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Re: CHAT: another new language to check out

From:Chris Bates <chris.maths_student@...>
Date:Friday, July 2, 2004, 7:24
Sally, everything takes blind trust at some point, even mathmatics for
mathematicians (which I am... kindof) and science for scientists. Any
"proof" is not absolute even within mathematics; rather to prove
anything in mathematics you have to establish a set of axioms which you
believe in without proof, because if you have nothing to start with then
you can't prove anything. Thus the truth of a proof depends not only on
its correctness in itself, but also in the truth of the axioms you built
it on. A lot of the axioms mathematics is build on are things most
people would consider simple or obvious if they were explained to them,
but they are nevertheless "taken on faith". The same is true of the
sciences, but more so, because there is no such thing as true proof of
most scientific theories. Rather in science proof takes the form of
probability, ie this theory agrees with all the experimental evidence we
have and we don't have a better one so its probably true. But that was
true of Newtonian Mechanics, and now we have the Theory of Relativity
and Quantum Mechanics which say Newtonian Physics is an approximation
that works a lot of the time, but isn't really "true" in a sense. The
problem is Relativity and Quantum Mechanics are somewhat incompatible so
a lot of physicists have been working on finding a model that fits both
(mainly string theory). If they find one, then Relativity and Quantum
Mechanics will both be approximations too, and thus not really 100% "true".
 You might also be interested to now the Godel's Incompleteness Theorem,
which is true according to Mathematics (given the axioms we've taken)
shows that no system can be both consistent and complete; ie there will
always be statements in any system we choose to build no matter what the
axioms, which cannot be proven (I'm excluding the axioms here since by
definition they are taken on faith). So there exist some non-axiomic
true statements in mathematics which cannot be proven, although its
difficult to provide an example because the fact I have no proof doesn't
mean that one doesn't exist.
 Anyway, my point was just that everything including science requires
faith, because to "know" anything, you have to take some basic knowledge
for granted to build the rest. :) If you decide to take nothing on faith
you end up like Descartes, who decided that the only thing he could
believe in was his own existence (the famous "Cognito ergo Sum" or
rather "Cognito, Sum" as Christophe corrected us last time).

>I don't know if religious trust ("faith") is necessarily "blind," (she said >cautiously.) I think aspects of the "rational" universe take just as much >unquestioning trust on a daily basis. For instance, I know that my computer >is operated by electricity, but I couldn't begin to make a battery, much >less a generator. Or a computer. They work almost like magic for me. More >to the point, I know that mathematicians and scientists can prove things >about the universe that I could never corroborate. Quantum physics is like >a Book of Secrets for me. I must trust it. I will never understand it >completely. Is that "blind"? Remember, now, I'm talking about all belief >structures, here. You can say that there are charts and documents that >"prove" quantum physics or mathematics, or show one how a battery works. >But look at the O.J. Simpson jury. They decided not to put their "blind >trust" into what the forensics scientists told them about DNA testing. And >O.J. walked. I'm not saying that's a good thing. I'm examining the nature >of trust and skepticism. It goes both ways. > >

Replies

Joe <joe@...>
Sally Caves <scaves@...>Trust, Consciousness, Dennett, Lem: was: another new language to check out