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Science Forum Index » Logic Forum » Intuitionistically valid?...
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| Jan Burse... |
 Posted: Thu Jun 05, 2008 7:24 pm |
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| MoeBlee... |
| Posted: Thu Jun 05, 2008 7:24 pm |
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On Jun 5, 5:24 pm, Jan Burse <janbu... at (no spam) fastmail.fm> wrote:
Quote: ~A, ~A->(B->A) |- ~B
Yes, intuitionistically valid.
1 ~A
2 ~A -> (B -> A)
3 B -> A ... 1, 2 {1 2}
4 B ... supposition
5 A ... 3, 4 {1 2 4}
6 ~B {1 2}
MoeBlee |
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| Balthasar... |
| Posted: Fri Aug 01, 2008 3:03 pm |
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On Fri, 06 Jun 2008 02:24:30 +0200, Jan Burse <janburse at (no spam) fastmail.fm>
wrote:
Quote:
~A, ~A -> (B -> A) |- ~B
Provable in an intuitionistic calculus and (Johansson's) minimal
calculus by one and the same proof:
1 (1) ~A A
2 (2) ~A -> (B -> A) A
1,2 (3) B -> A 1,2 ->E
4 (4) B A
1,2,4 (5) A 3,4 ->E
1,2,4 (6) A & ~A 1,5 &I
1,2 (7) ~B 4,6 ~I
B.
--
"For every line of Cantor's list it is true that this line does not
contain the diagonal number. Nevertheless the diagonal number may
be in the infinite list." (WM, sci.logic) |
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