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Parmenides holds that the purpose of inquiry is either to determine the existence of something (so as to say that whatever is, is indeed the case) or the nonexistence of something (so as to say that something is not the case). He then points out that the former mode of inquiry is justified in that it seeks that which is, while the latter is a matter of illusion, since we cannot determine or find that which is not. This thus leads Parmenides to conclude that there is only 'the one' that is constant and continuous.

But is Parmenides himself not assuming knowledge of that which 'is not', namely knowledge about the mode of inquiry that seeks that which is not? For in order to justifiably categorize such thought as illusion rather than his own thought, which he assumes to be truth, Parmenides must possess a comparative knowledge of that which is (namely the truth he possesses) and that which is not (namely the illusion that beguiles those whom he criticizes). But such comparative knowledge unavoidably is a knowledge that posseses sense of being and nonbeing. If Parmenides would counter with a point so as to say that the knowledge he possess about such nonexistence or nonbeing is indirect, as to be an inherent aspect of the 'one' ( though this would contradict Parmenides's rejection of pluarality), than his argument would become entirely trivial, in that those who speculate about that which is in terms other than Parmenides's could likewise be speaking of such nonbeing in an indirect way, and as such needn't be subject to the main criticism offered by Parmenides.

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  • What is "comparative knowledge"? And does it mean "to possess sense" of something?
    – ejQhZ
    Dec 10, 2015 at 2:13
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    Comparative knowledge is knowledge that one possesses that allows for a comparison to be made, in this case the comparison between two forms of inquiry. Parmenides cannot have knowledge of only one type if he postulates about both, and therefore has knowledge of both of the types that he postulates about. If he holds that he has knowledge of one, specifically inquiry into nonbeing, in an indirect way, his argument becomes trivial, since the force of the argument is to say that we cannot inquire into nonbeing.
    – Chosen One
    Dec 10, 2015 at 13:16
  • I see. At first I understood comparative knowledge as something like saying "this is something, that isn't something", which is to that say I understood it as either affirming or denying a predicate, for two different things. But am I far off in this? Because it seems to me that in order to compare any two things, I must have knowledge of each of them (given some definition "knowledge") and the knowledge of each must relate to which other. In the case of Parmenides, you mean that his saying "this way is true, that other way isn't true" would imply some knowledge of the latter?
    – ejQhZ
    Dec 10, 2015 at 13:52
  • As to the last question, yes (I think). Since I consider 'true' to be a synonym to 'exist', I view Parmenides's claim that the mode of inquiry into that which is illusion (aka, that which is not true) is to say that in some manner it 'is not'. But in order for Parmenides to make such a determination requires that Parmenides not only make a determination of the sense in which the inquiry is not true but also that he make a determination about that which simply is not, since the determination of an illusion comes in the knowledge of its object, which is nonbeing.
    – Chosen One
    Dec 10, 2015 at 17:06
  • Parmenides could of course counter with the point that such a determination is not a direct determination of literal nonbeing, but rather an indirect determination about how being must be (which therefore allows us to somewhat see the sense in which being cannot be). But as stated, this counter would only make Parmenides's point trivial, since those whom he criticizes as having knowledge of nonbeing (which is to him an impossibility) could simply hold that they have indirect knowledge of nonbeing, in the sense Parmenides does regarding his determination of illusion.
    – Chosen One
    Dec 10, 2015 at 17:09

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But Pamenides writed before the Greek "birth" of logic; see his Poem.

Thus, it is hard to analyze it in terms of "logical arguments".

In a sense, we can say that logic was "codified" by Aristotle also reacting on Parmenides' younger associate : Zeno of Elea and his paradoxical arguments.

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Parmenides is told by the unknown goddess that he meets, after being let through the gates of night and day by Dike (Justice); not that the 'purpose' of enquiry is to determine the existence of things, but that:

it is right to learn you learn all things -

both the unshaken heart of well-rounded Truth

and the beliefs of mortals, in which there is no true trust

He's told further that the:

the one, that is and that it is not possible for it not to be

is the path of Persuasion (for it attends on truth)

and:

the other, that it is not, and it is right that it not be

this indeed, I declare to you to be a path that is entirely unable to be investigated

For neither can you know what is not (it is not to be investigated)

Nor accomplish it

One can concieve, obviously, what exists; for example, a Walrus; but also what can possibly exist, though in fact it doesn't, never has or might never be; for example, a unicorn.

He is told, it isn't possible to concieve what isn't possible to concieve.

This, itself, is a conception; something then can be possibly concieved - I just did it, and wrote it.

And not to be confused with what is in-itself, is not - at all.

This, then - doesn't nullify the path pointed out by the goddess.

It's worth pointing out that though Aristotle is dismissive of Parmenidean accounts of nature - this is as mere platitude or sophistry

Now, to enquire whether being is single and unchanging is no part of an enquiry into nature ... [and] because both Melissus and Parmenides argue sophistically; indeed, their premises are false and their conclusions don't follow.

But in fact, Aristotles onto-logic is pervasively influenced by Eleatic monism; as Hegel notes in his Logic.

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