Argument at Parmenides 127e1-128a2

• The text:
• 127e1-128a3
  “Zeno, what do you mean by this? That if existences are many, they must be both like and unlike, which is impossible; for the unlike cannot be like, nor the like unlike? Is not that your meaning?”
  “Yes,” said Zeno.
  “Then if it is impossible for the unlike to be like and the like unlike, it is impossible for existences to be many; for if they were to be many, they would experience the impossible. Is that the purpose of your treatises, to maintain against all arguments that existences are not many? And you think each of your treatises is a proof of this very thing, and therefore you believe that the proofs you offer that existences are not many are as many as the treatises you have written? Is that your meaning, or have I misunderstood?”
• "No," Zeno replied. "On the contrary, you grasp the general point of the book splendidly."
• ...
• 129a1ff.
• (Socrates is speaking) "... tell me this: don't you acknowledge that there is a form, itself by itself, of likeness, and another form, opposite to this, which is what unlike is?"....
•  129e5-a3 (I think this is commenting on what is quoted above)
  Now I think this has been very manfully discussed by you; but I should, as I say, be more amazed if anyone could show in the abstract ideas, which are intellectual conceptions, this same multifarious and perplexing entanglement which you described in visible objects.
• That amounts to claiming that the argument at 127e1ff. is about visible object, the ordinary things in our physical world, sensible objects.
• Let's Try to Understand that Argument
• How will we know we have it right?
• It has to make sense to us.
• It is preferable if our effort does not use technical/advanced claims.
• It is preferable if we don't need to make assumptions that Plato clearly rejects elsewhere.
• Our conclusion has to pass the sniff test of whether Plato likely meant that.
• ....?
• SO, here goes:
• 1. Existences are many.
• This is an assumption made by Zeno purely for the sake of disproving it: he need not believe it.
• "existences" must refer to physical objects: see the two texts above (127a1ff and 129e5-a3) and how they are linked.
• Let's try restricting its reference to physical objects only insofar as they exist
• In other words, we aren't talking about that rock in all its aspects, but only insofar as it is an existent thing.
• So this premise means that the many physical objects we encounter constitute multiple existences.
• How are they multiple?
• Let's try the following: they are multiple in that one could count them and refer to them as existent thing 1, existent thing 2, existent thing 3
• This would likely mean something like that this rock (thing1) really is separate from that rock (thing2)
• 'really is separate', I take it, means that it's not a matter of how you look at it and it's not like the top half of the water in a glass and the bottom half of the water (we could call the top thing1 and the bottom thing2, but a quick reality check tells us that they are not really separate in any meaningful sense of separation that justifies calling them existence1 and existence2 in a way that means we've got 2 existences. I hope you agree with that without further specification.
• 2. Therefore, they must be like and unlike.
• As it stands, with no further explanation, this conclusion is preposterous.
• So we must find a way for it to make sense (because Socrates and Zeno and Plato were all smart enough to not be obviously stupid and mistaken). We do that by making assumptions we think are plausible about what 'like,' 'unlike,' 'like and unlike,' 'must,' and 'be' refer to in this conclusion as well as what the things in 1 refer to.
• How do we know if our assumptions are good ones?
• Because they seem, at first glance, plausible and reasonable.
• Because they make this conclusion result from 1.
• Let's try this out:
• in order to 'be many,' the existences must at a minimum be different from each other in a way that reliably grounds that claim that there is more than one, that they are countable, that they are the sort of things that ordinarily one can label with "1" and "2" and "3" and ...
• So thing1 must be different from thing2, and that's what "unlike" refers to.
• but in order to be "existences," all the things must share whatever "existing" is, and that is how they are "like."
• That is very simple, makes very few assumptions, is readily plausible, and allows for the conclusion of 2 from 1.
• We're done-ish here.
• 3. Which is impossible.
• What does 'which' refer to? The easiest, closest, most plausible candidate is "that the multiple existences are like and unlike"
• It's obvious that this rock and that rock (and any other physical objects) are both like each other in that they are both rocks and unlike each other in that this one is located here and that one there and this one inevitably has some slightly different shape or weight than that one, etc.
• But most importantly, there is absolutely no plausible way to call that way of being like and unlike 'impossible.' At least none that I can think of. Suggestions welcome.
• But what if we consider thing1 and thing2 exclusively as things that exist, and abstract away all other aspects of them? In other words, we ignore every other quality they have except the single quality that they exist.
• We used their mere existence above to justify claiming that they are like, and the mere assumption that they are multiple to justify claiming that they are unlike. That was all we needed.
• Consider
• they both exist: in that way surely they are like
• but this one is this one and that one is that one, and this one is not that one, and so they differ.
• How do we know they differ? Because the hypothesis said that we are considering what would be the case if there were two existences.
• now, we decided early on that they are physical objects, because of 129e5-a3. That helps us here, because that means they both exist in a similar way, physically. It's not as though this one exists spatiotemporally or mentally or outside of space and time or in a parasitical way on things that exist_really: they both exist in the same way.
• Now, how do we count existence? Isn't it like counting weight? I mean, sure I can have 2 weights, but insofar as they are weights, they have just one weight. Isn't it like saying that the top half of the water glass is one water and the bottom half another water? What principle individuates the existences? It's not just that, it's a question of what principle could plausibly individuate the existences.
• Even if there were a huge expanse of empty space and we had a rock in one place and another an immense distance from it, there would still be just one existence. Two rocks, sure, but considered purely as things that exist, one one existence.
• It's not even like if we had two red billiard balls as precisely alike in color as possible and said there were two reds there. In that case, we could point to the balls and say this red is at least HERE, while that red is THERE, and so they differ, if we think that place makes colors different. Why? Because it's just plain extra-ordinarily strange to think that place makes existence different. It would be like saying that place is more basic than existence and existence is dependent on place: that just makes no plausible sense. Sure, it's possible, but it's a strange idea, not one that should start off a dialogue and never be explained.
• What makes immediate, easy sense is that existence is either like a species or like a bunch: if you have one species and add a bunch of new members, you don't get more species, and if you have a bunch and add a bunch more, you've still got one bunch. If you add butter to butter, you don't get two butters: you get butter.
• Consider: if you have one universe, and then you just snap your fingers and create another universe, do you really get two universes? or is it just one larger universe? I know, in science fiction, you can have lots of universes that are often only barely accessible to each other, but here's the thing: even there, that they are accessible to each other at all makes them ONE universe, no?
• I'm a little worried about that "immediate, easy sense," but it does at least seem, at first glance, acceptable.