# Re: Belief vs Truth

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On 31 May 2013, at 01:19, meekerdb wrote:```
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```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
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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.
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They believe that they publish papers, and usually share the consensual believes, like in rain, taxes, and death (of others).
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All humans have many beliefs. A genuine scientist just know that those are beliefs, and not knowledge (even if they hope their belief to be true). So they will provides axioms/theories and derive from that, and compare with facts, in case the theory is applied in some concrete domain.
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Of course they believe things in the common sense that they are willing to act/bet on something (at some odds).
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Yes. For example most believe that there is no biggest prime numbers.

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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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Very often, alas. But the israelites and the taoists encourage the comments and the discussion of texts. So there are degrees of dogmatic thinking.
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When it comes to Bp & p capturing the notion of knowledge, I can see
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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
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It is equivalent with the dream argument made by someone who believes he knows that he is awake.
```Gettier is right, but he begs the question.

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But the theaetetus' idea works in arithlmetic, thank to incompleteness, and that's is deemed to be called, imo, a (verifiable) fact.
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Bruno

http://iridia.ulb.ac.be/~marchal/

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