Parmenidean Arguments

Existence and Thought1. There are no non-existent objects.

2. If (1), then there are no non-existent objects that have any properties.

3. Therefore, there are no non-existent objects that have any properties. (1,2 MP)

4. If (3), then whatever has any properties exists.

5. Therefore, whatever has any properties exists. (3,4 MP)

6. If (5), then if A has the property of being spoken or thought of, then A exists.

7. Therefore, if A has the property of being spoken or thought of, then A exists. (5,6 MP)

8. If (7), then if A can be spoken or thought of, then A exists.

9. Therefore, if A can be spoken or thought of, then A exists. (7,8 MP)

10. If it’s true that if A can be spoken or thought of, then A exists, then it’s true that if A does not exist, then A cannot be spoken or thought of. (Law of logic)

11. Therefore, if A does not exist, then A cannot be spoken or thought of. (9,10 MP)

No Generation Argument12. If (11), then it’s not the case that what is came from what is not.

Explanation: Call what is ‘Gary’ and what is not ‘Bob’. Then the idea that Gary was generated/born/had a first moment is the idea that Gary came from Bob. But now suppose (11) is true. Then Bob is nothing; i.e., Bob is non-existent. So Bob cannot be spoken or thought about. So there is no proposition that Gary came from Bob. So it’s not the case that Gary came from Bob. So (12) is true.

13. Therefore, it’s not the case that what is came from what is not. (11, 12 MP)

Parallels to the

No Generation Argument may be given for the conclusion that what is is indestructible.

No Change/Motion Argument19. If what is changes, then what is goes from not being F to being F.

20. If what is goes from not being F to being F, then there is a state of affairs that what is is not F.

21. Therefore, if what is changes, then there is a state of affairs that what is is not F. (19, 20 HS)

22. If (11), then there is no state of affairs that what is is not F.

(Explanation: Call the fact or state of affairs of what is being F ‘Roy’. Then the thought that what is is not F is the thought that Roy does not exist. But by (11), it cannot be thought that Roy does not exist.)

23. Therefore, there is no state of affairs that what is is not F. (11, 22 MP)

24. Therefore, what is does not change. (21, 23 MT)

25. If what is does not change, then what is does not move.

26. Therefore, what is does not move. (24, 25 MP)

No Plurality Argument27. If there is more than one thing, then something is true of one thing and not another.

(Explanation: Suppose that there are at least two things, A and B. If A is distinct from B, then A must have some property that B does not have. One plausible candidate for the difference is that A must be located where B is not. An even more plausible candidate is that A has the property of not being B. A must have this property, given our assumption. So (27) is true.)

28. If something is true of one thing and not another, then there is a state of affairs that something is not F.

29. Therefore, if there is more than one thing, then there is a state of affairs that something is not F. (27, 28 HS)

30. If (11), then there is no state of affairs that something is not F.

31. Therefore, there is no state of affairs that something is not F. (11, 30 MP)

32. Therefore, there is not more than one thing. (29, 31 MT)