The Inconsistency of Nothing: Objective or Subjective?

In my previous post on this blog I argued that if we want to answer Leibniz' famous question ("Why is there something rather than nothing?") we have no choice but to start with the assumption that nothing at all exists and then investigate how we might derive existence from this state of nothingness. The rationale behind this approach is obvious: as long as we start with some primordial being (e.g. God or the laws of physics) as the cause of all other beings, we will not have truly answered Leibniz' question, since in that case we still have to explain why the supposedly primordial being existed. Why does God exist? Or where did the laws of nature come from? The late Robert Nozick put this problem succinctly as follows: "The question [of Leibniz] appears impossible to answer. Any factor introduced to explain why there is something will itself be part of the something to be explained". (Nozick 1981: 115) Hence, only if we start with the assumption that nothing at all exists will Leibniz' question become answerable.

Gottfried Wilhelm Leibniz

Answering Leibniz: The inconsistency of nothing
Of course, this does by no means imply that there is a true answer to Leibniz' question. Indeed, trying to explain being on the basis of nothing may seem such a logical absurdity that the question may appear as unanswerable as before. The received wisdom, after all, is that ex nihilo nihil fit, from nothing only nothing can come. As William James put it: "from nothing to being there is no logical bridge". (James 1911: 40) However, one of the things I argued in my previous post is that this problem becomes tractable once we focus on the paradoxes involved in the notion of absolute nothingness. These paradoxes have been with us since antiquity, from Parmenides up to modern thinkers like Lewis Carroll and Rudolf Carnap. The latter, for example, famously argued in his polemic against Heidegger that his talk of "the nihilating Nothing" ("das nichtende Nichts") ""involves a contradiction": "For even if it were admissible to introduce "nothing" as a name or description of an entity, still the existence of this entity would be denied in its very definition". (Carnap, 1959 [1931]: p.71) In other words, if we say that 'the nothing' exists, we create a paradox because 'the nothing' is by definition non-existent. From such paradoxes we might conclude that the concept of absolute nothingness is just logically incoherent. And if that is the case, then we appear to have a very simple answer to Leibniz' question, an answer that still starts with the assumption that nothing exists but then goes on to point out the contradiction in this assumption. In short, being is logically necessary because the existence of nothing is logically impossible.

Subjective or objective inconsistency?
In the following I want to investigate a question left hanging in the above answer to Leibniz' question. The question is this: Is the existence of nothing inconsistent in itself? Or is the inconsistency merely to be found in our concept of nothingness? In other words: Is the fact that the existence of nothing is ruled out by logic an objective fact, i.e. a fact that holds independently of us? Or is it a subjective fact, i.e. a fact about the limitations of our cognitive capacities, which are such that we simply cannot think coherently about nothingness? It is clear that the answer to these questions is crucial to how we can go about answering Leibniz' question. If the logical impossibility of nothingness is merely subjective, i.e. merely an effect of our inability to think nothingness, then we can't use this impossibility to answer Leibniz' question. After all, it would be absurd and indeed circular to say that there must be being since we cannot imagine it otherwise. The circularity of such a proposal follows from the fact that we ourselves are part of being, so on this proposal we exist because we cannot imagine ourselves as not existing, which is patently absurd. If the logical impossibility of nothingness is to explain why there is being, then this impossibility must be an objective fact.

Naming nothingness: Badiou's fallacy
The prospect, however, does not look good for the objective interpretation of the impossibility of nothingness. The problem simply seems to be that we cannot think about something without thinking about something. In short: thinking is inherently thematizing and objectifying. When we think about something we automatically turn it into an object, an object referred to by the grammatical subjects of our thoughts and statements. This is more or less unproblematic as long as we think about things that obviously exist. It becomes somewhat more problematic when we think about things that obviously do not exist (e.g. when we think about Pegasus; does it make sense to say that Pegasus itself is the object of our thought?). But it becomes outright paradoxical when we think about what is not anything at all, i.e. when we think about a 'state' where nothing exists. Just by thinking about such absolute nothingness we turn it into a something and thereby contradict its 'nature'. This point is nicely illustrated by some fallacious reasoning by the popular French philosopher Alain Badiou, who has built an entire ontology out of the set-theoretic construction of mathematics based on the empty set. Having developed the axioms of set theory (the Zermelo-Fraenkel system or "ZF" for short), Badiou writes:

Alain Badiou pondering the null set...

"We definitely have the entire material for an ontology here. Save that none of these inaugural statements in which the law of Ideas [i.e. the ZF axioms] is given has yet decided the question: 'Is there something rather than nothing?'... The solution to the problem is quite striking: maintain the position that nothing is delivered by the law of Ideas, but make this nothing be through the assumption of a proper name." (Badiou 2005: 66-67).

In other words: Badiou simply gives "this nothing" a name (namely, "the empty set"), et voilà, here we have our first being, the empty set, on the basis of which all other sets can be created. Now it will be obvious that, as an answer to Leibniz' question, this is totally unsatisfactory. I greatly admire the set-theoretic construction of mathematics out of the empty set. I'm even sympathetic to the idea that this construction may have some real ontological weight to it. But to answer the question "Is there something rather than nothing?" by simply giving a "proper name" to nothingness seems nothing more than a bad joke. Badiou's fallacy illustrates something of importance concerning the paradoxes surrounding the concept of nothingness. As soon as we start using "nothing" as a referring noun, we are in trouble: nothingness becomes a referent, an object. In that case, if we say that nothing exists, we imply that there exists this object called "the nothing", which is contradictory. It is clear that this contradiction is not an objective fact concerning the state where nothing exists. The contradiction is merely an effect of our objectification of this state. Just like Badiou cannot conjure being out of nothingness by giving the latter a proper name, so nothingness cannot be made inconsistent merely by our objectification of it.

Russell's theory of descriptions
But let's not jump to premature conclusions. The above analysis is predicated on the assumption that when we think about a state where nothing exists, we must use the word "nothing" as a noun to refer to this state, thus turning the latter into some mysterious entity. But is this assumption correct? Not according to an influential tradition in analytical philosophy, a tradition stretching back to Bertrand Russell's theory of descriptions. One of the reasons why Russell developed this theory was to solve a logical problem concerning the truth value of statements about non-existent objects. His famous example was the statement: "The present king of France is bald." Obviously, this sentence is false: if we consider all the bald men, the present King of France isn't among them, since there is no present King of France. But if it is false, then -- given the law of the excluded middle -- one would expect that the negation of this statement is true, namely, "It is not the case that the present King of France is bald" (or its logical equivalent: "The present King of France is not bald"). But this sentence is false as well: if we consider all the non-bald men, the present King of France isn't among them either. Thus it seems that the law of the excluded middle does not hold for all propositions! 

Bertrand Russell

Russell proposed to solve this problem (and save the universality of the excluded middle) by means of his theory of descriptions. According to Russell, a definite description like "the present King of France" simply isn't a referring expression at all, although it superficially appears that way. If we analyze the proposition "The present king of France is bald" we arrive at a logical deep structure that crucially involves existential quantification. What that proposition really says, according to Russell, is this: "There exists an object x such that x is the present king of France and x is bald" (formally: ∃x(Kx∧Bx) where K means "is the present king of France" and B means "is bald"). This existential statement has a definite truth value: it is clearly false. And its negation, -∃x(Kx∧Bx),  is clearly true. So problem solved.

Rudolf Carnap

Carnap contra Heidegger
That there is indeed some truth to Russell's theory of definite descriptions becomes especially apparent when we consider ordinary statements figuring "nothing" as the grammatical subject, for example "Nothing was stolen from my house" or "Nothing in this painting has the color green". In these statements we are obviously not referring to some mysterious entity, the nothing, which was stolen from my house and which has the color green in said painting. Clearly these statements must be analyzed, along the lines of Russell's theory, as negative existential statements: "There is no x such that x was stolen from my house" and "There is no x such that x has the color green in this painting". But if this holds for our ordinary use of "nothing" as a grammatical subject, then perhaps it also holds for the metaphysical proposition "Nothing exists". This was precisely Carnap's point in his polemic against Heidegger, where he used Russell's theory of descriptions to debunk Heidegger's talk of the "nihilating Nothing". When we issue the statement "Nothing exists", are we referring to some mysterious entity? No, says Carnap, that statement merely functions as shorthand for the negative existential statement "There is no x such that x exists" (formally: -∃x(Ex) where Ex means "x exists"). This negative existential statement does not commit us to the existence of 'the nothing'. Hence the air of paradox surrounding the claim "Nothing exists" evaporates. Heidegger simply violates the logical deep structure of language when he uses "nothing" as a referring noun. His talk of 'the nothing' is meaningless (Carnap, 1959 [1931]: 70).

Truth supervenes on being
So where does this leave us? It would seem that we can think about 'absolute nothingness' without contradiction after all! But wait a minute... Not all is well in Carnap's logical-positivist, Nothingness-less paradise! Trouble comes from a principle that is broadly accepted in Anglo-American philosophy and that captures a large part of our common sense attitude toward truth. This is the principle that truth supervenes on being (see Jackson 2000: 118). The basic idea is that for every truth there must exist a truthmaker, i.e. an objectively existing state of affairs or fact that makes it true. Thus the statement "It is raining now" is true iff it is an objective fact that it is raining now. Or more formally: "p" is true iff there is a fact that p. Note that this is almost a tautology and thus a logical truth. It is therefore extremely difficult to argue against the idea that truth supervenes on being. It is so deeply ingrained in our common sense mentality that it is virtually impossible to do without it. But it spells trouble for Carnap's logical diffusion of nothingness. Consider the negative existential statement: there is no x such that x exists (-∃x(Ex)). If this statement is true, then it too must supervene on being and so there must exist an objective fact which makes it true. Hence, there still exists something, namely, this fact. The statement -∃x(Ex) is therefore contradictory, even if we are not directly referring to some mysterious entity called "the nothing".

David Lewis

This conclusion, that -∃x(Ex) is contradictory because truth supervenes on being, was – to my knowledge – first drawn by the philosopher David Lewis. Suppose, he says, "that there might have been absolutely nothing at all. It would then have been true that there was nothing. Would there have been a truthmaker for this truth? -- If so, there would have been something, and not rather nothing. Contradiction." (Lewis 1999: 220)

Referring to an empty fact
It appears, then, that the contradiction in thinking about the state where nothing exists is inevitable after all. Moreover, it seems that when we think about this state we cannot shed the supposition that there exists this mysterious entity, the nothing, even if we explicitly try to avoid this through Russell's theory of descriptions. For, so we might ask, what kind of a fact is it that has to exist iff  "-∃x(Ex)" is to be true? It is a fact lacking any positive determination, a fact with no being in it, with virtually no propositional content, an empty fact therefore. What kind of an entity is this utterly empty, being-less fact if not nothingness itself? It is clear that if you accept the existence of facts as truthmakers for propositions, you are committed to the existence of a certain kind of entity, a kind of object even, insofar as facts can be referred to by noun phrases. Thus facts satisfy at least one traditional criterion for object-hood (namely, "must be a possible referent of noun phrases"). For example, nouns referring to facts can be grammatical subjects in statements like "The fact that p is F" (e.g. "The fact that it rains is lamentable / should not deter us / is welcomed by farmers etc."). And if you think that propositional that-clauses ("that p") make for dubious noun phrases, consider the fact that the reference of a that-clause can always be taken over by pronouns through anaphoric reference (e.g. "It is lamentable that it is raining", "I saw that the sun came up and it made me happy"). So if we take the common sense view that only objects can be referred to by noun phrases (which include pronouns), then facts are certainly a kind of object. Indeed, to be precise, facts are those objects which are referred to by true statements. But then the empty fact, the truthmaker for "-∃x(Ex)", becomes a very special kind of object: an empty, being-less, property-less object.

Obviously, this object which is not an object is the nothing if anything is. In conclusion, when thinking about the state where no beings exist, we cannot avoid assuming the existence of the nothing, even if we take the Russell/Carnap approach. Clearly this 'object which is not an object' is a paradoxical entity. This follows from the fact that "-∃x(Ex)" is a contradiction: its claim that no beings exist is contradicted by the existence of its truthmaker. Its truthmaker, then, makes it both true and false simultaneously, which is to say that this 'object' (the nothing) both exists and does not exist. The contradiction in thinking about nothing seems ineluctable.

The objective inconsistency of "-∃x(Ex)"
Let's return to our starting question: Is this contradiction objective or subjective? What has become apparent, I think, is that this issue turns on how we think about the ontological status of truth. If, so to speak, the truth is out there -- objectively, independent of us -- then it's hard to escape the conclusion that the contradiction of "-∃x(Ex)" is an objective one. Take for example elementary truths like "1 + 1 = 2" or "The earth orbits the sun". Isn't it obvious that they are true independently of whether they are conceived or not? Thus one might state as a general principle that if "p" is true, then it is true independently of any observer, and hence it is an objective fact that p.* For "-∃x(Ex)" this means that if it's true, then it's true independently of us, and then the fact that nothing exists is an objective fact, including its contradictory nature. The only way to avoid this conclusion is by saying that truth is not objective, that truths only arise when thinking subjects make assertions. Thus, one could say, the contradiction inherent in "-∃x(Ex)" only arises when it is uttered or thought, so that the contradiction is subjective after all. But this is a very problematical position which ultimately cannot be made coherent. There are, I think, basically two ways in which this position (i.e. that truths are relative to subjects who utter them) can be construed. A first, innocent construal would be to say that truth does not just require a truthmaker but also a truthbearer, i.e. something that is made true by the truthmaker, e.g. a thought or statement. On such a conception, truthbearers need to be produced by thinking subjects: if there are no such subjects, or if they simply fail to produce (i.e. utter or think) truthbearers, then there are no truths. So if no one thinks or utters the claim that -∃x(Ex), there can be no corresponding truth and hence no contradiction. But it is easy to see this solution fails to work. Even if there are no truthbearers, there are still the truthmakers, which exist independently from the truthbearers. So on this conception, even if there were no truth, there would still be objective reality as such, which would make truthbearers either true or false as soon as they are produced. Hence, if "-∃x(Ex)" is true when uttered or thought, then its truthmaker must (pre-)exist objectively and we are still faced with objective contradiction. The only way to avoid this objectivity is to construe the subjective relativity of truth in a second and much more extreme way, namely, by saying that both truthbearers and truthmakers are dependent on the subject who conceives them. But such a vision is tantamount to absolute idealism, where the existence of reality as such is produced by thought. I think we can safely say that in this case the cure is worse than the disease. Ultimately such extreme idealism is incoherent. For if all of existence is the product of thinking, then how did the thinking subject itself come into existence? It would be circular and thus absurd to say that the thinking subject thought itself up... In short, thought always presupposes independent being as its ontological basis. To paraphrase Marx: being does not depend on consciousness, consciousness depends on being. But if that is the case, then the contradiction inherent in "-∃x(Ex)" can only be an objective one. And then our answer to Leibniz' question still stands. That is to say: Why is there something rather than nothing? Because nothing is inconsistent!

Well, nothing does not exist, but whatever...

I would like to end this post with a cautionary note. The above analysis of the logical impossibility of nothingness turns on a great many questions, such as: what exactly is reference? when do we call something an object? wherein does truth consist? what are truthbearers? what is the ontological status of facts? These are issues about which philosophers of language, logic and knowledge have argued and continue to argue endlessly. In other words: there are many different ways to answer these questions. Hence there are also many different ways in which the logical status of "-∃x(Ex)" might be judged. Nevertheless, I think the above conclusion concerning the objectivity of the contradiction inherent  in "-∃x(Ex)" is pretty straightforward and commonsensical. Basically it turns on two presuppositions which are not easily put aside. The first is that truth supervenes one being, so that if a statement is true it is true by virtue of some objective feature of reality. The second is that truth (if not the truthbearer then at least the truthmaker) is independent of the thinking subject, hence that absolute idealism is false. Together these assumptions imply that if "-∃x(Ex)" is true, then there is an objective reality which makes it true. And this is basically all we need to show the objectivity of the contradiction involved.

* With the exception, of course, of subjective facts, i.e. facts concerning conscious experience, like the fact that I feel pain or that I see redness. Such subjective facts are obviously observer-dependent. But clearly we are not talking about subjective facts here. In particular, "-∃x(Ex)" cannot assert a subjective fact since by definition there is no consciousness to perceive it.

References:
-Badiou, Alain (2005), Being and Event. New York: Continuum.
-Carnap, Rudolf (1959 [1931]), "The Elimination of Metaphysics Through Logical Analysis of Language", in: A. J. Ayer (ed.), Logical Positivism. Glencoe, The Free Press, pp. 60-81.
-Jackson, Frank (2000), From Metaphysics to Ethics. Oxford University Press.
-James, William (1911), Some Problems of Philosophy: A Beginning of an Introduction to Philosophy. Longmans, Green, and Co., New York.
-Lewis, David (1999), Papers in Metaphysics and Epistemology. Cambridge University Press.
-Nozick, Robert (1981), Philosophical Explanations. Belknap Press, Cambridge Mass.