Parmenides' legacy is to challenge us either to forego talk of non-being
or to ensure that all such talk is conceptually coherent. He did not think that
any talk of non-being could be coherent, and so he urges us all to
abandon such talk. If we are not persuaded that a move this radical is
warranted, then we at least owe Parmenides the posthumous honor of showing him how
talk of non-being is not confused and mistaken at its very core.
We will see how pluralists Empedocles, Anaxagoras, and Democritus address
the problem. They agree with Parmenides that non-being cannot in any way exist
(except for Democritus' void), and agree with him that this entails that
fundamental change cannot happen (for then being would have to change into
something other than itself, namely, non-being). Where they reject Parmenides
is that they think that there is a less-than-fundamental change that does
happen. Empedocles, Anaxagoras, and Democritus think that although the
primitive things (the four elements, the seeds, and the atoms, respectively)
cannot come to be or pass away or even change at all, entities derived from the
primitives (e.g., tables, trees, people) come to be and pass away and
change their qualities and size, et cetera. We will later see that
Plato's solution is similar (the primitive things do not change), yet different in an important way (what sorts of things
are primitive).
In order to facilitate our discussion of a difficult topic, I want you to
feed upon this chart for a while. It contains twelve examples of declarative
sentences, categorized on four parameters: whether the sentence seems true or
false, whether the sentence is affirmative or negative, whether the subject of
the sentence exists or not, and whether the sentence seems to be existential or
predicational (a distinction I'll explain below).
|
|
Apparent
Truth Value (True/False) |
Affirmative/Negative |
Existent/ |
Existential/ |
Example |
|
1. |
T |
Aff |
ExS |
Ex |
Biden is. |
|
2. |
F |
Aff |
NExS |
Ex |
Santa Claus is. |
|
3. |
T |
Neg |
NExS |
Ex |
Santa Claus is not. |
|
4. |
F |
Neg |
ExS |
Ex |
Biden is not. |
|
|
|
|
|
|
|
|
5. |
T |
Aff |
ExS |
Pr |
Biden is Democratic. |
|
6. |
F |
Aff |
ExS |
Pr |
Biden is Republican. |
|
7. |
T |
Neg |
ExS |
Pr |
Biden is not Republican. |
|
8. |
F |
Neg |
ExS |
Pr |
Biden is not Democratic. |
|
|
|
|
|
|
|
|
9. |
T |
Aff |
NexS |
Pr |
Santa Claus is bearded. |
|
10. |
F |
Aff |
NexS |
Pr |
Santa Claus is underweight. |
|
11. |
T |
Neg |
NexS |
Pr |
Santa Claus is not underweight. |
|
12. |
F |
Neg |
NexS |
Pr |
Santa Claus is not bearded. |
A. The simplest cases of what cannot be declared
The Parmenidean would deny the legitimacy of all of these sentences, for
all that the Parmenidean thinks can be said (or even thought) is "Being
is," or its equivalents, like "Reality is," "The One
exists," "The existent is real, " etc. To assert
existence of anything else, to say that something is besides Being, is to say that something that is not Being
is. And this, to a Parmenidean mind, is to say that non-Being has being, a
proposition which I think we would all agree is at least conceptually
problematic, if not downright off-limits. So even the simplest of the above,
sentence (1), says that something that is not identical with Being
(namely, Biden) is Being (that is, exists), and would therefore be no
more sensible than saying that Biden is not Biden.
The Parmenidean will extend this objection to claims like (5) and (6).
Although not as simple as (1), it is still the case that in asserting (5) or
(6) we are asserting something which seems to require sense to be made of (1).
After all, if we can't say that Biden is, then
how can we say that Biden is something as opposed to something else?
These points are what Parmenides is making in the first four
lines of a fragment from him:
But come now, I will tell you—and you,
when you have heard the story, bring it safely away—
which are the only ways of inquiry that are for thinking:
the one, that is and that it is not possible for it not to be,
is the path of Persuasion (for it attends upon Truth),
the other, that it is not and that it is right that it not to be,
this indeed I declare to you to be a path entirely unable to be investigated:
For neither can you know what it is (for it is not to be accomplished)
nor can you declare it.
(fragment 2, from Proclus and from Simplicius, as rendered in Curd’s A Presocratics
Reader, pp. 57-58)
B. The
Parmenideans against non-existent subjects
The final four lines of this fragment point toward another counterintuitive
position of the Parmenideans: sentences (2), (3), and (9)-(12) are illegitimate
(that is, not declarable). These are sentences with a non-existent subject, and
so are attempts to say something about nothing. They are
attempting to say something about that which doesn't exist, and that which
doesn't exist is nothing. To try to say that Santa Claus is bearded is
to try to take something and describe it in some way. But what if there's no something
there? What is it that is being described? What is it that is being
"declared"? Parmenides' answer is "Nothing." And if nothing
is being described, then there's not any describing going on. We can no more
talk about something that is not (that is, that is nothing) than we can kick a ball
that doesn't exist. There's nothing there to receive the doing.
Sentence (9) certainly seems true, but if so, then how? For if (9)
is true, then the state of affairs described by the sentence would have to
obtain. Trouble is, how could Santa be bearded if he doesn't
exist? In other words, what does the subject of (9) refer to? (This
problem will sound familiar to you.) In response, we might say, "Sure,
there is something to be described, even if it's not Santa Claus. What
we're talking about when we talk about Santa Claus is our concepts of
Santa." This is the claim that (9) gets to be true because its subject
refers to "the concept of Santa" or to "stories about
Santa."
But the Parmenidean has two good objections to this attempt. First, then (9)
would be false; concepts are amazing things, but they can't grow hair.
Secondly, sentence (2) would become true and (3) would become false. If talk of
Santa is talk of the concept of Santa, then to say that Santa Claus doesn't
exist is to say that our concept of Santa Claus doesn't exist--and this
surely seems to be false. After all, how can we allow a reinterpretation of the
subject of (9) (through [12]) without consistently endorsing the
reinterpretation everywhere? How can we argue for different treatment without
being ad hoc?
C. The Parmenideans against negative
sentences
So far we have seen how the Parmenidean rejects nine of the above dozen
sentences--all but (4), (7), and (8). The final four lines of the above
fragment actually indicate that even these last three sentences are to be
rejected, though in a way more tricky to grasp. The Parmenidean will reject as
well-formed sentences (3), (4), (7), (8), (11), and (12)--in other words, any
sentence that is a negative. (Given the preceding paragraph, this means that [3],
[11], and [12] are to be doubly rejected.) The Parmenidean reasoning is that
these examples require that the subject be-not, which seems to entail that the
subject is not doing any being. To be not is to not be; to not
be is to not be anything at all; to not be anything at all is
to be nothing at all; and to be nothing at all is to not even
be a possible object of thought and discourse. So for something to be not
(whether it's "be not, period" or "be not bearded") would
require that something be nothing at all, which just about anyone
would grant is impossible.
D. Objection based on the existential vs. the
predicational "is"
One fairly common attempt to try to escape from the oddness to which
Parmenidean logic would seem to consign us is to insist that Parmenides is
running together two very different sorts of statements: the claim is that the
"is" in, say, (4) means something very different from the
"is" in (8). Yes, they have the same truth-value as each other, along
with matching in the other parameters listed above, but, the criticism goes,
they arrive at the same truth-value in two very different ways. To be not-something
(like not Republican) isn’t the same as to not-be. To not be
is to not exist, but this isn’t so for not
being this or not being that.
This criticism notes that the use of "is" is common to
(1)-(12), but maintains that this masks a fundamental difference in two senses
of "is." The "is" in (1)-(4) can be replaced by
"exists" without any loss of meaning. (In fact, the resulting replacement
would give us a more common way of speaking.) It is noted, however, that the
"is" in (5)-(12) cannot be so replaced. This points to what has come
to be called the distinction between the existential "is" (used in
the first four examples) and the predicational "is" (used in the
fifth through twelfth examples). And this claim amounts to the criticism that
the Parmenideans get themselves into trouble only by failing to distinguish
between the existential and predicational senses of being. (In case you’re
familiar with this term, this criticism would amount to charging Parmenides
with equivocating on the word “is.”)
I repeat that this criticism, if sound, is more general than driving a
wedge between (4) and (8). The wedge would insert itself between the first four
and everything else. So what might seem to be each of the first four and its
twin (in terms of the parameters listed in the three descriptive columns
above)—pairing (1) and (5), (2) and (6), etc.—would actually constitute
two very different items, the first being existential and the second
predicational.
E. Two Parmenidean defenses against this objection
There is something tempting about this criticism, for it does seem a
clean way to cut through the Parmenidean logical knot. But there are at least
two problems with dismissing Parmenides on this basis. Each of these problems
may or may not be solvable, and that is where the exercise of your noggin’s own
good judgment is called for.
First, is there a distinction between the existential use of
"is" and the predicational use? Mightn’t the
existential use predicate something of the subject, namely predicate existence, just as I predicate redness of the apple
when I call the apple red? If so, then the difference between, say, (1)
and (5) isn’t one of logical kind, but rather simply
that something different is being said of Biden in the two statements. It would
then seem that we could get no more philosophical mileage out of the
"predicating simply-existence" use of is vs. the "predicating
something-other-than-simply-existence" use of is than we could get out of any other two predications. For
example, since Parmenideans need not (on these grounds) be bothered by the fact
that some propositions predicate a certain age of Biden, whereas other
propositions predicate a certain height of him, why should the Parmenideans be
especially bothered by someone pointing out to them that some statements
predicate existence of Biden, whereas others predicate a political affiliation?
Second, even if this first attempted defense of the Parmenideans does not
work, and the Parmenideans have to give up on their objections to negative
sentences, note what the above criticism of the Parmenideans leaves untouched.
Concerned as it is with the alleged difference between the first four and all
the rest, it leaves unaddressed the Parmenidean claims made in sections (B) and
(C) above. After all, the Parmenideans object to the legitimacy of more than
the negative propositions above. There is much--just about all, in fact--about
which the Parmenideans would say, "nor may you
declare it."
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