"Have you guys never heard of reductio ad absurdum?" I ask my smart sandals and laugh at the irony of conversing with my feet.

"That's Latin, right? We're Greek."

"Pardon me. The argument is traceable back to the Greek hi eis átopon apagogi "reduction to the impossible" and was often used by Aristotle.

"Oh that."

"Shut up and keep flying, will ya? We're waaay behind and still have the Medusa to get past. Also known as an apagogical argument or reductio ad impossibile, it's a type of logical argument where one assumes a claim for the sake of argument, arrives at an absurd result, and then concludes that the original assumption must have been wrong since it led to this absurd result."

"Are you saying our argument is absurd?"

"You got that right me boyos! This is also known as proof by contradiction. It makes use of the law of non-contradiction—a statement cannot be both true and false. In some cases it may also make use of the law of excluded middle—a statement which cannot be false, must then be true. Now land behind those those rocks and watch while I demonstrate the motions needed to kill an illusory Medusa."

I open my travel guide to the section on Gorgons and read that Perseus killed her by cutting off her head. I root through my tote bag and pull out the bronze shield, the helmet of invisibility and the sword.

"Okay boys. Time to fly. Let's go meet the fearsome lady with the snaky dreads. You'll have to be my eyes so I don't turn to stone."

I hide behind the shield and swoop down with my sword as we fly above her. Off goes her head and we're finally on our way to Athens.

"Now where was I? To quote G. H. Hardy's A Mathematician's Apology, 'Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.' In other words, nice try, but I'm not buying. The only thing I am buying is a hot bath, a drink at Kallistos' bar & grill and one of those Greco-Egyptian Goth hairstyles that are all the rage in Athens."

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Source of philosophical discourse: Wikipedia