Zenos Paradox : An Example of Lousy Thinking

My kid watches a lot of videos like numberphile, recommended Zeno’s Paradox.

It seems to me that Zeno’s Paradox is a wonderful example of how you can be stuck for explanations == encounter a paradox, if you mix concepts == make a category error.  The explanation of the real world situation in the above is absolutely not commensurate in any dimension with the mathematical statement of the problem.  Physical hands are not mathematical points, which are concepts.  Physical hands have properties that allow clapping, mathematical concepts may not.  Infinite series may or may not converge, Achilles and tortoises don’t have same set of operations as the mathematical entity of a sum, and therefore will not behave in the same way.  Adding a fraction is not the same kind of operation as taking a step, however tiny.

Why would we expect different kinds of operations to produce the same result?

Physical objects moving through the world may be modeled by some math formalism successfully, but just because that works in one situation doesn’t predict much about the next case.

One should doubt the mapping of pure math thinking about infinite series onto anything in our physical reality.  Diogenes was right, that mapping produces the paradox, the inconsistency of math concepts and operations with physical actions in reality.

Why do that to yourself?

The Wikipedia discussion is no help, the many different philosophical points of view generally include discussions are about 3 completely different things: pure math, ways to use pure math in modeling physical reality, and the physical reality (as represented in other models, of course and without hints that the domain of discourse is changed, of course).  The various points of view on the Wikipedia page each have references to(confusions with, imho) the other domains, as tho one puts limits on the others or can be used to bolster an argument within this domain.,  Even the mathematicians aren’t clear (as one of the premier explainers of our age demonstrates above).

So these eminent philosophers, at least as presented by Wikipedia’s editors, do not appear to realize they are making category errors.  Wow.

Pat Corvini,  near the bottom of the discussion, comes to the same conclusion as I do, I am relieved to find.  That explanation is not singled out as special.

To me, the real paradox is that Zeno’s Paradox isn’t a widely-known example of lousy thinking about maps and territories and hidden-ignored remappings, category errors of great obviousness.

That kind of category error is the standard mental failure of the age : use the same word for N different somethings in the same argument and thereby come to some conclusion that the writer likes.   False premise –> any conclusion you would like, propaganda is so easy if you let them shift meanings or even use vague meanings.

Careful thinking is the first requirement for Justice, a Conservative goal in every age.

———————————————— Added a week later ———–

I just watched Wolfram discussing A New Kind of Science again :

Reading some of the reviews, nobody makes the distinction between the math, the usefulness of the models, and the possible reality they model.  Category error wall to wall, that despite the fact that Wolfram is very careful to emphasize ‘models’ of nature and how different models are useful for different questions, different purposes.

2 thoughts on “Zenos Paradox : An Example of Lousy Thinking

  1. I always considered these mental masturbation. Obviously, the pursuer catches up whenever his arm is longer than the remaining distance, no more halving is necessary. Works good if everyone is the size of a point.

    They should be restated, “If a philosopher climbs up his own ass, does he disappear?” Worked for Igly.

    Even if you stick to the math, it assumes a point can be divided.


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