Zeno’s logic and presuppositions
A dialogue between Socrates the stick and Emmanuelles the tortoises. Socrates knows he does not know anything and this leads him to ask many questions. He then carefully examines the responses. Les Emmanuelles are reasoners who love logic and are wary of emotions.
Socrates: dear turtles, my friend Zeno of Elea says that in the event of a race with light-footed Achilles, you will win if you start early because he will never be able to catch up with you. Can you tell me why?
Emmanuelles: dear Socrates, it is a classic of our education intended to train us in logic and reflection and here is how it is presented. Achilles, knowing we are slow, gives us a hundred yards ahead.
Socrates: yes, this is how the story begins.
Emmanuelles: well, by the time he gets to where we were when he sets out, you will admit that we will have taken the opportunity to move at our own pace and that he will then need to run this extra distance?
Socrates: yes, it seems obvious the way you put it.
Emmanuelles: the time he manages to cover this distance we will have taken advantage of it to progress.
Socrates: yes because you are moving slowly but with determination.
Emmanuelles: so now Achilles has to cover that extra distance again, do you agree?
Socrates: if he wants to join you, he has no choice.
Emmanuelles: that’s why he can’t catch up with us, we are always a little ahead, as small this lead becomes over time.
Socrates: this all makes a lot of sense, but it is false and you know it. Achilles is faster than you and will overtake you easily.
Emmanuelles: dear Socrates, we have thought about this paradox at length and it seems solid to us even if it does not reflect reality.
Socrates: it looks solid because you assume you and Achilles live in the same world with the same rules but therein lies the problem.
Emmanuelles: we are listening to you …
Socrates: your time and space are yours. Achilles evolves in a different time and space so there is never a meeting of the two and the divisions you make in yours do not affect his. So he can easily overtake you because it’s in his nature to be faster than you.
Emmanuelles: so how can we get along if you are telling the truth and we live in different worlds?
Socrates: because you share the same notions but not the same realities. You think you are talking about the same thing but it’s only an illusion. This allows you to advance a theory that only holds in theory. In practice, it does not make sense. Kind of like telling me you’re cold. I can understand this because I know I can get cold but it is not sure that your cold is mine. Beware of pure logic and fallacious comparisons.
Emmanuelles: your analysis is interesting and difficult to contest, dear Socrates, we had never met it and it offers us new perspectives.
Socrates: we must always go beyond appearances and question the presupposed because logic is only a tool, not a truth. If you use it badly, your final edifice may be logical, but it will not be solid.
Analysis
Logic is a tool of reasoning, but if it has a wrong foundation, its conclusions will also be wrong.
Socrates asks the turtles to explain Zeno of Elea’s paradox that if he gives them a head start, he can never catch up with them. He then explains that this is an impossible situation because Achilles and the turtles do not live in the same world. Only language can make people believe that they have an identical perception and experience of time and space.
Les Emmanuelles show that, logically, Achilles will never be able to catch up with them because every time he reaches the point where they were, they will have progressed further.
Possible discussions
Manipulating language, is this the best way to arrive at truths?
Have we always lived in a virtual world?
Finally
Want to know more about Zeno of Elea? See, for example, Zeno’s paradoxes.
Want to help improve these dialogues? Write your comments and questions below.
Want to know more about the tastes of Socrates and Emmanuelles? Their favorite books are in the domain library.