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I was aware from mid-teens of Zeno's paradox about Achilles and the Tortoise* (for example as a Tortoise and Rabbit in Tom Stoppard's play Jumpers) - but I never properly got around to understanding just precisely what led to the paradox, why the mode of reasoning was wrong.
I see now this was an oversight and an error.
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The penny dropped when reading pages 137-9 of The Master and his Emissary, by Iain McGilchrist:
Zeno's paradoxes ... rest on the adoption of the left hemisphere's view that every flowing motion in space or time can be resolved into a series of static moments or points that can then be summed to give back the living whole. The 'seamless' fluidity of motion in space or time is 'reduced' to a series, akin to the series of still frames in a cine film.
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In essence, the paradox arises from the inbuilt assumption that every dynamic phenomenon can be resolved into a series of static units that can then be summed to recreate the dynamic whole.
There is absolutely no grounds for this assumption - this metaphysical assumption concerning the nature of reality, this basic assumption which frames all further analysis - indeed the assumption is obviously refuted by experience as demonstrated by the paradox.
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(A further assumption is that metaphysics ought not be contradicted by plain, commonsense experience - since the best Ancient Greek philosophy was meant to enrich normal life and plain commonsense experience - not usurp and replace it. This is a major constraint on philosophizing, and if it is abandoned - as modern culture has abandoned it - then philosophy becomes an open-ended and unbounded activity with no grounds for choice between philosophical ideas, only subjective preferences or varieties of instrumental expediency.)
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But with the paradox we (somehow) fail to notice we have made this metaphysical assumption and built it into the analysis - hence the paradox.
And it is suddenly obvious how deep an insight it was to understand this paradox, and what trap it is for humans to fail to recognise it.
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All my life in science, medicine and education I have observed the progressive destruction of these professions by the failure to recognise Zeno's paradox; the failure to recognise that dynamic skills cannot be broken down into static units then rebuilt. They cannot. They cannot.
It does not matter how long you make the forms to be completed, how elaborate the checklists, how comprehensive the managerial oversight.
The problem remains: in making movement static you have frozen the movement - movement is not movement any longer if it has been frozen.
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Achilles never catches-up with the tortoise.
Because both have been killed.
(To freeze a living entity is to kill it.)
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What complexity of static summaries does is to make things worse not better - because few, crude and simple static pictures of a complex activity cannot be mistaken for the real thing, whereas humans are bewildered by complexity into assuming it is completeness.
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*Achilles races the tortoise. He allows that tortoise a 'start' at point A, a little ahead of Achilles. They both begin to run. Achilles runs to the tortoises starting point A; but by this time the tortoise has moved a little ahead from A to point B. Then Achilles runs to point B - but by this time the tortoise has reached point C. So Achilles runs to point C, but by now the tortoise is at point D. And so on. Achilles never catches-up with the tortoise.
I sometimes think the Ancient Greeks did all the philosophy that was worth doing, that needed doing (especially metaphysics); and everything else since has been worse than nothing at all, since it made us lose sight of their insights. All we need to do is retain and re-express.
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