- Oct 2, 2003
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-Paradox of the arrow
In the paradox of the arrow, Zeno asks us to consider an arrow in flight and argues that, in fact, the arrow must always be at rest. At each instant the arrow occupies a space equal to itself. Movement is impossible, because an instant by definition has no parts. If the arrow were capable of moving during an instant, we would contradict the definition of an instant, for the arrow would be in one position during the first part of the instant and in another position in the other part of the instant. Thus, the arrow never seems to be moving but rather, as Russell notes in his essay on infinity, "in some miraculous way the change of position has to occur between the instants, that is to say, not at any time whatever." If the arrow does not move at any given instant, how then does it make its flight?
-"Interesting" and "uninteresting" numbers
The question arises: Are there any uninteresting numbers? We can prove that there are none by the following simple steps. If there are dull numbers, then we can divide all numbers into two sets - interesting and dull. In the set of dull numbers there will be only one number that is the smallest. Since it is the smallest uninteresting number it becomes, ipso facto , an interesting number. We must therefore remove it from the dull set and place it in the other. But now there will be another smallest uninteresting number. Repeating this process will make any dull number interesting.
more can be found here. Text
In the paradox of the arrow, Zeno asks us to consider an arrow in flight and argues that, in fact, the arrow must always be at rest. At each instant the arrow occupies a space equal to itself. Movement is impossible, because an instant by definition has no parts. If the arrow were capable of moving during an instant, we would contradict the definition of an instant, for the arrow would be in one position during the first part of the instant and in another position in the other part of the instant. Thus, the arrow never seems to be moving but rather, as Russell notes in his essay on infinity, "in some miraculous way the change of position has to occur between the instants, that is to say, not at any time whatever." If the arrow does not move at any given instant, how then does it make its flight?
-"Interesting" and "uninteresting" numbers
The question arises: Are there any uninteresting numbers? We can prove that there are none by the following simple steps. If there are dull numbers, then we can divide all numbers into two sets - interesting and dull. In the set of dull numbers there will be only one number that is the smallest. Since it is the smallest uninteresting number it becomes, ipso facto , an interesting number. We must therefore remove it from the dull set and place it in the other. But now there will be another smallest uninteresting number. Repeating this process will make any dull number interesting.
more can be found here. Text
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