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Reductio Ad Absurdum

I have recently read The Fifth Postulate by Jason Socrates Bardi. It is about Euclid’s fifth postulate which states that two lines in a plane that are not parallel will eventually cross. Of the five postulates the fifth gave mathematicians the most trouble. It could not be proven. Various attempts at proving it just became restatements. It wasn’t until the priest Giovanni Girolamo Saccheri enabled the philosophical tool of reductio ad absurdum, which is proving something by examining what it would mean if it were not true, that headway with the problem was made. Saccheri discovered a new world of space, but since he was a Jesuit his writings could have been condemned as heresay, so he explained the new space was false. Carl Fredrich Gauss, Nikolai Lobachevski and Jonas Bolyai independently rejected the fifth postulate and in turn examined what the world of it’s contrary would look like. As a result Non-Euclidean geometry was born, which eventually acted as a tool for Einstein in the developments of special and general relativity. Non-Euclidean geometry can be imagined not taking part on a flat plane, but on a sphere, whose implications can be seen in much larger spaces, like outer space.

The fifth postulate is a successful example of reductio ad absurdum to prove a point.

On a recent trip to the grocery store I remembered I was running low on toothpaste, so visited the toothpaste aisle and noticed "Pro-Health" toothpaste. Right next to it, by the same makers, was “Anti-Health” toothpaste with flavours of diarrhea and vomit. I checked the ingredients on the package and as it turns out the toothpaste was gelled sugar. Seeing as how I want to fuck up my teeth, I went ahead a purchased the anti-health toothpaste.


sybil law said...

I love things that can't be proven. Usually. Until I think about them too much.

Anti Health toothpaste! That makes my teeth hurt!

John Dantzer said...

Just like no one can prove you are the devil.

dogimo said...

But one can't disprove the postulate by taking it out of a plane - that's just fighting the hypothetical. One can't disprove a postulate by changing the postulate - by voiding one of its key provisions!

Of course, once you take the lines out of a plane, all bets are off and the lines may never intersect. This is no disproof, it's just a new set of ground rules which can be valid as formulated without offering the slightest conflict to the original scenario.

Still, it's all worth it to get reductio ad absurdum! What a great instrument in the toolbox of logic and reason.

John Dantzer said...

Philosophy is a difficult field when considering the abstract.