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.
(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.