Parmenides, Stage 2

Parmenides: Stage 2

After establishing his central thesis, that it is impossible to think or talk about what does not exist, Parmenides attempts to deduce from this thesis the following conclusions:

There is no coming into existence or ceasing to exist.
There is no alteration or change.
There is no movement.
There is no plurality.

How did Parmenides get from his central thesis to these extraordinary conclusions?

Generation & Destruction
Suppose you say that something, x, comes into existence. That means that you are committed to saying that there was a time when x did not exist. So you are committed to talking about what does not exist. But you can’t do that. So you can’t say (i.e., it makes no sense to say) that anything comes into existence. (Parallel argument for the impossibility of ceasing to exist.)
Given that there can be no coming into existence or going out of existence, important consequences follow. Parmenides seems to have thought that it followed that there could be no difference between past, present, and future. Cf. 8=B8:

Nor was it ever nor will it be, since it is now, all together, one, holding together. ... it is right either fully to be or not.
Parmenides would no doubt support this inference as follows: How could the present differ from the past, or from the future? Any difference from one time to another would involve some (previous) state of affairs going out of existence, and some (new) state of affairs coming into existence to replace it.
That is: if there is no generation and no destruction, then there can be no temporal differences. The world is exactly the same at one time as it is at any other time.
Change
It is clear that without temporal differences, there can be no change. For change involves the world being different from one time to another, and such differences would involve things coming into or going out of existence.
We can get some confirmation that this was Parmenides’ line of thought by looking at what his follower Melissus wrote (7=B7). If something were to change or alter, what was previously the case would have to cease to be the case, and what previously was not the case would come to be the case. I.e., if the barn changes color, it (say) becomes red. I.e., the barn’s being red comes into existence. But that’s already been ruled out.
(Melissus puts it in terms of arrangements, not states-of-affairs: if a thing changes in any respect, it is “rearranged”; if it is rearranged, a new arrangement comes into existence. But nothing can come into existence.)
Movement
Melissus’s version of the argument has it that movement can occur only if the moving thing has an empty space to move into, and that the empty is the same thing as nothing, or not-being. But not-being can’t be. So there can’t be any movement.
Parmenides might, however, reach the same conclusion by a different route: movement is just a kind of change (change of location), and change cannot occur unless temporal differences are real. But Parmenides has rejected temporal differences. Suppose you move from Seattle to Chicago. That means that you are in Seattle at one time and in Chicago at another time. But that’s impossible, for there’s no difference between the way the world is at one time and the way it is at any other time.
Plurality
Here it is hardest to see what Parmenides’ argument might have been. Why can’t there be a world of many ungenerated, unchanging, indestructible things? (Cf. atomism). Parmenides does not seem to give any argument against plurality, but the tradition has counted him as a monist, who believes that reality is one and that there cannot be a plurality of things.
A number of recent interpreters, including Barnes, go against the tradition, claiming that Parmenides was not a monist! Cf. Presocratics, p. 207. This is an intriguing idea, but not completely convincing. For when Zeno argued against plurality, he thought he was supporting Parmenides. If Zeno had been wrong about this, Parmenides could have corrected him!
Certainly Melissus, a follower of Parmenides, thought that it was a consequence of Parmenides’ arguments that there could be no plurality. So it is worth considering how one might construct a Parmenidean argument against plurality. There are several possible lines one might take. It is not clear, however, which (if any) of these Parmenides would have followed.
1. Suppose there were more than one thing. Then there would have to be something separating one from the other, otherwise they would not be two. But then what separates one from the other? Is there a space between them? No, that can’t be, for there is no empty space. Is there then no space between them? Then they run together, and are one, not two.
2. If there were two things, (say) Castor and Pollux, it would be true to say that one of them is not the other, i.e., that Castor is not Pollux. But then we are “saying what is not,” which is impossible.
  [But how is that a case of talking about what does not exist? When we say that Castor is not Pollux, what is the non-existent thing we are denying the existence of? A devout Parmenidean would have to say that we are denying the existence of Castor’s being Pollux.]
3. A more plausible line might go like this: Parmenides thinks that the world is devoid of movement or qualitative change. He would presumably also hold that there cannot be any qualitative difference; indeed, there cannot be difference of any kind.
  For suppose there is a difference between a and b. That means there must be some property, F, such that a is F and b is not F. But when you say that b is not F you are violating Parmenides’ rules; for you are saying that the F-ness of b does not exist.
  So the universe is devoid of difference of any kind. So how can a and b be two things? There is no difference between them. There is no property that a has and b lacks. So a = b. And, generalizing:
  
  For any x and for any y, x = y
Negation and non-existence
On any interpretation, it seems that Parmenides would say that any denial (any negative statement) is a denial of existence. And it is easy to see why a Parmenidean would hold that a denial of existence cannot be both meaningful and true. For if it were true, then what it is about would be non-existent. So it wouldn’t be about anything. And if it’s not about anything, then it is not even meaningful. If you can’t talk about what doesn’t exist, then you can’t even deny its existence. So denials of existence (“negative existential statements”) are impossible.
[“x does not exist” is not true unless x does not exist. But if the subject of a statement does not exist, the statement is not meaningful. The problem with negative existentials is this: a necessary condition of their truth is a sufficient condition of their meaninglessness.]
The best response to Parmenides here is to point out (as Plato did) that not all denials are denials of existence. When one says that cows don’t fly, one is not referring to flying cows, and saying of them that they don’t exist. One is referring to cows, and saying of them that they don’t fly.
Conversely, the statement that birds fly should not be analyzed as referring to the flying of birds and saying of it that it exists (even if it seems harmless to do so). It is not the statement as a whole that refers, but only its individual parts.
“A statement must have existential force”: yes, but only in the sense that its (simple) terms must refer to things that exist. But that doesn’t mean that the statement itself must refer to something else (a “fact,” or a “state of affairs”) that exists.
A summary of Parmenides’ views
1. He makes some basic assumptions about thought and existence:
  1. x can be thought about iff x can exist.
  2. if x does not exist, then x cannot exist.
2. From these basic assumptions, he derives his central thesis:
  
  It is impossible to talk or think about what does not actually exist.
3. From this central thesis, he derives several important corollaries that fly in the face of common sense:
  
  There is no such thing as: generation and destruction, motion, change, qualitative difference, plurality.
4. The argument for these corollaries is that anyone who tries to assert that there is such a thing as change (etc.) is reduced to attempting to talk about what does not exist.
A summary of Parmenides’ errors
1. He thought that what does not exist could not exist (possibly confusing this idea with the truism that, necessarily, if something does not exist then it does not exist).
2. He thought that denials of existence are impossible (i.e., they cannot be both meaningful and true).
3. He thought that all denials, all “is not”s, are denials of existence.

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