On 03 Jun 2013, at 01:41, Stephen Paul King wrote:

How do we integrate empirical data into Bp&p?



Technically, by restricting p to the "leaves of the UD*" (the true, and thus provable, sigma_1 sentences). Then to get the physics (the probability measure à-la-UDA), you can do the same with Bp & Dp & p. Think about the WM-duplication, where the W or M selection plays the role of a typical empirical data.

More on this when you came back to this, probably on FOAR.

Bruno







On Saturday, June 1, 2013 3:41:56 PM UTC-4, JohnM 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. 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.
..."
Interesting difference between 'scientific' and 'mathematical'
(see the Nobel Prize distinction) - also in falsifiability, that does not automatically escape the agnostic questioning about the circumstances of the falsifying and the original images. Same difficulty as in judging "proof". "Scientific knowledge" indeed is part of a belief system. In conventional sciences we THINK we know, in math we assume
(apologies, Bruno).
John M


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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