Monday, March 23, 2009

Spatial and Temporal Zeno Walls

We might be familiar with the following puzzle.  Suppose that there is a football field at the end of an inclined plan.  On the field there are a bunch of walls, each facing the inclined plane.  One wall is at the 50 yard line, another wall closer to the inclined plane, at the 25 yeard line.  Still another wall is even closer to the invlined place at the 12.5 yard line and so one all the way to the end zone.  The walls form a zeno series whose open end is at the end zone at the foot of the inclined plane.  Now, suppose we roll a ball down the inclined plane.  The laws of nature in this world include the law that an object in motion remains in motion.  Moreover, there are no impuritied in the plane that will make the ball deviate from its course toward the zeno series of walls.  Finally, there are no stray objects that will intervene in the balls trajectory.  The ball will make it to the end zone and it will make it all the way to the zeno series of wells.  However, there are also physical laws that prevent the ball from passing through any walls and discontinuously passing through space.  So, the ball must stop before it passes through the end zone.  But, what makes it stop?  It can't be any one of the walls.  After all, if any one of the walls made it stop, then it must have reached that wall.  But, in order for it to reach that wall, it would have to pass through some previous wall.  That, however, is not physically possible.  Hawthorne has suggested that the fusion of the walls stops the balls.  This commits Hawthorne to a liberal view of composition.  I am inclined to say that the walls have irreducibly plural causal powers.  In any case, some thing or things has to stop the ball from moving.  Since there are no other objects in the vacinity, it must be that some walls or fusion of walls stops the ball from moving.  

Here is a new puzzle though.  Suppose that there is a man who is happily persisting through time.  He is healthy and the laws of nature are inconsistent with his sudden and unexpected demise.  However, at 12:20 tomorrow a solid object composed of a single substance and filling all of space comes into existence for a mere instant.  At 12:10 tomorrow, a solid object composed of a single substance and filling all of space comes into existence for a mere instant.  At 12:05 tomorrow, a solid object composed of a single substance and filling all of space comes into existence for a mere instant . . . and so on . . .  There is a zeno series of walls in time whose open end is at 12:00 and no member of which exists before 12:00.  The young healthy man will persist all the way to 12:00.  However, the laws of nature prevent a young healthy man from passing though the solid objects or discontinuously persisting through an interval of time.  So, the young man must stop persisting through time.  In other words, the young man must cease to exist at 12:00, he must die.  But, what stops him from persisting, what makes him cease to exist or die?  Just as before, we might think that the fusion of the walls stops the man from persisting.  But, that commits us to a liberal view of diachronic composition.  In fact, that solution seems to commit us to the existence of something that has temporal parts.  We might say that the walls have irreducibly plural causal powers.  But, then something that doesn't yet exist seems to cause something else to go out of existence.  These are strange consequences.  Nevertheless, something must make the young man cease to exist.  

This last puzzle is particularly troubling for a presentist.  We can describe a world like the one above using only presentist friendly phrases.  There is a man and at 12:20 tomorrow a solid object composed of a single substance that fills all of space will come into existence for an instant.  At 12:10 tomorrow  solid object composed of a single substance that fills all of space will come into existence for an instant . . . The laws of nature guarantee that the young man will make it to 12:00 in perfect health.  However, the young man will not exist after 12:00.  So, it must be that something will make him cease to exist.  But, at no time will there be anything that makes him cease to exist.  So, nothing will make him cease to exist.  But, it cannot be that something will make him cease to exist and yet nothing will make him cease to exist.  Perhaps we have a reason, then, to think that presentism is false.  

1 Comments:

Blogger Joshua said...

Update: I no longer think this poses a significantly more serious problem for presentism than the typical problem of causation. So, now I am most interested in the fact that a Hawthornean solution to these kinds of zeno puzzles commits him to a liberal view of diachronic composition. A plurals solution does not commit one to a liberal view of diachronic composition.

6:58 PM  

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