Monday, March 06, 2006

I came across why Black's argument is fallacious on the Stanford Encyclopedia of Philosophy (

Black's argument, in case you don't remember it or didn't read, says basically that you've got a machine that can take a ball and move it from point A to point B over some time t. It keeps moving it back and forth, until at some final time it's oscillating back and forth infinitely fast, so that in the time t the machine performs a super task. We ask whether this is logically possible in order to deduce whether a supertask can be performed... Of course, Black derives a contradiction from this, saying that if a supertask was performed, then the state of the ball (whether its at A or B) cannot be determined (by one argument it's at A; by another, it's at B; it can't be at both places at the same time, so there's a contradiction.) What the Stanford Encyclopedia of Philosophy says is that Black's entire reasoning is false for the following reason: the state of the ball (whether it's at A or B) is not determined by what has occured to the ball before that time. In their own words:

"His argument is fallacious because he seeks to reach a logical conclusion regarding instant t* = 1 P.M. from information relative to times previous to that instant.. In the standard argument against Zeno's dichotomy one could similarly specify Achilles's position at t* = 1 P.M. saying, for instance, that he is at B (x = 1), but there is no way that this is going to get us a valid argument out of a fallacious one, which seeks to deduce logically where Achilles will be at t* = 1 P.M. from information previous to that instant of time."

What do you guys think about this?


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