Rolled back to previous version.

This is not a form of the straw man fallacy. Reductio ad absurdum is a logical argument which attempts to disprove a claim by assuming it as the major premise and demonstrating that the claim cannot be true by arriving at a false conclusion in a valid argument with a minor premise which is known to be true. The principle is that a logically valid syllogism is one where if both premises are true, the conclusion must be true. If the conclusion is false, one or more of the premises must be false. By demonstrating that the minor premise is true, the suspect premise must be false. - Sans Deity 20:48, 30 August 2006 (MST)

Umm... what "second premise"? The article only mentions a single premise, the one that ultimately gets rejected. - dcljr 01:58, 31 August 2006 (MST) Irrelevant now that above comment has been reworded. - dcljr 22:55, 1 September 2006 (MST)

I reworded my explanation above...and I'll try to get examples into the article soon. -- Sans Deity 06:38, 31 August 2006 (MST)

The part of the proof starting with "or it is divisible by a prime number which has not yet been listed" is not necessary since we already assumed we'd multiplied all the primes. It's like saying, "Assume 1, 2, and 3 are the only numbers. Now consider a new number, 4." If the premise is correct, then 4 must be one of the other three numbers and not something different! The previous version of the proof, while admittedly not as precise, didn't make any such immediately falsifiable statements along the way, and yet lead to an absurdity. I've reworded the proof yet again to be even more precise. The argument is now even closer to Euclid's (Elements, Book IX, Proposition 20). Unfortunately, it relies on a result that must be proved separately (Bk. VII, Prop. 31). Such is the cost of added precision... - dcljr 16:00, 16 October 2010 (CDT)