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Antinomy has been defined as a fundamental and apparently unresolvable conflict or contradiction. A student tries her definition of antinomy and says it's when "perfectly logical reasoning brings about a seemingly ridiculous conclusion." Antinomy was considered by philosophers like Zeno of Elea and Emmanual Kant and dismissed as nonsense by Wittgenstein. I am with Wittgenstein. We need not accept the proposition that perfect reasoning can produce a ridiculous conclusion. If a ridiculous conclusion has been reached it's because the reasoning that took it there was in some way faulty or incomplete. I see antinomy as similar to paradox. So does my Mac dictionary, which describes paradox as "a statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory."

Zeno of Elea is described by the Stanford Encyclopedia of Philosophy as a fifth century BCE "thinker known exclusively for propounding a number of ingenious paradoxes." Zeno believed in permanence and that change was illusion – not a proposition that can be claimed as a product of "perfect reasoning." He argued that at any instance an object is still. His paradox: an object both still and in motion. Can we dismiss this as nonsensical? We know what a nanosecond is: one-billionth of a second. Maybe we can say that an "instant" as non-motion is just fantasy. In my opinion, antinomies and paradoxes are fantasies.

Zeno played with numbers. If one adds 1/2 + 1/4 + 1/8 + 1/16th, on and on adding small amounts, one gets closer and closer to the number 1 but never actually reaches it. It is described as also perplexing to do this backwards, subtracting from 1/2 rather than adding. And, of course, one never reaches zero. Nothing strange about that. Like math itself, it is something of the human imagination. But into modern times, people have confused this little game with profundity.

The ancient Chinese philosopher and legendary founder of Taoism, Laozi, had been into paradoxes long before Zeno. For example, one of the paradoxes attributed to him reads: "The usefulness of a pot comes from its emptiness." What some see as a paradox here is really a practical matter. If you want to use a pot that's full you may need to empty it. Nothing profound.

Kant, the great Enlightenment philosopher, discussed antinomy while arguing about space and time: the argument that there must have been a beginning and yet the question remains what happened before the beginning. This is entertainment rather than the stuff of empirical science with which we draw conclusions applicable to anything that matters.

Another antinomy that he pointed to was the issue of free will versus tracing every notion that pops into our head having a cause that traces to another cause – in other words, universal causality. This is something more for entertainment. The object of thinking beyond games, impossible or silly puzzles is to manipulate. If your philosophy includes metaphysics and you accept the idea that Allah is great then you can try to manipulate Him through prayer. If you are like me, or like Wittgenstein, you will direct your thinking to the manipulation of something that you apprehend through your senses.

As I suggested in support of philosophy at the end of my article on Wittgenstein, we can employ reason to clear our minds of clutter.

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