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?
Brent
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