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 <[email protected]> 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/> >> >> >> >> > -- > 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+unsubscribe@**googlegroups.com<everything-list%[email protected]> > . > To post to this group, send email to > everything-list@googlegroups.**com<[email protected]> > . > Visit this group at > http://groups.google.com/**group/everything-list?hl=en<http://groups.google.com/group/everything-list?hl=en> > . > For more options, visit > https://groups.google.com/**groups/opt_out<https://groups.google.com/groups/opt_out> > . > > > -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
