Unformatted text preview: t and t 1 The argument then looks like this: 1c. If there is a p such that for every i , L ( p , i ), then R . 5 p 2200 i L ( p , i ) → R 2c. For every i , there is a p such that: L ( p , i ). 2200 i €5 p L ( p , i ) But (2c) is not equivalent to, and does not entail, the antecedent of (1c): There is a p such that for every i , L ( p , i ) 5 p 2200 i L ( p , i ) The reason they are not equivalent is that the order of the quantifiers is different. (2c) says that the arrow always has some location or other (“at every instant i it is located at some place p ”)  and that is trivially true as long as the arrow exists! But the antecedent of (1c) says there is some location such that the arrow is always located there (“there is some place p at which it is located at every instant i ”) and that will only be true provided the arrow does not move! So one cannot infer from (1c) and (2c) that the arrow is at rest....
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 Fall '09
 JorgeRigol
 Logic, arrow, instant

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