Editing 1153: Proof
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{{w|Zeno of Elea}} was an ancient Greek philosopher who devised several apparent paradoxes of motion called {{w|Zeno's paradoxes}}. Here are the two relevant to the comic: | {{w|Zeno of Elea}} was an ancient Greek philosopher who devised several apparent paradoxes of motion called {{w|Zeno's paradoxes}}. Here are the two relevant to the comic: | ||
− | :'''Arrow paradox:''' At any instant in time, an arrow suspended in mid-air is no different from an arrow in motion. How, then, can motion occur? | + | :'''Arrow paradox:''' At any instant in time, an arrow suspended in mid-air is no different from an arrow in motion. How, then, can motion occur? The lawyer presumably intends to use this argument to prove that his client could not have used the arrow to commit murder. |
− | :'''Dichotomy paradox:''' Suppose I need to go from point A to point B. First I must walk halfway there | + | :'''Dichotomy paradox:''' Suppose I need to go from point A to point B. First I must walk halfway there. Then I must walk a quarter of the way there, then an eighth of the way there, and so on. Since I have to make an infinite number of non-zero steps, I will never reach point B. By the same argument, the lawyer in the cartoon can approach the bench, but never reach it. |
− | + | {{w|Gottfried Leibniz}}, who discovered {{w|calculus}}, is called (in the title text) to bring a mathematical point of view. Since mathematics started to be able to handle infinite processes, it has been suggested that the Dichotomy paradox is resolved by showing that the infinite number of terms involved add upp to a finite sum. However, Zeno is rather saying "it is impossible to traverse an infinite number of things in a finite time", and is so arguably not concerned with finding a sum, but with finishing a task with an infinite number of steps. It therefore remains a question of debate whether a mathematical approach addresses the central points in Zeno's arguments. | |
− | + | The use of the word "proof" is ambiguous, and can mean {{w|mathematical proof}} or {{w|Evidence (law)|legal proof}}. | |
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==Transcript== | ==Transcript== | ||
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{{comic discussion}} | {{comic discussion}} | ||
[[Category:Philosophy]] | [[Category:Philosophy]] | ||
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