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 <li...@hpcoders.com.au > 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

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