Brent,
thanks for your clear ideas - not controversial to what I try to explain in
my poor wordings.
No proof is "valid", or "true". Applicable, maybe.
In our 'makebilieve' world-model many facets SEEM true in our terms of
explanation, i.e. using conventional science and wisdom. Mathematicians are
even more stubborn.
JohnM

On Fri, May 31, 2013 at 1:43 PM, meekerdb <meeke...@verizon.net> wrote:

> On 5/31/2013 10:35 AM, Bruno Marchal wrote:
>
>>
>> On 31 May 2013, at 01:19, meekerdb wrote:
>>
>>  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"
>>>>>
>>>>>  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.
>>>
>>
>> They believe that they publish papers, and usually share the consensual
>> believes, like in rain, taxes, and death (of others).
>>
>> 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.
>>
>
> But those are not beliefs in the mathematicians sense, they are beliefs in
> the common sense.  They don't just believe the axioms and that the theorems
> follow from them.  Scientists usually call them hypotheses or models to
> emphasize that they are ideas that are held provisionally and are to be
> tested empirically.
>
>
>
>>
>>
>>
>>
>>  Of course they believe things in the common sense that they are willing
>>> to act/bet on something (at some odds).
>>>
>>
>> Yes. For example most believe that there is no biggest prime numbers.
>>
>>
>>
>>  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.
>>>
>>
>> Very often, alas. But the israelites and the taoists encourage the
>> comments and the discussion of texts. So there are degrees of dogmatic
>> thinking.
>>
>>
>>
>>
>>
>>>
>>>> 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<http://www.ditext.com/gettier/gettier.html>
>>>
>>
>> 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.
>>
>
> What question is that?
>
>
>
>> But the theaetetus' idea works in arithlmetic, thank to incompleteness,
>> and that's is deemed to be called, imo, a (verifiable) fact.
>>
>
> But does it work outside arithmetic?
>
> Brent
>
>
>
>> Bruno
>>
>>
>> http://iridia.ulb.ac.be/~**marchal/ <http://iridia.ulb.ac.be/~marchal/>
>>
>>
>>
>>
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