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Melissus reaffirms Parmenides by explaining how there cannot be many without the existence of that which is empty, and since that which is empty is nothing, and nothing can't exist, thus there cannot be many.

It seems to me that they associate "nothing" (that which is not) with "empty" (not spatially extended) by definition, and then furthermore "nothing" cannot exist by definition. So, the only rationale for the nonexistence of that which is empty is an "intuitive" one rather than a logical one?

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    The argument is clearly based on "analogy" and not on rigorous logical steps (in modern sense...) It says : (i) many (read as : many things, in a more or less "physical" meaning) can be "separated" in some way only if "contained" in some "empty vessel" : see the newtonian concept of space. (ii) the empty is nothing, presumibly because we cannot perceive/interact with it. (iii) nothing can't exists. Therefore... We can argue against (ii) : see modern set-theoretic notion of "the emptyset", that in the framework of set theory exists, and against (iii) : exists is a quantifier and not ... 1/2
    – Mauro ALLEGRANZA
    May 11 '15 at 8:01
  • ... a property of an "object"; thus saying that something (the empty) does not exists (is nothing) means exactly "the empty does not exists" and we have reached no new information, because all stands on assumption (ii) : the empty does not exists.
    – Mauro ALLEGRANZA
    May 11 '15 at 8:04
  • If the reasoning is as you say, then it's a simple equivocation: that of deception or misunderstanding based on the same word being used in two or more different senses. Nothing is better then butter. But lacking butter, margarine is better than nothing. Hence, margarine is better than butter.
    – Cheers and hth. - Alf
    May 11 '15 at 9:59
  • See Melissus of Samus for details.
    – Mauro ALLEGRANZA
    May 11 '15 at 12:57
  • @MauroALLEGRANZA, so then the entire argument rests on that one assumption that "the empty does not exist" with the rationale: "because we cannot perceive/interact with it", which we might claim is false in an attempt to argue against it, it seems? Well that makes sense, and I think that matches my understanding. Thank you!
    – personjerry
    May 12 '15 at 3:18

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