![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif){kind=small}
rysmiel wrote on
2004-05-04:
"reductio ad absurdum is a really stupid tool to use on scales other than that for which the human brain is optimised, because the further it is from what we are used to the less what seems absurd to us is a reasonable guide. Witness to a first approximation every development in physics since James Clerk Maxwell. There should probably be a metric for scaling how unlikely common sense is to fit any given problem."
(no subject)
But ... reducto ad absurdum isn't a method of judging whether something matches common sense. It's the mathematical logic process of proving that a new postulate must be true because, were it not true, it would lead to a contradiction. (This almost invariably assumes the existence of a set of axioms taken to be true whether or not the new postulate is true or false.) As a new postulate must be either true or false, if we've proven it would be a contradiction for it to be false, and we suppose our logical systems can't have contradictions, then the postulate must be true.
It's worth noting there's a school of mathematics, ``Intuititionists,'' who aren't satisfied with this and avoid reducto ad absurdum proofs. That thinking -- and it's hard not to sympathize -- is that showing a postulate can't be false isn't quite the same as proving it has to be true. So far, however, no one's found a theorem which can be proven by reducto ad absurdum which can't also be proven by ``constructive'' methods -- showing something is true by virtue of following from the axioms and the given laws of deduction -- so it's not an urgent matter of mathematics.
In any case it hasn't a place in physics except for where it's used to show some hypothesized result would be inconsistent with a physics theory taken to be reliable.