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Martin Heidegger in his Being and Time criticized the connection between Spirit and Time proposed by Hegel saying that:

Hegel shows the possibility of the historical actualization of spirit "in time" by going back to the identity of the formal structure of Spirit and time as the negation of a negation" (Heidegger's Being and Time, P.396)

About this, I have 3 questions:

  1. I'd like to know where Hegel proposed such a formal, logical correlation between these two in his operas (assuming that Heidegger's thesis is correct); and, if it's not, why for Hegel Spirit has to "fall" in time;
  2. About the "negation of a negation": I know that time corresponds to that in the figure of the point, as the point it is the negation of space; but what about Spirit? In which sense it is the "negation of a negation"?
  3. Even if the formal structure of Time and Spirit would be the same, why should this assumption bring to the conclusion that "Spirit has to fall in time"?
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Hegel is not known for making "formal logical correlations", in fact he despised formal logic, on time specifically see Safatle's Hegel Against a Formal Concept of Time. As for Heidegger's grounds for his interpretations, in this case he is very explicit about them on the pages preceding the quote. The parts on Time come from Philosophy of Nature, and the parts on Spirit from Phenomenology of the Spirit, he even gives page numbers. Here is Philosophy of Nature §260 (quoted from Foldes' Hegel’s Deduction Of Matter):

"...time is the immediate collapse into indifference, into undifferentiated asunderness or space, because its opposed moments which are held together in unity, immediately sublate themselves. In this way, the negative determination in space, the exclusive point, no longer only implicitly [in itself] conforms to the Concept, but is posited and concrete within itself."

It helps to remember Hegel's ubiquitous dialectic triad of abstract-negative-concrete, and how the concrete (or the more concrete) appears as sublation (negation of a negation) of the abstract and its direct negation. Thus, everything appears as a negation of a negation in its maximal concretion, which does not preclude it however from entering the next triad as the next "abstract". Here is how the Spirit appears as a negation of a negation in Heidegger's words:

"Since grasping the non-I presents a differentiation, there lies in the pure concept, as the grasping of this differentiation, a differentiation of the difference. Thus Hegel can define the essence of Spirit formally and apophantically as the negation of a negation... Since the restlessness of the development of Spirit bringing itself to its concept is the negation of a negation, it is in accordance with its selfactualization to fall "into time" as the immediate negation of a negation."

As a reminder, Being-Essence-Concept is the overarching triad of the Spirit's dialectic that the Science of Logic is devoted to, see e.g. Kaag's Hegel, Peirce, and Royce on the Concept of Essence. Or, as earlier in Phenomenology, Reason becomes Spirit when it achieves the full consciousness of itself. As for the Spirit "falling into" time, it is perhaps best to quote the last chapter of Phenomenology of the Spirit directly:

"Time is the Concept itself that exists there and is represented to consciousness as empty intuition. Consequently, Spirit necessarily appears in time, and it appears in time as long as it does not grasp its pure concept, which is to say, as long as it does not annul time. Time is the pure self externally intuited by the self but not grasped by the self; time is the merely intuited concept. Since this concept grasps itself, it sublates its temporal form, comprehends the act of intuiting, and is intuition which has been conceptually grasped and is itself intuition which is comprehending... Thus Time appears as the very fate and necessity of Spirit when it is not in itself complete - the necessity of its giving self-consciousness a richer share in consciousness, of setting in motion the immediacy of the in-itself...".

In other words, the Spirit has to "fall into time" not because of some formal analogy (which applies to everything in Hegel) but because of how Hegel set it up to "grasp" itself. As Heidegger puts it, "Spirit necessarily appears in time, and it appears in time as long as it has not grasped its pure concept, that is, has not annulled time."

One of Heidegger's problems with all of this is the most people's problem with Hegel in general, that he spins concrete out of abstract, the world out of nothing, and randomly at that, that he reaches "each category from the last preceding by virtually calling 'next'!", as Peirce put it. Heidegger's approach is the opposite (as one would expect from existentialist vs. essentialist), it "begins with the "concretion" of factically thrown existence, and reveals temporality as what makes such existence primordially possible. "Spirit" does not first fall into time, but exists as the primordial temporalizing of temporality", i.e. time is not encountered externally but is a primordial aspect of "self"'s (Dasein's) existence.

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The wording in your quote and the wording in the questions are a bit different, but I'll do my best to address both.

First I'm going to extend the quoted bit a little and bring the language of one of your questions into the quotation:

Hegel shows the possibility of the historical actualization of spirit "in time" by going back to the identity of the formal structure of Spirit and time as the negation of a negation But since at the same time, time is yet conceived in the sense of world time that has been absolutely levelled down, so that its provenance thus remains completely covered over, it simply confronts spirit as something objectively present. For this reason spirit must first fall "into time" (Martin Heidegger Being and Time P.396 (Stambaugh translation - SUNY))

There's quite a bit going on here that would be hard to grasp if you don't know Hegel very well, particularly because of the technical vocabulary at work here.

  • For Hegel, Spirit is the activity that is moving forward through history towards a full understanding of everything. (in a weird way, Spirit is partially a synonym for us, because -- to steal a surprise in the way it happens in Phenomenology of Spirit, the one comprehending things is us).
  • For Hegel, negation is the primary way that the "dialectic" moves forward. Here, dialectic means the way that Spirit understand things. And the way it moves forward is by negating things. But Negating for Hegel does not mean simply to take B and make it "not B" (like a negation in what we now call logic). Instead, it refers to any of a number of things that bring B under something. In other words, "this is a ball" is for Hegel a negation, because it negates that this is anything other than ball." So oddly, the first type of negation is consumption. But it's basically anything in which we grasp things.

  • Time is a negation of negation means that time too is a discovery of sorts for Spirit. I didn't read it too carefully, but this looks like a helpful commentary on the passages in Hegel's Philosophy of Nature where he talks about that.


Now to try and answer your questions,

For 1, I assume by "these two", you mean Spirit and time. On my reading, time is not a very important concept for Hegel. Instead, he's more concerned with Spirit and/or the Concept. Spirit (Geist) and Concept (Begriff) are two sides of the same coin for Hegel. Spirit is the active part -- the mind -- and concept is the receptive part -- the matter, and the whole final product is thought thinking itself (just like Aristotle -- but now the thought is the whole of the universe itself thinking about itself with a thinking part (us) and a part being thought about (us + things that don't think)).

For 2, there's going to be an identity between Spirit and the activity of negating the negation as it happens through time. If you look at the Phenomenology of Spirit, one of the interesting claims that Hegel has is that all consciousness is self-consciousness. (Or to reword that, Hegel is a Kantian insofar as concepts organize our thoughts and knowledge, but not a Kantian in not being committed to two categories and in rejecting that we can't know things in themselves) So then we have a procession that looks something like this: 1. We already knew that "space" (here not to be confused with how the term is used in physics) is a negation whereby we carve the world into bits. 2. We learn "time" is the negation of "space". 3. We then realize that the carving of the world into "time" (on top of the carving of it into "space") is the activity of Spirit. 4. Ergo, there's an identity between "time" as the negation of negation and Spirit as the term for the consciousness that encounters the world with this framing.

For 3, there's two senses, for Hegel, in which Spirit must fall into time. First, the activity of spirit happens in time. This is important for Hegel, because Hegel is not positing a world of Platonic forms. Instead, all of the distinctions that Spirit makes are for Spirit in time. Thus it "falls into time" insofar as it is not atemporal. Second, since "time" is a category Spirit is imposing on its world, then the Spirit is of course under time whenever it's doing anything -- since Hegel is a realist about the things Spirit is discovering (reworded: Spirit's discovery about time is not merely that Spirit has time as a category but that everything is under time -- including Spirit).

There's an extra reason of course for Heidegger to be interested in this in the second part of Being and Time which is that time is the existentiell of the self and temporality is the fundamental category of Da-Sein (see 397). This last point is not something Hegel (or Hegelians) would agree to.

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