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Parmenides’s Argument in the “Way of Truth”

  1. Necessarily: anything one cares to consider either exists or doesn’t exist (but not both). [Premise]
  2. It’s impossible that anything should both exist and not exist. [From 1]
  3. Consider any one of the things that exist, x. [Premise]
  4. It’s impossible for x not to exist. [From 2, 3]
  5. x necessarily exists. [From 4]
  6. Thus, everything that exists necessarily exists. [From 3, 5]
  7. We can speak/think of x iff x exists. [Premise – cf. frag. 3]
  8. So any sentence of the form ‘x doesn’t exist’ is meaningless. [From 7]
  9. Hence, everything exists. [From 8]
  10. Therefore, everything necessarily exists – “It is, and it is not possible for it not to be.” [From 6, 9]

The Determination of  “It”

The first stage of the Way of Truth seeks to establish Parmenides’s thesis that “it is, and it is not possible for it not to be.”  Within that context, the referent of ‘it’ is indeterminate: ‘it’ can pick out anything you like (witness premise 3 in the argument above).

However, the second stage of the Way of Truth seeks to establish the consequences of the thesis, and these are substantive:

  • It is ugenerated and imperishable (CCR passage #8, ln. 3, lns. 26-7)
  • It is homogeneous – “of a single kind” (ln. 4)
  • It is timeless/atemporal (lns. 19- 20)
  • It is solid/continuous (lns. 22-4)
  • It is unchanging (ln. 26)
  • It is immobile (lns. 29-30)
  • It is unique (ln. 29)
  • It is perfect/complete (lns. 32-3)
  • It is spherical (lns. 42-5)

In short, it is a timeless, unmoving, homogeneous sphere, and it is all that exists!  (Parmenides’s “it” comes to be known as “the One” by subsequent philosophers.)

Question #1: is Parmenides’s argument in the first stage of the Way of Truth sound?

Answer (a): No.  The inference at line 4 is invalid.  Compare:

2.’ It’s impossible that any door should be both closed and open.
3.’ Consider any of the closed doors, x.
4.’ It’s impossible that x should be open.

Both inferences take the following form:

It’s impossible that conditions A and B should jointly obtain.
Condition A obtains.
So it’s impossible that condition B should obtain.

This is a bad inference, and those of us inclined to use the jargon call it a “modal scope fallacy”.  What follows is that B doesn’t in fact obtain, not that it’s impossible that it should obtain.  So what really follows from premises 2 and 3 in Parmenides’ argument is that x (whatever you chose) doesn’t in fact not exist – i.e., that it does in fact exist.  But that’s hardly surprising!  So this crucial stage of the argument fails.

Answer (b): The premise at line 7 stands in need of justification.  Why would he make this claim?  I conjecture that Parmenides might have had a peculiar view about the nature of meaning.  Compare:

The extension (or reference or denotation) of the word ‘cat’ is just all the cats that there are (and, perhaps, ever have been, will be, etc.).

The intension (or sense or connotation) of the word ‘cat’ is ‘furry, four-legged mammal that meows, chases mice, likes milk (etc.)’

Extensional meaning connects words with objects (nonlinguistic objects, typically); intensional meaning connects words with other words.

If Parmenides thought (only implicitly, since such distinctions were not explicitly drawn in his time) that the only legitimate variety of meaning is extensional (or referential/denotational), he could insist that terms like ‘unicorn’ have no meaning at all, since there are no unicorns.  Thus, to assert that unicorns do not exist is (in his view) not true.  Nor is it false.  It is, on this understanding, strictly meaningless, because it fails to assert anything in particular.

But this is to adopt an impoverished view of meaning.  Surely (right?) one can meaningfully say that ‘unicorn’ means ‘horse-like creature with a single horn protruding from its forehead, often possessing magical powers’ even if one is prepared to deny the existence of unicorns.  One is free to argue that the notion of intensional meaning is somehow incoherent, but Parmenides offers no such argument.

Question #2: what about Parmenides’s determination of “it” – is that compelling?

Answer: Not obviously so.  Most of the alleged consequences rely on Parmenides’s apparent (and very general) proscription against “saying what is not” – that is, his proscription against making negative assertions of any kind.

For example, the first alleged consequence might be argued for as follows:

  1. If it were generated, there would have been a time at which it did not exist.
  2. It is meaningless to assert that it does not exist.
  3. So to assert that it was generated is meaningless – it is therefore ungenerated.

The uniqueness of “it” might be argued for this way:

  1. If there were a plurality of things, then one thing would not be the other.
  2. It is meaningless to assert that one thing is not the other.
  3. So to assert that there is a plurality of things is meaningless – there is therefore only one thing.

And so on.  But the underlying proscription against making negative assertions seems to be something that Parmenides takes as self-evident (or perhaps to be a corollary of his thesis?), and it is not at all self-evidently true.

Conclusion: the argumentation in Parmenides’s Way of Truth is flawed, and in several distinct ways.  Nonetheless, these flaws are interesting and instructive.  Moreover, the very fact that Parmenides undertook such an ambitious project and urged us to not “direct [our] sightless eye and sounding ear and tongue, / but judge by reason the heavily contested testing spoken by [him]” marks a fundamental turning point in philosophical methodology.  He set a new standard for doing philosophy.