I don't often write about late Heidegger. One reason is that I think late Heidegger often does something that resembles religious thinking more, and in that specific vein, even with his idiosyncratic commitments, there are more interesting figures. Nevertheless, I've recently been thinking about a new interpretation of late Heidegger that continues basic lines of my interpretation of early Heidegger, and it may have interesting implications precisely for clarifying some of the more difficult parts of his later thought. But before we get into the matter, a brief introduction about what we're talking about.

Late Heidegger relies considerably on Hölderlin to speak about what is called in the literature the fourfold. As we shall see, I'm not suggesting we forget this context, but that we should take it with a grain of salt. There are two dominant presentations of this story in his work, which I think are worth presenting as a starting point. One dominant interpretation that began with William Blattner, in my opinion, but whose dominant expression comes from Thomas Sheehan, is that early and late, what occupies Heidegger is the question of the world's intelligibility. In this sense, the horizon of this interpretation is to understand Heidegger as a kind of transcendental thinker without a subject. Heidegger's fourfold includes four parts: earth, mortals, immortals (gods), and sky. These are "present" to some extent in every being in our world and constitute our world. An equally dominant interpretation of Heidegger's fourfold is that of Julian Young, who argues that humans and earth versus immortals and sky represent the tension between nature and culture, respectively. Both of these interpretations seem flawed to me, the second more than the first, but both capture something correct about the Heideggerian fourfold. There are better interpretations than these, say Caputo's, but this is not the place to enter into a full literature review.

I want to suggest something slightly different, but I think I can support this with Heideggerian texts and certainly with his motivations as I think I understand them. Heidegger notes in several places the importance of studying Aristotle, in one place even noting that, in his opinion, it's advisable to do this for ten to fifteen years before moving on. The teens and twenties of the twentieth century were essentially full of courses dealing with Aristotle directly or indirectly, and later, too, one can find this intensive engagement. Indeed, one can say that there is no other philosopher that Heidegger engages with more consistently throughout his entire career than Aristotle. Moreover, it should be remembered that Heidegger, like Husserl, initially studied mathematics—and apparently remained updated on developments in the field throughout his life. While his actual remarks in the field are somewhat superficial (at least until some of his correspondence is released from the archive), one can identify the "fingerprints" throughout all his work. Indeed, Heidegger's remarks in the field might create the mistaken impression that Heidegger despised these areas and saw them as part of the scientific enterprise that increasingly detaches itself from Being. While as a general description, this is certainly correct, God in this case is in the small details. These two lines will serve to give basic outlines for a renewed interpretation of Heidegger's fourfold, which, for now at least, I'll leave in the realm of a small post and hopefully thought-provoking. Maybe sometime I'll be able to do this more systematically.

Let's start precisely with the mathematical background, where I think we're dealing with analogical thinking that's somewhat more abstract, more than a concrete influence. Toward the end of the 19th century, Riemann (1826-1866), and after him Einstein (1879-1955), Brouwer (1881-1966) and Weyl (1885-1955) gradually freed the concept of "dimension" from the spatial intuitiveness to which it had been bound in the neo-Kantian intellectual climate. The rise of topology in particular helped free geometry itself from Euclidean space. Within physics, disciplines began to develop in which concepts of stretching had a place of honour. Topology, in particular, did much to show the importance of the concept of 'place' in mathematical thinking, which gradually began to advance to concepts of spaces with local properties that cannot be simply derived from the properties of global space. It seems to me that many interesting insights will be involved in how much Heidegger remained updated on these developments, but first, we need to map generally what we're talking about here. At the risk of over-poeticization, the renewed attention to the internal logic of something like "place" rather than mere Cartesian space reopened the door to Aristotelian thinking, and to those who engaged with it, like Heidegger.

In 1927, Heidegger gave his course "Basic Problems of Phenomenology." This is a long and detailed course, and it perhaps allows a "glimpse" into the thinking behind "Being and Time" within the contexts in which it was created. In this course, Heidegger gave a long and detailed discussion of the concept of time in Aristotle, and tried to move beyond it. However, what interests us in the context of the fourfold is precisely a side discussion by Heidegger of the concept of dimension in Aristotle, a concept that would become more central to his later philosophy, and specifically in "...Poetically Man Dwells..." (1951) which will be the focus of our discussion here.

Heidegger opens his discussion of the concept of dimension with an emphasis precisely that dimension denotes movement. Movement, following Aristotle, is not necessarily kinetic movement. It can also be a movement of qualitative change, for example, of colour. Although movement is not necessarily spatial, it does formally denote a transition "from a certain place to another place." If I may be permitted a paraphrase of Gadamer on Strauss, it's hard to believe that Heidegger would have arrived at this analysis if the topology of his time had not been advanced, or if he had not been a close reader of Brouwer, to whom he paid respect throughout the twenties as a mathematician influenced by phenomenology (as we shall see, this is not the most interesting case of this connection). Moreover, following Aristotle, Heidegger thinks of this dimension as a kind of stretching. Something that stretches from here to there. The dimension has another property that Heidegger attributes to it, and that is continuity. Space is a special case of dimensionality, but so too, what interests Heidegger more at this stage is time, which in the course of his discussion there gradually takes ontological primacy. What's interesting for our purposes is that the "moment" is grasped by Heidegger not atomically, but as a certain "stretching" (spandness, Durchmessen) of the spanned—the moment presupposes dimensionality, not the reverse.

Heidegger's course also contains an explicit reference to Aristotle's "On the Heavens"; however, his presentation, at this stage, of the heavens remains dry. In "Being and Time", the heavens play a role somewhat similar to that which they play in Aristotle. A kind of natural presence that, on one hand, doesn't depend on the human world of tools, but one that also allows using it as if it had the kind of being of tools (Zuhandenheit) that designates it to be a kind of natural public clock. The heavens appear in several other places in Being and Time as an aside, say in the movement of stars around the church, but mostly they are absent. Therefore, at this point, we must temporarily abandon philological piety and see whether Aristotle's text "On the Heavens" presents interesting insights that might help us later. I argue that it does.

I will mention again in this context the excellent research of Richard Bodéüs, Aristotle and The Theology of the Living Immortals. One of the interesting things that Bodéüs shows is that Aristotle addresses in "On the Heavens" the ancient Greek tradition according to which "the gods dwell in the heavens" in order to explain that the heavens are the natural candidate to be something divine and possessing the perfect properties that he attributes to the kind of circular movement he thinks about. According to Bodéüs, it seems that the traditional gods that Aristotle commits to there are gods who hide and may reveal themselves to the sublunary world according to their will. The heavens as a whole, as Aristotle emphasizes, are a hidden realm that we mainly use analogies to understand how it functions. We have some sensory access to them, but it is very limited. What's important, in my opinion, is what Bodéüs doesn't quite notice but seems significant to me in Heidegger's context. Aristotle presents the traditional consideration, which he attributes to all peoples as such, roughly thus: the place of the gods is certainly the most honoured place, that is, the highest. The heavens are the highest. Hence, the gods dwell in the heavens.

That the place of the gods is the highest, and it is the heavens, may begin to explain, in my opinion, Heidegger's motivation in constructing his fourfold. Like early Heidegger and his intensive engagement with Aristotle, late Heidegger also tries to offer a kind of revival of Aristotelian concepts. But he becomes more radical. Heidegger tries to revive in some way not only Aristotelian concepts (as in the early twenties, "Basic Concepts of Aristotelian Philosophy") or a certain form of Aristotelian ethics and science (as in the years around "Being and Time," for example in the course "Plato's Sophist"), but to restore in some way Aristotle's cosmological understanding. It seems to me that we wouldn't be far wrong if we saw in the taxonomy of the fourfold at least a partial expression of this kind of motivation.

In his essay "...Poetically Man Dwells..." on Hölderlin's poem, Heidegger unfolds his fourfold. This is one of perhaps four or five central texts of late Heidegger in which he deals with these concepts, but for our purposes here, it provides me with the most material for thought. Hölderlin hardly thought through Aristotle, but mainly through Plato. His own philosophical thinking is quite impressive, but ultimately, we're dealing with two or three works that there's not much to do with if you don't have the (lack of) work ethic of Derrida or Nancy. Most of Hölderlin's thinking is concentrated in his poetry, and for this reason, although Heidegger offers some discussion of his philosophical writings, they are by no means in his interpretive focus. On the contrary, Heidegger is certainly capable, if his Nietzschean interpretations of Rilke are any indication, of bringing the philosophical apparatus and issues that interest him from home to poetry. His methodological remarks on thinking's approach to poetry in the mentioned work also suggest that Heidegger is not interested in reaching common ground with poetry, but in "encountering" it from within his thinking.

Heidegger says several interesting things about the relationship between sky and earth in "...Poetically Man Dwells..." First, he pays extraordinary attention to the fact that the place where man dwells is the earth. Man's place, and thus also poetry's, is the earth. In contrast, the dwelling place of the gods is in the heavens. Heidegger returns to engage in this work with the concept of dimension, and as he describes it, the dimension is what lies between "from the earth to the heavens." The formal structure of dimensionality completely repeats the formal structure of dimensionality that Heidegger finds in Aristotle. At this point, it's worth noting an interesting difference. Aristotle explicitly discusses the subject of dimensions in "On the Heavens", but he does so in a completely different way than Heidegger. For Aristotle, dimensions, where he understands in a completely spatial way and claims there are none other than the three dimensions (quite unlike early Heidegger's attempt to construct temporality as a separate dimension in Aristotle)—he also claims that each dimension constitutes a "form of division" of space. One dimension can be divided only in one direction. The second dimension is only in two directions. And the third dimension in three directions. Since space is given to division, Aristotle believes it is continuous. This is important because for Aristotle, there is a divider and there is what is divided. Denominator and numerator. Space has what is called a metric.

In Heidegger, on the other hand, who interprets Aristotle such that time too is to some extent a dimension (and this is a problem in interpreting Aristotle, but he's not the only one who interprets thus), the dimension has no metric. The continuity of the dimension is obtained precisely from another property of it, from the fact that the dimension has to some extent a direction, as we saw in the general formal structure, "from here to there." The sheets that can be stretched from here to there, since they can be wide or dense, are continuous. The continuity of the stretching doesn't require a metric of space. At the time of the course "Basic Problems of Phenomenology", a distinction of this kind might have been understood in a way that is at most metaphorical. However, by the time Heidegger writes "...Poetically Man Dwells..." (1951), his statements already have an echo that begins to emerge in the mathematics of the generation.

If we take Bodéüs at his word, there is here a deeper analogy between the mode of man's dwelling and the mode of the gods' dwelling. In the work, Heidegger speaks of how in his gaze toward the heavens, man is "stretched" from his place in the heavens upward. Analogously, as we have seen, the gods are able at will to peek downward, which may explain the agency that Heidegger attributes to them in his later philosophy.

(Drapery Study for a Seated Figure c1470 Leonardo da Vinci)

Beyond this, we might and should think about things perhaps from the viewpoint of topology as it was understood among others by the mathematician René Thom (1923-2002, a Fields Medal-winning mathematician who became an interpreter of Aristotle): following Aristotle and Heidegger one can think that the space in the heavens and the space on earth have quite different local properties and yet they maintain a connection between them. For example, man's dwelling on earth takes the form of confronting death, which constitutes man. For the gods death remains external, they don't "confront" time, and yet according to Heidegger there is another meaning to their activities, such as for instance understanding Greek tragedy as the war of new gods against old ones—a war that certainly had an effect on the world in which humans dwell. In Aristotle's "On the Heavens" the contrast between humans being mortal versus the gods being immortal is also present. The externality of time to the gods suggests that dwelling in the heavens proceeds differently. This leads Aristotle to think about the different material composition of the heavens that enables a kind of movement not possible in the sublunary world. Nevertheless, it seems there is a certain relationship between these two spaces, each of which has, as it were, quite different local properties. Perhaps the gods constitute a kind of singular points on the "surface" of the earth: from the side of the earth, if one looks only at it, these are a kind of "holes." A kind of places where if man encounters them he will lose orientation. However, from a perspective that takes the stretching into account, perhaps these are precisely the points that carry upon them properties of another kind that we have no understanding of if we take the surface of earth alone as what we consider.

I'm not interested in taking the topological analogies too far without continuing to anchor in the interpretation of the text, but as already said, I'm not the first to think about Aristotle at least from this perspective. If I may steal a bit from Heidegger, even if he didn't remain updated on new mathematical developments, thinking of "the same thing" (Aristotle) enabled him and mathematicians of the new generation, like Thom, to arrive at analogous insights, even if from different places.

In any case, the important change in Heidegger's approach is noticeable. While earlier in "Basic Problems of Phenomenology" he discusses dimension mainly as a means and preparation for his discussion of time, which is the ontologically prior dimension, later Heidegger uses the concept of dimension to denote precisely the connection between sky and earth. If earlier man is the one who must confront time and thus measure himself against it, later the poet is the one who produces a kind of "denominator" by which man "counts" himself. But we're not dealing here with a quantitative denominator, but with an imagistic denominator. The poet's images. The poet's images are supposed to be able to encompass the gap between sky and earth.

The general lines I've set out here don't begin to constitute a comprehensive interpretation, even for the Heidegger work I've chosen to discuss here. Especially the part about Heidegger's hidden god and its unique role. Nevertheless, I hope there are some lines of thought here that might be worth reading.

Basic Outlines for a New Interpretation of…