Negation and non-existenceOn 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 meaningfuland 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 denyits existence. So denials of existence (“negative existential statements”) are impossible.[“xdoes not exist” is not true unless xdoes 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
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Existence, Necessary and sufficient condition