On 2/27/2018 2:42 AM, Telmo Menezes wrote:
Depends on what you mean by "proof", we sentence people to prison based on
proof of their crime. Not all proof is mathematical. And mathematical
proof is only relative to the axioms.
I think that this is one of those cases where the term is overloaded.
I would argue that, for most people, proof has a strong connotation of
"case closed". Mathematical proof is the only domain where this is
actually true.
But "true" in mathematics is a marker you attach to some axioms and then
use rules of inference which preserve the marker. It only means
"corresponding to a fact" if the axioms correspond to facts.
Everywhere else it is relative: it means sufficient
evidence for some course of action to be taken. I suspect that judges
and lawyers like the term because it makes everyone sleep better at
night.
I'm sure they are glad that it is usually the jury's task to say what
the facts are. But in a criminal case the jury must unanimously agree
on the facts of crime beyond a reasonable doubt. If you've ever served
on a jury (I've been on four and served as foreman once) you know the
jurors take their task very seriously.
I never see contemporary scientists using the term, only
science journalists. Again, this makes sense: the general public likes
to feel that science is settling matters. I think it is anti-pedagogic
to talk about scientific theories being "proven", because it conveys
the wrong idea about what science is and what science does. For a
serious scientist, nothing is ever settled and no cases are closed.
There are strong hypothesis at a given time, there are effective
models for certain domains, and one does the best one can with them.
The lack of this "case closed" attitude is precisely what makes
science such a magnificent endeavour, and why it shines so bright
above the certainties of the religious fundamentalists and the
ideologues.
I agree. But it is also used by those who find scientific findings
inconvenient and obfuscate by saying the findings of science are not
conclusive and nothing is proven. They obscure the point that one must
act and science the best way to inform the action.
So what do you find more convincing: An axiomatic */proof/* that God
exists, e.g. St Anslem's or Goedel's. or The mere empirical absence of
evidence.
Brent
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