The phrase negation of the negation is best known from Karl Marx’s work, as when he uses it to describe capitalist production in Capital. It’s an odd phrase that seems simply redundant in the formal logic taught to analytic philosophers and computer scientists. There, the principle of double negation elimination tells you ¬¬P -> P: that is, the negative of the negative is the positive, and nothing more. Russell and Whitehead in Principia Mathematica say simply: “a proposition is equivalent of the falsehood of its negation.” On that account, to “negate the negation” of something just leaves you with its affirmation, the original thing you were negating: all you’re doing is being unnecessarily wordy, by saying not-not-P when you could have just said P.

But in Marx’s inspiration Hegel, there is much more to the phrase than this redundancy. A great deal of Hegel’s thought proceeds in the kind of three-part progression that introductions to Hegel often call thesis, antithesis, and synthesis (though Hegel never used those terms in that way). When thinking through a particular idea we begin in a first, unquestioned or immediate, position – a prejudice. This idea gets challenged by its opposite, the negation or negative moment. The third and final step is in some ways closer to the first than to the second, but it is crucially different: it takes up the truth of the second within it, transcends and includes it. This is negating the negation: negating here is a process, not a simple inversion or opposite but a rational movement forward. That movement is at the heart of Hegel’s thought.

I was startled recently to encounter the phrase “negation of negation” in a rather different place: the medieval Christian mystic Meister Eckhart. At first, Eckhart’s only obvious commonality with Hegel and Marx is that they are all German. But the commonalities go deeper, at least with Hegel. Hegel isn’t obviously a mystic: his logocentrism leaves little room for ineffability or mystery, and leaves him to be disdainful of mystical experience. Yet depending on how one defines mysticism, there is a mystical dimension at least in Hegel’s nondualism, where everything comes back to a spirit or mind (Geist) that is both subject and object, both God and self. And Hegel traces that nondualism directly back to Eckhart himself. In the Lectures on the Philosophy of Religion, Hegel describes Eckhart as having “a thorough grasp of the divine depth” in this passage from Eckhart’s sermons:

the eye with which God sees me is the eye with which I see Him; my eye and His eye are one. By a righteous standard I am weighed in God, and God in me. If God were not, I would not be; if I were not, then He were not.

Hegel and Eckhart share the idea that reality is ultimately one, and that that one is in some way both human subjectivity and God. (And yes, in case you’re wondering, the Church did convict Eckhart of heresy for all this.) For Eckhart, at least, it’s in the context of this divine oneness that he employs the term “negation of negation”.

Eckhart says that God’s divine nature should be described with the predicate “one” (unum). In his Commentary on Wisdom he says that to describe God as one “sounds negative but is in reality affirmative; it is the negation of negation, which is the purest affirmation and the fullness of the term affirmed.” In their introduction to Eckhart’s writings, Edmund Colledge and Bernard McGinn explain the “negation of negation” in this passage as “the affirmation that it is not other than itself.” (Meister Eckhart 34) That affirmation signifies the purity of God’s being in a way that even the term “being” itself does not.

I’m taking that explanation largely from Colledge and McGinn; I don’t understand Eckhart’s difficult ideas well enough to know exactly what he means by all this. But it seems clear enough that when Eckhart says the negation of negation is “the purest affirmation and the fullness of the term affirmed”, he is already disagreeing with the later formal logic of Russell and Whitehead: negating the negation is not just any affirmation, and is therefore not merely equivalent to affirmation. You’re doing something special, something different, something essential to the understanding of God’s purity. I don’t think this is exactly what “negation of the negation” means in Eckhart’s fellow nondualist Hegel, but they clearly share the understanding that negating the negation isn’t just the positive or affirmative.

Now Marx takes up none of Eckhart’s or Hegel’s nondualism. In Marx’s thought, from a very young age, reality is not fundamentaly spirit but matter; that is his deepest break from Hegel. And I don’t think there’s any unity that Marx sees in that matter, the way that Hegel and Eckhart do in divine spirit. But Marx does take up the core idea that negating the negation isn’t just equivalent to the original affirmative. Here’s the key passage in Capital:

The capitalist mode of appropriation, the result of the capitalist mode of production, produces capitalist private property. This is the first negation of individual private property, as founded on the labour of the proprietor. But capitalist production begets, with the inexorability of a law of Nature, its own negation. It is the negation of negation. This does not re-establish private property for the producer, but gives him individual property based on the acquisitions of the capitalist era: i.e., on co-operation and the possession in common of the land and of the means of production.

As I understand it here, the idea is that private property is a negation of common property, but that socialism or communism will reach a higher level by negating that negation. Hunter-gatherer societies have a “primitive communism” that precedes private property, and that is the mere affirmative; the advanced communist state that Marx seeks is at a higher level, a negated negation, that follows private property. This is how Engels takes the phrase in the Anti-Dühring, at least:

common ownership becomes in the course of the development of agriculture a fetter on production. It is abolished, negated, and after a longer or shorter series of intermediate stages is transformed into private property. But at a higher stage of agricultural development, brought about by private property in land itself, private property conversely becomes a fetter on production, as is the case today both with small and large landownership. The demand that it, too, should be negated, that it should once again be transformed into common property, necessarily arises. But this demand does not mean the restoration of the aboriginal common ownership, but the institution of a far higher and more developed form of possession in common which, far from being a hindrance to production, on the contrary for the first time will free production from all fetters and enable it to make full use of modern chemical discoveries and mechanical inventions.

As in Hegel – and perhaps Thucydides and Plato – there is a third stage, after negation, that leaves you somewhere different than where you were before the negation. The technologically enabled communist utopia envisioned by Engels is something very different from the common property of hunter-gatherers. It’s trans rather than pre.

None of this is to say Eckhart or Hegel or Marx are right about the particular ways in which they apply the negation of the negation. (After all, we are nearly 150 years after Marx’s death, and the negation of private property doesn’t seem any closer.) But it’s striking that such different thinkers share the idea in common. And I do think they are on to something important with the idea: the process of negating a negation really isn’t just the same thing as affirming the original affirmation. That’s a point that formal logic doesn’t catch.