The Two Opposites of 'Nothing' and the Logical Irreducibility of Being (2018 Version)

This entry is part of the ongoing debate with the Opponent a. k. a. the Dark Ostrich.

It is interesting  that 'nothing' has two opposites.  One is 'something.'  Call it the logical opposite.  The other is 'being.'  Call it the ontological opposite.  Logically, 'nothing' and 'something' are interdefinable quantifiers:

D1. Nothing is F =_df it is not the case that something is F.

D2. Something is F =_df it is not the case that nothing is F.

These definitions, which are part of the articulation of the Discursive Framework (DF), give us no reason to think of one term as more basic than the other.  Logically, 'nothing' and 'something'  are on a par.  Logically, they are polar opposites.  Anything you can say with the one you can say with the other, and vice versa.

We also note that as quantifiers, as terms expressing logical quantity, 'nothing' and 'something' are not names or referring expressions.

So far I have said nothing controversial.

Ontologically, however, being and nothing are not on a par.  They are not polar opposites.  Being is primary, and nothing is derivative.  (Note the ambiguity of 'Nothing is derivative' as between 'It is not the case that something is derivative' and 'Nothingness is derivative.'  The second is meant.)

Now we enter the arena of controversy. For it might be maintained that there are no ontological uses of 'being,' and 'nothing,' that talk of being and nothing  is replaceable without remainder by use of the quantifiers defined in (D1) and (D2).

Quine said that "Existence is what existential quantification expresses."  (Ontological Relativity and Other Essays, p. 97)I deny it:  there is more to existence than what the existential quantifier expresses.  Quine's is a thin theory of existence; mine is a thick theory.  Metaphorically, existence possesses an ontological thickness.  This is very important for metaphysics if true.

I won't be able to prove my point because nothing in philosophy can be proven.  But I can argue for my point in a fallacy-free manner.  I am justified in holding my view so long as no one can convict me of a clear-cut error. 

Suppose we try to define the existential 'is' in terms of the misnamed because question-begging 'existential' quantifier.  (The proper moniker is 'particular quantifier.')  This is standardly done as follows.

D3. y is/exists =_df for some x, y = x.

In plain English, for y to be or exist is for y to be identical to something. For Quine to be or exist is for Quine to be identical to something.  In general, to be is to be identical to something, not some one thing of course, but something or other.   This thing, however, must exist, and in a sense not captured by (D3).  Thus

Quine exists =_df Quine is identical to something that exists

and

Pegasus does not exist =_df nothing that exists is such that Pegasus is identical to it

or

Pegasus is diverse from everything that exists.

The point, which many find elusive, is that the items in the domain of quantification  must be there to be quantified over, where 'there' has not a locative but an existential sense.  For if the domain includes nonexistent objects, then, contrary to fact, Pegasus would exist in virtue of being identical to an item in this widened domain, namely, Pegasus.

The conclusion is (to me!) obvious: one cannot explicate the existential 'is' in terms of the particular quantifier without circularity, without presupposing that things exist in a sense of 'exist' that is not captured by (D3).

Mere logicians won't accept or perhaps even understand this since existence is "odious to the logician" as George Santayana observes. (Scepticism and Animal Faith, Dover, 1955, p. 48, orig. publ. 1923.) You have to have metaphysical aptitude to understand it. (But now I am tending toward the tendentious.)

Intellectual honesty requires that I admit that I am basing myself on an intuition, what J. Maritain calls the intuition of Being.  I find it self-evident that the existence of a concrete individual is an intrinsic determination that makes it be as opposed to not be. This implies a real distinction between x and the existence of x. Accordingly, the existence of an individual cannot be reduced to its self-identity: the existence of Quine does not reduce to Quine's being (identical to) Quine, as on the thin theory.  And the nonexistence of Pegasus does not reduce to its being diverse from everything.  (If to be is to be identical to something, then not to be is to be diverse from everything.)

The Opponent does not share my intuition.  In the past I have berated him for being 'existence-blind' but he might plausibly return the 'compliment' by accusing me of double vision:  I see Socrates but I also 'see' the existence of Socrates when there is no such 'thing.' 

So far, not good:  I can't refute the Opponent but he can't refute me.  Stand-off.  Impasse, a-poria.

Let me try a different tack.  Does the Opponent accept 

ENN. Ex nihilo nihil fit?

Out of nothing nothing comes.  Note that 'nothing' is used here in two different ways, ontologically and logically/quantificationally. For what the hallowed dictum states is that it is not the case that something arises from nothing/Nothingness.  

Now if the Opponent accepts the truth or even just the meaningfulness of (ENN), then he must (!) admit that there are two senses of 'nothing,' the logical and the ontological, and correspondingly, two senses of 'something.'  If so, then being and nothing cannot be exhaustively understood in terms of logical quantifiers and propositional negation, and then the thin theory bites the dust.

But if the thin theory succumbs, then there is more to existence than can be captured within the Discursive Framework.

Related articles

Maverick Philosopher: Singular Existence and Quantification

The Riddle of Evil and the Pyrrhonian 'Don't Care'

A Defense of David Benatar Against a Scurrilous <i>New Criterion</i> Attack

Comments

[The Dark Ostrich]

I am having a hard time following the argument following from 'In plain English ..'.

I can half see it.

[The Black Ostrich]

Reading this again, I take it you mean the following make no sense unless we understand ‘exists’ in a broader sense than the Quinean one.

Quine exists =df Quine is identical to something that exists
Pegasus does not exist =df nothing that exists is such that Pegasus is identical to it

Picky point: you have ‘exists’ on both sides of the definition, so it is not a definition, but I understand what you mean.
Reply: we often say that some things could exist outside the domain. Or that there could be things outside the domain. But isn’t that equivalent to the claim that some things, e.g. Pegasus, are outside the domain of the space-time continuum. This would be consistent with the Quine definition.

[David Brightly]

>> The point, which many find elusive, is that the items in the domain of quantification must be there to be quantified over, where 'there' has not a locative but an existential sense.

Yes and No! No, because quantification---how the words 'some' and 'all' operate---works perfectly well in fiction and in history, and there is a definite sense in which the things of fiction are not there, or the things of history are not here now. Yes, because the words 'some' and 'all' make sense only relative to some assumed or understood context or 'domain' of things taken to be the extants that 'are there' in the context. In everyday dialogue there is a default context, namely the actual world or some part of it, though there can be some ambiguity as to whether this includes its past and/or future or not. I suggest it's this context-sensitivity of 'some' and 'all' that make it impossible to capture actual world existence in purely logical terms. After all, the Quine equivalence holds in all contexts. It fails to single out the actual world in any way.

Unfortunately, the context-sensitivity of 'all' and 'some' invades the sense of 'being there' and 'exists'. These words make perfect sense in fictional contexts. One(*) can't define a term that 'breaks out', as it were, from its context and becomes absolute. In a fiction such a term would remain relative to the fictional context. All it seems one can do is say, I'm now talking about the actual world, and hope one's interlocutor switches context. But a character in fiction can say this too, of course.

Having agreed that the wretched Quine formula is useless, how does its failure justify the distinction between a thing and its existence? And the existence of its existence...?

(*) Unless one is Borges, perhaps.

[BV]

Still no glimmer of understanding from you gentlemen, but thanks anyway.

[The Black Ostrich]

Then it is up to you to make it clearer, Bill. My first comment was 'having a hard time following [your] argument'. The second was an attempt to play your argument back, so you could confirm.

[The Dark Ostrich]

>>Ex nihilo nihil fit

Not for some x, not some y was before x