On 31 May 2013, at 19:43, meekerdb wrote:

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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 youbelieved the axioms and rules of inference. What mathematiciansgenerally believe is that a proof is valid, i.e. that theconclusion follows from the premise. But they choose differentpremises, and even different rules of inference, just to see whatcomes out.I believe inthis theorem because I can prove it. If I can't prove it, then Idon'tbelieve 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 theconsensual believes, like in rain, taxes, and death (of others).All humans have many beliefs. A genuine scientist just know thatthose are beliefs, and not knowledge (even if they hope theirbelief to be true). So they will provides axioms/theories andderive from that, and compare with facts, in case the theory isapplied in some concrete domain.But those are not beliefs in the mathematicians sense, they arebeliefs in the common sense.

?

`The beliefs of the mathematicians are beliefs in the common sense. It`

`seems to me.`

They don't just believe the axioms and that the theorems follow fromthem.

?

Scientists usually call them hypotheses or models to emphasize thatthey are ideas that are held provisionally and are to be testedempirically.

`Mathematicians do the same. It is just than on arithmetic we have kept`

`the same hypothesis for long, and only weaken them, like replacing the`

`induction axiom with set of numbers by the induction axioms on first`

`order formula. But I am not sure there is any significant change. Only`

`what is studied is different.`

Of course they believe things in the common sense that they arewilling 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; thereligious 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 thecomments and the discussion of texts. So there are degrees ofdogmatic thinking.When it comes to Bp & p capturing the notion of knowledge, I canseeit captures the notion of mathematical knowledge, ie truetheorems, asopposed to true conjectures, say, which aren't knowledge.Gettier (whom I know slightly) objected that one may believe aproposition that is true and is based on evidence but, because theevidence is not causally connected to the proposition should notcount as knowledge.http://www.ditext.com/gettier/gettier.htmlIt is equivalent with the dream argument made by someone whobelieves he knows that he is awake.Gettier is right, but he begs the question.What question is that?

The question of how to distinguish belief from knowledge.

But the theaetetus' idea works in arithlmetic, thank toincompleteness, and that's is deemed to be called, imo, a(verifiable) fact.But does it work outside arithmetic?

`AUDA is after UDA. We "know" (in the comp theory, 'course) that there`

`is no outside of arithmetic ever needed to be assumed. The bosons and`

`fermions are inside too.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.