I have to respond that in Judaism in the high holiday service there is a prayer praising doubt. I think that may be unique to Judaism? Richard
On Sun, Jun 2, 2013 at 8:54 AM, Bruno Marchal <[email protected]> wrote: > > > > Russell wrote: > *"...When it comes to Bp & p capturing the notion of knowledge, I can see it > captures the notion of mathematical knowledge, ie true theorems, as opposed > to true conjectures, say, which aren't knowledge. > * > > > I can see your point, at least for arithmetic, but I am not sure that > distinction is interesting, at least for awhile. In both case we assert > some proposition, that we cannot prove. Then with some luck it can be true. > > > > * But I am vaguely sceptical it captures the notion of scientific knowledge, > which has more to do with falsifiability, than with proof. > * > > > But the Löbian point is that "proof", even when correct, are falsifiable. > Why, because we might dream, even of a falsification. > > On 01 Jun 2013, at 21:41, John Mikes wrote: > > * And that's about where I left it - years ago.* > *..."* > Interesting difference between 'scientific' and 'mathematical' > (see the Nobel Prize distinction) > > > That's one was contingent. > Nobel was cocufied by a mathematician who would have deserved the price > (Mittag Leffler I think). Hmm.. Wiki says it is a legend, and may be it is > just the contingent current Aristotelianism. Some people believe that math > is not a science, like David Deutsch. That makes no sense for me. Like > Gauss I think math is the queen of science, and arithmetic is the queen of > math ... > > > > - also in falsifiability, that does not automatically escape the agnostic > questioning about the circumstances of the falsifying and the original > images. > > > Excellent point. > > > > Same difficulty as in judging "proof". > > > Formal, first order proof can be verified "mechanically", but they still > does not necessarily entail truth, as the premises might be inconsistent or > incorrect. > > > > "Scientific knowledge" indeed is part of a belief system. In conventional > sciences we THINK we know, > > > Only the pseudo-religious or pseudo-scientist people think they know. > > > > in math we assume > (apologies, Bruno). > > > > ? > On the contrary I agree. I thought I insisted a lot on this. Except for > the non scientific personal (not 3p) consciousness it is always assumption, > that is why I say that I assume that 0 is a number, that 0 ≠ s(x) for all > x, etc. > > In science there is only assumption. We never know-for-certain anything > that we could transmit publicly. > > Science is born from doubt, lives in doubt and can only augment the > doubts. > > In the ideal world of the correct machines, *all* certainties are madness. > > Bruno > > > > > * > * > On Thu, May 30, 2013 at 6:43 PM, Russell Standish > <[email protected]>wrote: > >> On Thu, May 30, 2013 at 12:04:13PM -0700, meekerdb wrote: >> > You mean unprovable? I get confused because it seems that you >> > sometimes use Bp to mean "proves p" and sometimes "believes p" >> > >> >> To a mathematician, belief and proof are the same thing. I believe in >> this theorem because I can prove it. If I can't prove it, then I don't >> believe it - it is merely a conjecture. >> >> In modal logic, the operator B captures both proof and supposedly >> belief. Obviously it captures a mathematician's notion of belief - >> whether that extends to a scientists notion of belief, or a >> Christian's notion is another matter entirely. >> >> When it comes to Bp & p capturing the notion of knowledge, I can see >> it captures the notion of mathematical knowledge, ie true theorems, as >> opposed to true conjectures, say, which aren't knowledge. >> >> But I am vaguely sceptical it captures the notion of scientific >> knowledge, which has more to do with falsifiability, than with proof. >> >> And that's about where I left it - years ago. >> >> Cheers >> >> -- >> >> >> ---------------------------------------------------------------------------- >> Prof Russell Standish Phone 0425 253119 (mobile) >> Principal, High Performance Coders >> Visiting Professor of Mathematics [email protected] >> University of New South Wales http://www.hpcoders.com.au >> >> ---------------------------------------------------------------------------- >> >> -- >> 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 [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/everything-list?hl=en. >> For more options, visit https://groups.google.com/groups/opt_out. >> >> >> > > -- > 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 [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list?hl=en. > 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 [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list?hl=en. > For more options, visit https://groups.google.com/groups/opt_out. > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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