Evaluation of the argument It is clearly a formally valid argument. But is it sound? The first premise seems plausible: how could a thing exist if it is not even possibleto speak or think about it? And how could one speak or think about something that could not even possiblyexist? But what of the second premise [(5) in our reconstruction of Parmenides’ argument]? It seems false to say that only what actually, in fact, exists could possiblyexist. Why should Parmenides believe this? a.Barnes (Presocratics, p. 167) suggests the following: “What doesn’t exist can’t exist” is ambiguous. It might mean either of the following (which are not equivalent): i.It is not possible that what does not exist exists.2200x¬(Ex& ¬Ex) i.e., for any object, necessarily, if it doesn’t exist, then it doesn’t exist.2200x(¬Ex→¬Ex) [‘’ means ‘it is necessary that’.]ii.If a thing does not exist, then it is not possible for it to exist.
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