The reduction ad absurdum argument to prove X generally goes not-X => ... => false, a contradiction, therefore X is true. e.g. not-X => A, not-X => not-A, hence x => A and not-A => F, therefore X is true. I've always found such arguments, while effective, in a way unsatisfying, because by the time you find your contradiction, you have wander far from your premise. I was wondering if there might always be a way to turn such an argument around, so that a proof of not-X => false, can be flipped to prove the contrapositive, true => X. I'm obviously not talking about building the argument around not-X => false and then invoking the contrapositive, but rather inverting the entire argument into a direct argument where X appears only as the last statement proven, not as part of an earlier supposition.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Brent Meeker Sent: Wednesday, February 01, 2017 10:00 PM To: math-fun Subject: Re: [math-fun] Logic question
On 2/1/2017 6:19 PM, David Wilson wrote:
Can a reductio ad adsurdum argument be rearranged into a direct argument that does not require a supposition?
As well as any logical argument. Any logical argument proceeds from premises and shows they entail a conclusion. Whether the premises are suppositions or facts is not relevant to the logic. An argument from absurdity is of the form X=>Y, Y is absurd and therefore false, not-Y => not-X ... which seems direct to me. Do you just mean you want it to prove a positive? in which case you can substitute Z = not-X so it becomes not-Z=>Y, Y is absurd and therefore false, not-Y=>Z.
Brent Meeker
In short, are suppositions necessary for logical arguments?
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