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The paradox of dichotomy – The walker


a—-“In order for a walker to travel a distance, he must first cover half of it. However, it is impossible for him to get to the middle of the total distance, if he previously hasn’t covered half of the above initial half etc. Nevertheless, in this way, the walker will always be unsuccessfully seeking the primary half. Because there are certainly infinite halves before any observed half.

b—-“This means” according to Zeno, “that the walker can’t reach his target because he is unable to move”. He then adds:

c—-“The question isn’t about when the walker will cover the total distance, but how will he achieve this when he will always have to be en route. (on the way) Because he will previously have to cover the infinite halves of the halves which will be ahead of him.”



The paradox of dichotomy is Zeno’s most significant paradox, as this prohibits the start and therefore, the general movement of every material objects. Therefore, the question regarding “if” and “how” the arrow, Achilles and the turtle will move has no further meaning. As it is seen below, Zeno’s serious omission was that he did not define (determine) “where”. Taken into consideration that everything in our world moves in a direct or an indirect way, every start is impossible to take place.

* the english texts may not represent a professional translation of the original
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