(May 11, 2015 at 10:30 am)Hatshepsut Wrote: ... We had Zeno's paradox of the arrow arguing that motion or change can't be real when obviously Zeno must have seen arrows in flight. ...
It should serve as a warning for trusting an abstract argument too much and not paying attention to counter-evidence that is readily available. The error of Zeno's reasoning is explained in Calculus, but even without the explanation, it should be clear enough that he made a mistake somewhere, even if one does not know what the mistake is.
This also reminds me of Voltaire's Candide, in which he mercilessly ridicules Leibniz's insane idea that this is the best of all possible worlds. I have heard some complain about that, that they imagine that Voltaire should have used abstract reasoning and looked for the precise mistakes Leibniz made in his reasoning. But Voltaire took the approach that is analogous to dealing with an abstract argument that it cannot be raining, by pointing out the window at the rain. One need not bother with the precise mistake, when one can directly prove that the conclusion is wrong. Some positions are so absurd that they are more worthy of ridicule than of argument.
Of course, if someone wishes to tease out the precise errors in someone's reasoning, they may do so, and it can serve a useful function. But it is far from necessary in many instances. As, for example, with these specific cases involving Zeno and Leibniz.
"A wise man ... proportions his belief to the evidence."
— David Hume, An Enquiry Concerning Human Understanding, Section X, Part I.
