The Dichotomy Argument

Question 1

the Dichotomy Argument

Answer 1

1) In order for anything to move, it must do an infinite number of things in a finite amount of time.
2) It is impossible to do an infinite number of things in a finite amount of time
3) So, it is impossible for anything to move

Question 2

explanation for (1) in the Dichotomy Argument

Answer 2

• In order for an object to reach a distance (x) in front of itself, it must first travel half of that distance (½x). Zeno argues, once an object has traveled this distance, it must travel half of the distance between itself and (x) again – (¼)… ad infinitum.
• Every time the object gets to a halfway point, there will always be a next halfway point to be reached.
• “Chicken crossing road example”

Question 3

explanation for (2) in the Dichotomy Argument

Answer 3

• Zeno appeals to intuition in the sense that it seems absurd that anyone can do an infinite amount of things in a finite amount of time.

Question 4

infinitely divisible

Answer 4

To be infinitely divisible, something must be able to be broken into an infinite amount of parts. For example, a distance (or time)

Question 5

infinite in extent

Answer 5

To be infinite in extent, is to have an endless magnitude. For example, a slope on a Cartesian plane extends in both directions to infinity.

Question 6

objection to the dichotomy argument

Answer 6

When something moves in a finite amount of time,it is not traveling a distance which is infinite in extent. It is simply traveling a finite distance which can be infinitely divisible. Both time and the length of the road are finite but also are infinitely divisible.

Question 7

outline for the Dichotomy Argument

Answer 7

1) explain (1)
2) explain (2)
3) infinitely divisible
4) infinite in extent
5) distinction in use of infinite
6) object by denying premise (2)