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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 Modal Logic as Metaphysics. 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.

Recent Comments

  1. gordon fiala

    Nothing DOES NOT Nothing.
    Nothing, Prevails. Nothing, alludes. Nothing, persuades (reality away from it’s nature). Nothing, is a real thing. Nothing, IS. Nothing does not. Nothing is not, none existence. Nothing Does, it does not “nothing” .

  2. anthony curtis adler

    This is very clever, but your analysis takes its departure from a misinterpretation of the meaning of the German based on the ambiguities of the somewhat flawed English translation. “Das Nichts nichtet” in German is literally “The nothing nothings” — not “nothing nothings.” Formally, it is an affirmative judgment regarding a particular subject. That, of course, the content of the judgment complicates and indeed contradicts its form is something else, of course— but there is no warrant for reading it the way you do. If this is what Heidegger meant to say he would have expressed himself quite differently. “Es gibt nichts, was nichtet” or even “Es gibt nights,was es night gibt.”— Heidegger would have never said this, since it seems like a banal tautology … Heidegger may be obscure, but he is rarely banal…

  3. Chido Houbraken

    Santa Claus exists, although he does not exist.

  4. gabriele colombo

    not completely sure about your argument, but still nice transatlantic link

  5. Maz

    Very well written. Perhaps “Nothing nothings” should be changed to “nothing nothings,” as not to give “Nothing” a proper name, otherwise you would be referring TO “Nothing.” However, this would likely mean that we are saying “t does not exist.” I find this much more reasonable than to say “t has no properties.” A property-less thing cannot be, it seems, and thus is not sufficient for t (assuming t is not a proposition – but perhaps propositions have properties too, such as truth values.). Furthermore, a property-less thing can cannot do (it cannot even exist!). Therefore, I would assert that it is invalid to say that the thing which does not exist can do “not everything.”
    We can try to represent this logically, but it fails.
    Ex(~Px & ~Qx & ~Rx…). However, we already stated that it Ex exists. You can negate this, and by the distributive property, have ~Ex(Px & Qx & Rx…), which is what I believe was being stated in the article. However, if we symbolize “nothings” or “x does nothing” as “Nx” (the property of doing nothing), then we cannot include that in the set of negated properties that “nothing” holds. “Nothing” would then be Ex(~Px & ~Qx & ~Rx… & Nx). Likewise, you must say ~Ex(at least Px… & ~Nx). All we have done is symbolized “something which exists is not doing nothing, and something that doesn’t exist is doing nothing (has the property of nothing [verb]).” Therefore, nothing exists which nothings. Can a property DO? I say no, but that may be disputed. Either way, you must negate the second statement (to get to the first, where Ex) to say nothing DOES. This is because once you say nothing does, it also Ex. If nonexistent things can do, than this is untrue and Heidegger’s thesis is true, but that would require substantial proof. The argument may be valid, but the premise is untrue.

    I believe this is a perfect example of how logic is a very small realm of philosophy (not in scope, but application).

  6. Angululus

    “Nothing” also has a straightforwardly nominal reading, where it denotes a certain amount or quantity, as in “A dollar is better than nothing”. Here we are denying and not affirming that a dollar is the worst thing in the universe.

    If we read the subject “nothing” in “nothing nothings” in such a way, then the sentence comes out false on both of your articulations of what “nothings” might mean.

    By the way, it seems to me that those articulations of yours are a bit of a cheat. Maybe “to nothing” is a verb in Roylish, but it is not a English word, and consequently “nothing nothings” is not an English sentence.

    Nonetheless, I think one can argue that it is true for precisely that reason: “x knirpshes” is not a predicate of English, and so nothing can possibly satisfy it; or to put it more concisely: nothing knirpshes. Similarly, nothing nothings. (Not, of course, on the nominal reading of “nothing” I alluded to earlier: on that reading, nothing is just another thing that fails to nothing.)

    (For a more systematic explication of this kind of talk, see Ken Shan’s amazing article on mixed quotation: http://link.springer.com/article/10.1007%2Fs10988-011-9085-6)

  7. Tom

    This article seems caught up in logic games. I thought Heidegger was articulating an aspect of experience. We experience the nothing. We experience it intellectually through abstraction and the simple logic of numbers. But we also experience it in other ways – in boredom, loss, disappointment. In these modes, the nothing nihilates, which to my understanding, means that we are aware of it in a way that is unique to dasein and it brings a corresponding urge, movement, towards being, or not, if it moves one to become nothing. It’s a subtle truth, but it is real. 99.999999% of all existence is ‘nothing’, empty space, within which the something takes its meaning.

  8. Sara

    Very interesting piece, thank you! I was wondering, though, why the switch to the past tense at (9)? It shifts the focus of the reasoning from the possibility of x’s existence in the present (i.e. at the time we claim it exists) to the question of x’s original coming into being. In other words, shouldn’t (9) be ‘It is not the case that there exists an object x such that it is possible that x DOESN’T exist.’? Couldn’t this be the reason why such a surprising conclusion is reached?

  9. Matt Titchenal

    Nothing nothings, just as a tree apples and the earth peoples. Nothing bares the infinite fruit of nothings.

  10. Lillian

    Is it not Lear’s

    “Nothing comes of Nothing”?

  11. Lillian groag

    It’s been filled in!!!!

  12. Ryan A

    This to me reads more like “the empty function is the unique function ∅:∅→A where A≠∅” which is of course vacuously true.

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