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Re: Matheology § 203
Posted:
Jan 29, 2013 4:53 AM
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On Jan 29, 10:36 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 29 Jan., 10:18, William Hughes <wpihug...@gmail.com> wrote:
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> > On Jan 29, 10:09 am, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > On 29 Jan., 09:54, William Hughes <wpihug...@gmail.com> wrote:
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> > > > On Jan 29, 9:33 am, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > "All" and "every" in impredicative statements about infinite sets.
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> > > > > Consider the following statements:
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> > > > > A) For every natural number n, P(n) is true.
> > > > > B) There does not exist a natural number n such that P(n) is false.
> > > > > C) For all natural numbers P is true.
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> > > > > A implies B but A does not imply C.
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> > > > Which is the point. Even though A
> > > > does not imply C we still have
> > > > A implies B.
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> > > > Let L be a list
> > > > d the antidiagonal of L
> > > > P(n), d does not equal the nth line of L
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> > > > We have (A)
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> > > > For every natural number n, P(n) is true.
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> > > > This implies (B)
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> > > > There does not exist a natural number n
> > > > such that P(n) is false.
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> > > > In other words, there is no line of L that
> > > > is equal to d.
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> > > And how can C be correct nevertheless? Because "For all" is
> > > contradictory.
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> > B: There is no line of L that is equal to d
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> > does not imply
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> > C: For all n, line n is not equal to d.
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> > B correct does not mean "C correct nevertheless"-
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> But we know of cases where C is correct nevertheless.
B correct does not mean "C is incorrect"
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