# Re: Belief vs Truth

```On 5/30/2013 3:43 PM, Russell Standish wrote:
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```On Thu, May 30, 2013 at 12:04:13PM -0700, meekerdb wrote:
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```You mean unprovable?  I get confused because it seems that you
sometimes use Bp to mean "proves p" and sometimes "believes p"```
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```To a mathematician, belief and proof are the same thing.
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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.
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```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.
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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.
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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.
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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
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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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