Re: Question regarding incompleteness in formal systems without sufficient power for arithmetic.
- From: Scott <ToaTerra@xxxxxxxxx>
- Date: Wed, 2 Apr 2008 17:06:20 -0700 (PDT)
On Apr 2, 12:52 am, Aatu Koskensilta <aatu.koskensi...@xxxxxxxxx>
wrote:
No. All we need is to exhibit a formula P such that neither P nor
not-P is provable in first-order logic. And it's trivial to find such
examples: ExEy(x =/= y), AxEyP(x,y), ...
Just to make sure I understand... Given a formula P, if neither P nor
not-P is provable in FOL, then, if FOL is consistent, it must be
incomplete. Okay.
But what are the examples you provided? Are these examples of formula
P that are neither provable or not provable in FOL? Or are these
examples of formula that might be "true" or "false" depending up the
interpretation?
.
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