As anyone who reads this blog (both of you!) should know, I’m a huge fan of logic, reasoning and the scientific method; I’m also, shall we say, somewhat against the concepts of religion as they violate logic, reasoning, and the scientific method. Magic fairy farts out universe and all life as we know it; right, gotcha.
The great thing about logic is that it doesn’t matter what you’re speaking about; logic is applied using patterns of thought, so the idea in question is actually irrelevant. For example, take post hoc ergo propter hoc; doesn’t matter what I’m examining, it only matters if I’m trying to assign causation based solely on correlation. The pattern holds regardless of the underlying argument.
Reductio ad absurdum, or a proof by contradiction, actually requires that we examine the actual argument and then, for argument’s stake, treat it as being true. We take a premises, assume that it is correct, and take it to its logical conclusions to an absurd degree. If the logical conclusions are simply absurd, we conclude that the premises must also be absurd, thus we assume that the argument is wrong.
Simple example: Cuius est solum eius est usque ad coelum et ad inferos, which basically means that if you buy land, you own everything above it and below it, to the heavens above and to hell below. Let’s follow this to the logical conclusions, shall we?
Let’s assume that the land I own can be represented by a circle (say I’ve got a circular yard). Then, let’s extend that circle both above and blow my yard, so we would basically be turning the circle into a circular rod (a 3D shape) that extended above and below my yard. With me so far?
So if I extend that rod way below the surface of my yard, I may hit China. Does that mean I own that piece of land in China? What if I took the rod and went way above the surface of my yard? Well, I’d certainly claim that I owned all of that airspace, plus I may end up hitting another planet or star. Do I own those pieces of other planets or stars? What about other peoples’ yards and their rods? Surely I would intersect with somebody else’s rod, so what then? Do we have to share that particular intersection?
So, the idea that I own everything above and below my yard is absurd, thus we refute the premises simply because the logical conclusions are ridiculous.
That, in a nutshell, is reductio ad absurdum.