On 20 Aug 2011, at 04:24, meekerdb wrote:

On 8/19/2011 6:14 PM, Craig Weinberg wrote:
> Perhaps later. See a bit below. Bp is meant for "the machine believes > p" when written in the language of the machine. If the machine is a
>  theorem prover for arithmetic, Bp is an abbreviation for
> beweisbar('p') with beweisbar the arithmetical provability predicate > of Gödel, and 'p' is for the Gödel number of p (that is a description > of p in the language of the machine). The "#" is for any proposition.

Don't you need some temporality? B means "proves", but you use it an tenseless form also to mean "provable" and then also to mean "believes". But a machine being emulated by the UD doesn't "prove" everything provable at once. It works through them (and takes a great many steps) and so it does "believe" everything that is provable. Does that mean no thread of it's emulation is Loebian until induction has been proved/believed in that thread?

At some level yes. Human "induction rule" (which makes them Löbian) is probably hardwired by our biological history.



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