On 23 Feb., 16:54, William Hughes <wpihug...@gmail.com> wrote: > On Feb 23, 1:24 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 23 Feb., 11:51, William Hughes <wpihug...@gmail.com> wrote: > > > > On Feb 23, 11:42 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 23 Feb., 10:59, William Hughes <wpihug...@gmail.com> wrote: > > > > > > On Feb 23, 12:03 am, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > Does > > > > > > > For every natural number n, P(n) > > > > > > is true. > > > > > > > imply > > > > > > > There is no natural number m such > > > > > > that P(m) is false. > > > > > > Does > > > > > > There is a line, l, of L > > > > > such that l has property P > > > > > > imply > > > > > > There exists a natural number > > > > > m such that the mth line of L > > > > > has property P. > > > > > > ? > > > Yes if we interpret "there exists" in the correct way. > > Are the statements > > There exists a natural number > m such that the mth line of L > has property P. > > There does not exist a natural number > m such that the mth line of L > has property P. > > contradictory?
Not if you mean by "to exist" in the first case " we can find" and in the second case "we can prove".
And it appears to me as if you would do so. Otherwise I cannot understand your Nos in our dialogue:
====================== > Can you identify a FIS of d that is not in a line l of L?
No
> You cannot. Nevertheless d consists of FIS of lines of L, and of > nothing else, by definition and by construction of d.
> Or do you object to this fact?
No.
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Why then are you raising the impression as if you were trying to argue that d is not with *all its existence* in the lines of the list?
