Lately I’ve been reading through Roy Sorensen’s A Brief History of the Paradox and it got me thinking about how important of a role paradoxes have played historically in the progression of thought. What’s so great about them is that they tend to infuriate the reason to the point of seeking out another way to attack a problem that can be completely revolutionary. A great example of this can be seen in the antimonies Kant purposes in the Critique of Pure Reason. The ingenious strategy employed consists of utilizing a series of reductio ad absurdum arguments to show the validity of competing metaphysical theses. Take for example the thesis that the world has a beginning in time. Kant argues that if you assume the opposite of that thesis (that the world does not have a beginning in time), then it follows that for every elapsed portion of time we experience there has been an infinitely long expanse of time that has preceded it. But an infinite time series can never actually be represented mentally and so becomes an empty concept we use as a mere placeholder. But now lets assume that the world does have a beginning in time. Then there must be some preceding void in which time and the world spring out of (Kant calls this “empty time”). But without time, how can we even talk about worlds springing to life or causal lines of creation? Faced with this dilemma, it would seem safe then to conclude that the world has existed for an infinitely long time. What we end up with is a paradox: The world has existed infinitely AND has a beginning in time. And it was this sort of problem that prompted Kant to search out a new path and pen out a revolutionary method of thought.
The great advantage of paradoxes is that they illuminate the paths of thought that aren’t really worth pursuing in our great quest to try and grasp some sort of understanding of this crazy world we live in. We see a particular path of inquiry, see that it leads to contradicting answers, and realize that we need to find a new and different path that will hopefully not lead to the same entanglements.