Parmenides’ Argument

  1. There is a reason for everything. (Premise)
  2. No reason is possible for why the universe came into existence at t rather than at some other time. (Premise)
  3. Therefore, the universe did not come into existence at any time. (By 1 and 2)

 

Variant on Parmenides

  1. There is a reason for everything. (Premise)
  2. No reason is possible for why changing events in history happened when they did rather than all shifted over in either temporal direction. (Premise)
  3. Therefore, there are no changing events in history. (By 1 and 2)

Zeno’s Paradoxes

 

The Arrow

  1. If something during a period of time occupies exactly one location, it is at rest during that period of time. (Premise)
  2. In a now, something occupies exactly one location. (Premise)
  3. The arrow is always in a now. (Premise)
  4. The arrow is at rest in a now. (By 1 and 2.)
  5. The arrow is always at rest. (By 3 and 4.)

 

Dichotomy

  1. If something is to move to a goal, it must first move to the half-way point. (Premise)
  2. Before every movement, there is a prerequisite movement. (By 1)
  3. If before every prerequisite there is an earlier prerequisite, one will never have done the prerequisites. (Premise)
  4. Therefore, one will have never done the prerequisites to a movement. (By 2 and 3)
  5. One cannot do something without having first done its prerequisites. (Premise)
  6. Therefore, one cannot move. (By 4 and 5)

 

Achilles

  1. To catch the tortoise from a starting point behind the tortoise, Achilles always first move to where the tortoise is. (Premise)
  2. When Achilles gets to where the tortoise was, Achilles will be behind. (Premise)
  3. Therefore, to catch the tortoise, Achilles needs to make a series of movements, after each of which there is another. (By 1 and 2)
  4. If after every movement one needs to make to complete a task, there is another to be made, one will never be finished the task. (Premise)
  5. Therefore, Achilles will never be finished catching the tortoise. (By 3 and 4)

 

Stadium

  1. Time is discrete and points in time are evenly spaced. (Premise)
  2. BB and CC are moving linearly towards each other at a speed of one unit of length per unit of time, with each B and each C being of unit length.  Moreover, there are A’s of the same length arranged as follows initially.  (Premise)

BB->

 AA

 <-CC

  1. If two things are moving linearly towards each other and are of equal length, at some time they are side-by-side. (Premise)
  2. At some time t, BB and CC are side-by-side. (By 2 and 3)
  3. Two units of time after the start of the experiment, BB will stick out past AA, but CC will be under AA, and so they will not be side-by-site.  Nor will they be side by side at any time after that. (By 2)
  4. They are not yet side-by-side at the start of the experiment. (By 2)
  5. Thus, they are side-by-side at one unit of time after the start of the experiment. (By 1, 5 and 6.)
  6. One unit of time after the start of the experiment, BB is aligned with AA. (By 2)
  7. One unit of time after the start of the experiment, CC is aligned with AA. (By 7 and 8, and because alignment is transitive).
  8. Over one unit of time, BB has moved by one unit of length. (By 2 and 8.)
  9. Over one unit of time, CC has moved by two units of length. (By 2 and 9.)
  10. BB and CC move equal distances in equal time. (By 2)
  11. 1=2. (By 10, 11 and 12.)