How is reductio ad absurdum a valid proof method?

In summary: R \to (\lnot \lnot R \to \lnot R)The other tautology.\lnot \lnot R \to \lnot RFrom steps 2 and 3...modus ponens.\lnot \lnot S \to \lnot RFrom steps 1 and 4...hypothetical syllogism.S \to (\lnot \lnot S \to S)One more tautology.(\lnot \lnot S \to S) \to (S \to \lnot \lnot S)Another tautology.S
  • #36
peos69 said:
I am not sure i get you point please be a bit more specific

I think Hurkyl is asking 'what does it mean for Nature to "prove" something?'.
 
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  • #37
you are inside your apartment and you ask your friend.How long do you thing it will take if i jump from the top of the Empire Building?your friend takes out his pencil and he does a few calculations and he tells you the time.Then you go to the top of the building,you set your watch,you jump and when you land on the ground you check your watch.If the time is the same with the time calculated by your friend then nature has |"proved" the Newtonian theorem in mechanics,which your friend used to find out the time.
 
  • #38
peos69 said:
If the time is the same with the time calculated by your friend then nature has |"proved" the Newtonian theorem in mechanics,which your friend used to find out the time.
No, it hasn't. Newton's laws are not mathematical theorems. They are scientific theories. Mathematic theorems and scientific theories are quite different things.

Gathering evidence does not prove a scientific theory to be true. The evidence instead shows that the theory is consistent with reality to within experimental error, and only in the case of the evidence at hand. Experimental evidence provides confirmation. It does not provide proof. On the other hand, one crummy piece of well-validated conflicting evidence makes a scientific theory fall apart. In the case of Newton's theory of gravitation, that one crummy piece of conflicting evidence is the precession of Mercury. Newton's laws predict a different value for the precession of Mercury than observed. Those observations falsify Newton's laws.
 
  • #39
D H said:
No, it hasn't. Newton's laws are not mathematical theorems. They are scientific theories. Mathematic theorems and scientific theories are quite different things.

Gathering evidence does not prove a scientific theory to be true. The evidence instead shows that the theory is consistent with reality to within experimental error, and only in the case of the evidence at hand. Experimental evidence provides confirmation. It does not provide proof. On the other hand, one crummy piece of well-validated conflicting evidence makes a scientific theory fall apart. In the case of Newton's theory of gravitation, that one crummy piece of conflicting evidence is the precession of Mercury. Newton's laws predict a different value for the precession of Mercury than observed. Those observations falsify Newton's laws.

Lets not forget Einsteins relativity either :)
 
  • #40
Lets put that way.
Suppose you kick MATHEMATICS to oblivion ,Can you have science
 
  • #41
Then it wouldn't make much sense to have the discussion in a math forum. :-p
 
  • #42
true indeed
 

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