rationals of the rationals-complete list. Obviously d contains somewhat more than every digit d_i.