Is “Nothing nothings” true?

In a 1929 lecture, Martin Heidegger argued that the following claim is true:

“Nothing nothings.”

In German: “Das Nichts nichtet”. Years later Rudolph Carnap ridiculed this statement as the worst sort of meaningless metaphysical nonsense in an essay titled “Overcoming of Metaphysics Through Logical Analysis of Language”. But is this positivistic attitude reasonable? Is the sentence as nonsensical as Carnap claimed?

In this essay I want to examine Heidegger’s claim that nothing nothings. I will argue that there are at least two ways to read the claim, and on either reading the claim comes out as true (at least, given certain common and plausible assumptions regarding the underlying logic). In addition, the truth of a slight modification of the claim hinges on the outcome of a metaphysical debate currently raging in the philosophical literature.

Before arguing for any of this, however, the following caveat is important to note: I am not claiming that any of the claims or interpretations given below were, or even should have been, held by Heidegger. In short, I am not interested (at least for the purposes of this essay) in sorting out in detail why Heidegger believed that “Nothing nothings” is true. Rather, I am interested in whether we should believe that this sentence is true, and if so, why.

I will divide the task of understanding the sentence “Nothing nothings” into two parts. The first and simpler part is to determine how to understand a sentence of the form “Nothing Fs” where F is some arbitrary predicate. “Nothing Fs” (or, equivalently, “Nothing is F”) is, from a logical perspective, equivalent to the following claim:

(1)        It is not the case that there exists an object x such that x is F.

So far, so good. The second, and somewhat more complicated, task is to sort out how we should understand a sentence of the form “t nothings”, where t is some arbitrary name. First, we shall assume that “t nothings” is equivalent to “t is nothing”. Then the question becomes this: do we read the “is” in “t is nothing” as the “is” of identity, or the “is” or predication? On the “is” of identity reading, “t is nothing” becomes something like:

(2)        t is not identical to anything.

Or, even more simply:

(3)        t does not exist.

On the “is” of predication reading, “t is nothing” becomes something like:

(4)        t does not have any properties holding of it.

Now, in order to better understand “Nothing nothings”, we need only combine the recipe illustrated in (1) for statements of the form “Nothing is F” with the recipe in (3) and (4) for statements of the form “t is nothing”. Thus, “Nothing nothings”, on the “is” of identity reading, is just:

(5)        It is not the case that there exists an object x such that x does not exist.

This statement is easily formalized in the standard classical first-order logic taught to undergraduates, and is a logical truth. Thus, not only is “Nothing nothings” true on this reading, it is true as a matter of logic alone.

Things are slightly more complicated on the “is” of predication reading. If we combine the recipes illustrated by (1) and (4) above, we get the following:

(6)        It is not the case that there exists an object x such that x has no properties holding of it.

Since it involves generalizing over properties rather than merely generalizing over objects, formalizing this statement requires what is known as second-order quantification. The logical status of second-order quantification is a matter of some philosophical debate. Nevertheless, those logicians who do accept second-order quantification as legitimate and logical almost unanimously accept that sentence (6) is a logical truth, and even those that don’t think second-order quantification is logic proper typically accept that (6) is true (and perhaps even necessarily true).

Thus, Heidegger’s claim seems straightforwardly true (at least, on these ways of understanding it, which as I noted at the outset, might not be the way that Heidegger understood it). But what happens if we modify the statement slightly, inserting the word “possibly” and obtaining:

(7)        Nothing possibly nothings.

On the “is” of predication reading, this becomes:

(8)        It is not the case that there exists an object x such that it is possible that x has no properties holding of it.

In other words, “Nothing possibly nothings”, on the “is” of predication reading, amounts to the claim that every object that exists not only has some properties that hold of it, but in addition must have properties holding of it (i.e. it is impossible that no properties hold of it). This claim is a bit obscure, but is accepted by most logicians who work on systems containing both second-order quantification and modal notions like “necessity”, “possibility”, and “impossibility”.

It is the “is” of identity reading of “Nothing possibly nothings” that is really interesting, however. On this reading, “Nothing possibly nothings” becomes something like:

(9)        It is not the case that there exists an object x such that it is possible that x didn’t exist.

This is equivalent to the slightly less cumbersome:

(10)      Everything that actually exists, necessarily exists.

This statement expresses a metaphysical view known as necessitism: the view that every object that exists at all exists necessarily. According to necessitism it is impossible that you, or that chair, or this blog post, could have failed to exist (i.e. there is no possible way that the world could have turned out where you, or that chair, or this blog post didn’t exist).

Necessitism has been recently defended by Timothy Williamson, in a lovely book titled Modal Logic as Metaphysics (Oxford, 2013). While his defense of necessitism is subtle and interesting, the view is extremely counterintuitive, and thus remains a subject of much contention within metaphysics and the philosophy of logic. In short, although “Nothing nothings” seems, at least on the readings given above, uncontroversially true, whether “Nothing possibly nothings” is true remains an exciting open question in philosophical research.

Image credit: The Scream by Edvard Munch. Public domain via WikiArt.

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