I find paradoxes really entertaining. They make me think in new ways about reasoning, the way I understand the world and the way we use language. What is a paradox? Well the old definition is that it is something 'beyond belief' or 'contrary belief'. It uses the same Greek root as 'orthodox' - meaning 'right belief'. Apparently it used to be applied more to things in the natural world that were just really weird. The platypus is an example of such a paradox. A duck-billed, egg laying, mammal that nursed its young was, for many Europeans, simply beyond belief (so it was named Ornithorhynchus paradoxus).
These days we just seem to accept that science and nature are weird and don't really make sense and so reserve 'paradoxes' for logical contradictions. You could say that a paradox is a true contradiction. Start with an obvious truth and then discover another obvious truth that seems to directly contradict the first - and you have a paradox. Here is an example:
Zeno's Paradox
Dan had a lot of fun with this problem here, and here. I remember there was even a facebook group dedicated to the 'nood turtle olympiad' implied by the paradox.
My plan for the next few months is to outline some of the more interesting paradoxes that have come up in philosophy over the years and think a bit about what they mean for our understanding of the world and the use and limits of reason and logic. Should be fun.
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