On 5/30/2013 3:43 PM, Russell Standish 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"## Advertising

To a mathematician, belief and proof are the same thing.

`Not really. You only believe the theorem you've proved if you believed the axioms and`

`rules of inference. What mathematicians generally believe is that a proof is valid, i.e.`

`that the conclusion follows from the premise. But they choose different premises, and`

`even different rules of inference, just to see what comes out.`

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.

`I don't think scientists, doing science, *believe* anything. Of course they believe`

`things in the common sense that they are willing to act/bet on something (at some odds).`

`The Abrahamic religious notion of 'faith' is similar to that; the religious person must`

`always act as if the religious dogma is true (at any odds). This precludes doubting or`

`questioning the dogma.`

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.

`Gettier (whom I know slightly) objected that one may believe a proposition that is true`

`and is based on evidence but, because the evidence is not causally connected to the`

`proposition should not count as knowledge.`

http://www.ditext.com/gettier/gettier.html Brent

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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