On 23 Oct 2013, at 23:42, meekerdb wrote:

On 10/23/2013 5:53 AM, Bruno Marchal wrote:On 22 Oct 2013, at 19:01, meekerdb wrote:On 10/22/2013 5:48 AM, Bruno Marchal wrote:On 21 Oct 2013, at 20:07, meekerdb wrote:On 10/20/2013 11:12 PM, Russell Standish wrote:On Sun, Oct 20, 2013 at 08:09:59PM -0700, meekerdb wrote:Consistency is []p & ~[]~p. I was saying []p & ~p, iemistaken belief.ISTM that Bruno equivocates and [] sometimes means "believes"and sometimes "provable".And I'm doing the same. It's not such an issue - amathematician willonly believe something if e can prove it.But provable(p)==>p and believes(p)=/=>p, so why equivocate onthem?Both provable('p') -> p, and believe('p') -> p, when we limitourself to correct machine.(And incidentally mathematicians believe stuff they can't proveall the time - that's how they choose things to try to prove).Then it is a conjecture. They don't believe rationally inconjecture, when they are correct.They believe it in the real operational sense of "believe", theywill bet their whole professional lives on it. How long did ittake Andrew Wiles to prove Fermat's last theorem? Since one cannever know that one is a "correct machine" it seems to me amuddling of things to equivocate on "provable" and "believes".On the contrary. It provides a recursive definition of the beliefs,by a rational agent accepting enough truth to understand how acomputer work.We can define the beliefs by presenting PA axioms in that way Classical logic is believed, '0 ≠ s(x)' is believed, 's(x) = s(y) -> x = y' is believed, 'x+0 = x' is believed, 'x+s(y) = s(x+y)' is believed, 'x*0=0' is believed, 'x*s(y)=(x*y)+x' is believed,and the rule: if "A -> B" is believed and A is believed, then (soonor later) B is believed.But the point of Seth Lloyd's paper was that later can effectivelybe never and since given any time horizon, t, almost all B will notbe believed earlier than t.

`But Seth Loyd assumes some physical universe. In the arithmetic`

`context from which we start (and have to start by UDA, at some`

`recursive equivalence) soon or later means "once". It never means`

`"never".`

So really you call it "believe", but you use it as "provable".

`You miss the point. The incompleteness forces the provability logic to`

`behave like a believability logic.`

`After Gödel, provable (which was for many the best case of knowledge)`

`becomes "only" 'believable'.`

`That's why I agree with Popper, that science = only belief, because`

`the big difference between a belief and a knowledge, is that the first`

`is corrigible and the second is incorrigible.`

`(Popper and Deutsch uses non-standard vocabulary here, but I agree`

`with them).`

Then the theory will apply to any recursively enumerable extensionsof those beliefs, provided they don't get arithmetically unsound.The believer can be shown to be Löbian once he has also the beliefsin the induction axioms.Not really. You have add another axiom that the believer is correct.

`Why would I need to do that? It is not a new axiom, it is that I limit`

`the interview to correct machines. (Everett does the same, it is`

`natural. If you predict that a comet will appear in the sky, you will`

`not be refuted by a paper explaining that when astronomers are`

`sufficiently drunk, they miss to see it. You don't have to assume that`

`the observer is not drunk, sane of mind, etc. (At the level of the`

`scientific paper, in real life you know that a talk after dinner, at`

`some conference, will count for nothing, as people are full, and`

`sleepy!).`

He doesn't believe any false propositions - which means it is anidealization that doesn't apply to anyone.

`To derive physics, that is enough. Theoretical approach starts from`

`the simpler assumptions, and change them, or improves them only if`

`needed.`

`If not, you would have rejected Newton's at once, as he consider the`

`sun being a point, when recovering Keepler laws from his gravitation`

`theory.`

`The interesting happening, I think, is that by G* proving <>[]f,`

`somehow, the laws of physics and the whole machine's theology have to`

`take into account the consistency of incorrectness, at some basic`

`fundamental level. The idealization makes justice itself of your`

`remark, somehow.`

Bruno

BrentBruno--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To unsubscribe from this group and stop receiving emails from it,send an email to everything-list+unsubscr...@googlegroups.com.To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.

http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.