Re: Goldbach Conjecture & the Foundation of First Order Logic.
- From: Barb Knox <see@xxxxxxxxx>
- Date: Tue, 26 Sep 2006 16:53:42 +1200
In article <t81Sg.40226$R63.29472@pd7urf1no>,
Nam Nguyen <namducnguyen@xxxxxxx> wrote:
However *counterintuitive* to our knowledge of FOL reasoning,
I think that:
1) If GC is *genuinely* true, it will be impossible to (informally and
arithmetically) know that. Equivalently, it will be impossible
to know a proof of GC in "PA".
Why do you think that? The converse of it is certainly true, but that
doesn't help any.
2) If GC is *genuinely* false, it's still possible that it's impossible
to prove that in PA.
No. Iff it is false, there is at least one particular n such that ~GC
for such n. Simple calculation (in PA) can verify it. The hard part of
course is finding such an n.
Again, I know that doesn't sound right. But it just doesn't _sound_.
so.
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