Topology of being and its limit theorem

“What is originary and primary is, and constantly remains, the full undifferentiated manifold out of which . . .”1


In a lecture of November, 1925, Heidegger ridiculed the tradition’s “seemingly profound question about bridging the gap between the real and the ideal, the sensible and the non-­sensible, the temporal and the timeless, the historical and the supra-historical . . . First you invent these two regions, then you put a gap between them, and then you go looking for the bridge. ‘Take the gap and build the bridge.’”2

Now with ‘being and beings’ we do have two sides of a distinction plus their bridging ‘and.’ What remains obscure is that medium in which their distinctness can occur at all. Heidegger sees that any two coordinate, correlative, or complementary regions are embedded in the dimension of their order, relation, or whole. “Basically we are in a situation where we have to see these two separate orders or fields or spheres or regions [Reihen, Felder, Sphären, Regionen] as coming together in a unity [eins zusammen].”3 His question then becomes ‘what is the dimension in which that unity is embedded?’

At the age of eighteen, as the old Heidegger tells the story, he was handed a text On the Manifold Meanings of Being in Aristotle. He writes of this experience,

“On the title page of his work, Brentano quotes Aristotle's phrase: τὸ ὄν λεγέται πολλαχῶς. I translate: ‘A being becomes manifest (sc. with regard to its Being) in many ways.’ Latent in this phrase is the question that determined the way of my thought: what is the pervasive, simple, unified determination of Being [durchherrschende einfache, einheitliche Bestimmung von Sein] that permeates all of its multiple meanings? . . . whence does Being as such (not merely beings as beings) receive its determination [Bestimmung]?”4

In his “crash course”5 on Being and Time for psychiatrists Heidegger brings up psychosomatic illness for discussion. He characterizes the critical issue as

“which distinction [welche Unterscheidung] we are talking about regarding the theme of the psychosomatic. How can this distinction be made? What different things stand in question regarding their difference [hinsichtlich seiner Verschiedenheit]? In respect to what sameness and unity [Selbe und Eine] do the different things [psyche and soma] show themselves as different?”

To help us see what he’s driving at he puts the case of color: “Green and red are only distinguishable insofar as something like colour is pregiven [insofern uns dergleichen wie Farbe vorgegeben ist]. It [the pregiven ‘something like colour’] is the same regarding which distinction can be performed in the first place.” Heidegger says he is trying to illustrate what he means by ‘genuine critique,’ echte Kritik: it means “to allow the different as such to be seen in its difference [das Verschiedene als solches in seiner Verschiedenheit sehen lassen].” Because,

“What is different is different in only one respect [in einer Hinsicht]. In this respect, we catch sight of what is the same beforehand [erblicken wir zuvor das Selbe] regarding what different things belong together. This same must be brought into view in each distinction [Dieses Selbe muss bei jeder Unterscheidung in den Blick gebracht werden].”6

Now a raven differs from a writing-desk in many respects. Heidegger means, apparently, that each respect of difference descends from, or occurs within, its proper, unique antecedent or pregiven dimension: the “what is the same beforehand” with respect to the difference at issue.7

In Being and Time the antecedent general notion ‘being’ admits of two different modes of determination or Seinscharakter:– who and what; Seiendes ist oder ein Wer oder ein Was.8

“Existentialia and categories are the two basic possibilities for characters of being [Seinscharakteren]. The entities which correspond to them require different kinds of primary interrogation respectively: any entity is either a ‘who’ (existence) or a ‘what’ (presence-at-hand in the broadest sense [Vorhandenheit im weisten Sinne]). The connection between these two modes of the characters of being [Zusammenhang der beiden Modi von Seinscharakteren] cannot be handled until the horizon for the question of being [Seinsfrage] has been clarified.”9

Being and Time designates this distinction between existential and categorial as ‘das ontologischen Unterschied’: “In the first instance it is enough to see the ontological difference between being-in as an existentiale and the category of the ‘insideness’ which things present-at-hand [Vorhandenem] can have with regard to one another.”10 I.e., the ontological difference between existential and categorial Seiendes; a difference between types of beings.

‘Being as such’ is ‘the same beforehand’ which enables the first ontological difference. Yet there’s a difference here, too – between being and beings (whos + whats). Beings are what-and-whoever show up to us as meaningful, and being is ‘meaningful presence as such,’ that beings show up to us as meaningful. In light of Heidegger’s later thinking this is the ‘narrow’ sense of ontological difference; the difference between being and beings; between meaningful presence as such and beings meaningfully present to us.11

Heidegger claims that

“Somehow the Dasein knows about something like being. Since it exists, the Dasein understands being and comports itself toward beings. The distinction between being and beings is there [ist da], latent in the Dasein and its existence, even if not in explicit awareness. The distinction is there, ist da [i.e., it exists]; that is to say, it has the mode of being of the Dasein: it belongs to existence.”12

The distinction between being and beings, the narrow sense of the ontological difference, he says, must be brought into explicit awareness. Once it enters explicit awareness there arises the question of what sameness and unity underlies that difference; what is the same beforehand of that distinction between being and beings? Heidegger’s recursive move is to ask about that which subtends the difference between being and beings; thus to arrive at a ‘broader’ (Sheehan’s term) ontological difference.

“We speak of the ontological difference [Differenz] as the distinction [Unterschied] within which everything ontological moves: being and beings. And yet—how do things stand with regard to this distinction itself? . . . with the intrinsically clear distinguishing of ontic [beings themselves] and ontological [beings as such; the being of beings] – ontic truth and ontological truth – we indeed have that which is different in its difference, but not this difference itself [das Differente einer Differenz, aber nicht diese selbst].”13

Heidegger therefore now seeks out the dimension which makes possible “this difference itself.” His idiom describes the narrow ontological difference between being and beings as a movement, a performance, which takes place within, or as, a fundamental occurrence:

“The question concerning this difference [between being and beings] becomes all the more urgent when we see that this distinction [the narrow ontological difference] does not arise subsequently by merely distinguishing two separate things lying before us, but in each case belongs to that fundamental occurrence [je zum Grundgeschehen gehört] in which Dasein moves as such [als solches bewegt].”14
“Existence means, as it were, ‘to be in the performance of this distinction.’ Only a soul that can make this distinction has the aptitude, going beyond the animal’s soul, to become the soul of a human being.” 15

This movement or performance of the narrow ontological difference must take place in some heretofore undescribed situs of “that fundamental occurrence.” “What kind of distinction is this: ‘being of beings’? Being and beings . . . Here the difficulty does not lie in first determining the kind of distinction, rather we are already unsure and at a loss to begin with, when we wish merely to attain the field or dimension [das Feld, die Dimension] in which to make the distinction. For this dimension is not to be found among beings.” Even if being and beings are distinct, “then nevertheless they are still related to one another in this distinction: the bridge [die Brücke] between the two is the ‘and’. Thus this distinction as a whole is in its essence a completely obscure distinction . . . obscure with respect to the very dimension in which the distinction is possible.”16 To connect being and beings the bridge has to extend within some dimension in which all three – being, beings, and bridge – are embedded.

The unity now in question – the object of die Seinsfrage, Being and Time’s question about being – is “der Herkunft der ontologischen Differenz,” the provenance – the dimension, the embedding space – of the narrow ontological difference, being/beings.17

“The unifying connection [das einigende Band] is missing, or rather the origin of this distinction [der Ursprung dieses Unterschiedes] in which, in accordance with the uniqueness [Einzigartigkeit] and originary character [Ursprünglichkeit], the distinguishing is earlier [das Unterschieden früher ist] than the two terms that are distinguished. That is, we are missing the origin that first lets these two terms [being and beings] spring forth [entspringen].”18

Only by going beyond the difference between being and beings can we reach this obscure origin. Richardson comments that “As time goes on and his language clarifies, it becomes more and more clear that what really interests him is not so much the meaning of Being but the meaning of the ontological difference as such . . . that is, as the e­‐vent out of which Being and beings issue . . . the e­‐vent of truth (A­‐lētheia) out of which both Being and beings issue forth . . . a unified e-­vent called ‘mittence’ (Geschick) . . . out of which the [narrow] ontological difference issues forth.”19

Part I, Division 3 of Being and Time was intended to treat of “Time and Being.” Heidegger’s later marginal note gestures at the very dimension in which the distinction is possible: “The difference bound to transcendence [transzendenzhafte Differenz]. The overcoming of the horizon as such. The return into the source [Herkunft]. The presencing out of this source.”20

In the horizon­‐metaphor of the (narrow) ontological difference the horizon bounds the space of meaningful presence; beings are what show up as meaningfully present within that horizon. So horizon-and-the-appearance-of-objects-within-it embodies the narrow ontological difference being-and-beings. Heidegger suggests in Gelassenheit that “what lets the horizon be what it is has not yet been encountered at all. . . . We say that we look into the horizon. Therefore the field of vision is something open, but its openness is not due to our looking. . . . What is evident of the horizon, then, is but the side facing us of an openness which surrounds . . .”21

Caputo observes that

“Horizonal conditionality—upon which metaphysical conceptuality turns—turns out to be itself conditioned, itself a function of deeper sources. For, beyond the object-with-horizon, there is the Open itself of which the object bound by its horizon is but a perspectival or partial view. If the horizon lets the object be—as it does, that is how horizonal thinking is possible—it remains true that something lets the horizon be, and that is the Open.”22

And Sheehan describes Heidegger’s thinking as progressing

“(1) through the ‘narrower’ ontological difference that defines the problematic of metaphysics, and (2) beyond it to (3) the ontological difference in the ‘broader’ sense: the difference between things-in-their-meaningfulness and the clearing that makes the ‘narrower’ difference possible. Heidegger moves beyond transcendentalism to the a priori fact of the clearing.”23

Sheehan’s term ‘things­‐in­‐their­‐meaningfulness’ subsumes both being and beings, i.e. the two terms of the narrow ontolological difference, Caputo’s ‘object­‐with­‐horizon.’ The ontological difference in the broader sense is between ‘being­‐and­‐beings’ on the one hand and the clearing/the Open (die Lichtung, A-­lētheia, Geschick, das Offene, etc.) on the other.

So what about that difference, the broader difference? What is “the same beforehand,” the “origin” that lets these two terms – things-­in-­their-­meaningfulness on one hand and on the other the clearing – spring forth? “In respect to what sameness and unity” do the two terms – horizon-­with-­object and Open – “show themselves as different?”

This question marks the limit of Heidegger’s dimensional analysis, what he calls “topology of being.”24 Sheehan explains that when Heidegger says the clearing is “hidden in the first and primary sense” he is arguing “that the clearing is instrinsically unknowable, if ‘knowing’ means discerning the reason for something, what Aristotle would call ‘knowing the αἰτία of something;’” “available to the discursive intellect.”

“As the ultimate presupposition,” Sheehan continues,

“the clearing must always be presupposed in any attempt to know it. It always lies ‘behind’ us, so to speak, and it will always remain behind us (i.e., unknowable) even when we turn around to take a look at it. Consequently, we cannot go ‘beyond’ or ‘behind’ it without contradicting ourselves. We cannot (without moving in a vicious circle) seek the presupposition of this ultimate presupposition of all our seeking.”25

Seeking the presupposition of the clearing – going beyond or behind or outside it to the order or field or sphere or region or dimension of its origin or source or provenance so as to discern the clearing’s dimensional aitia – is here ruled out. Sheehan quotes Heidegger: “There is nothing else to which appropriation could be led back or in terms of which it could be explained.”26 Just as ‘What is nature?’ cannot be determined by an answer distinct from nature,27 so also ‘Why is there sense-­making?’ cannot be determined by an answer distinct from sense-­making.

Nevertheless the clearing itself, Sheehan writes, “can be experienced in the non-­discursive immediacy of dread or wonder.”28 In Graham Priest’s formulation, “though one cannot have knowledge by description of nothing, one can, according to Heidegger, have knowledge by acquaintance. It is precisely in the experience of anxiety, that a person (Dasein) comes face to face with nothing.”29 Heidegger says that

“The ‘fact’ that Dasein [sense-­making] ‘is’ at all and ‘is not not’ . . . can be experienced by Dasein itself in an original experience [in einer ursprünglichen Erfahrung erfahren werden]; this is nothing but the disposition of dread. . . . Dread is nothing other than the pure and simple experience [die schlechthinnige Efrahrung] of being in the sense of being-in-the-world.”30

Many of Heidegger’s pronouncements about this experience intimate that it also gives us a glimpse of the embedding dimension; e.g., “the decisive experience where we might learn with that abysmal depth the richness of being sheltering itself in the essential nothingness.”31 The idea is that by way of some Grundstimmung we can experience meaningfulness, world, as a whole within a surrounding abyss of meaninglessness, widersinnig, the embedding space. Sheehan puts that idea in these terms:

“But surprisingly, the no-thing we encounter [in dread], this yawning abyss under our feet, is a nihil that is neither absolutum nor even negativum. . . . You cannot make sense of the absurd—trying to do so would itself be absurd—but you can make sense of everything else as you stand there with your back pressed up against your death. You now see that, against the encompassing dark, you sustain a fragile bit of space within which things appear as meaningful.”32

Scaling up now, this image depicts Dasein itself sustaining a fragile bit of space embedded in a dimension of encompassing dark, the abyss. In this image it appears we can “catch sight of what is the same beforehand regarding what different things belong together;” thus we can take ‘the dark’ as the embedding space of the distinction horizon/Open. But that interpretation is misleading; ‘the dark is us’ fully as much as the light.

The limit theorem of the topology of being is concisely expressed by Sheehan: “I cannot not make sense of everything I meet because I cannot not be a priori opened up.”33 Most recently he has characterized it this way: “What we do through all our waking hours (perhaps even during REM sleep) is make sense of stuff, whether of people, things, ideas, or experiences—whatever we happen to encounter. We make sense of things even when we get it wrong, or go insane, or babble incoherently on our death beds.”34 This formulation restates Heidegger’s “Everything we talk about, everything we have in view, everything towards which we comport ourselves in any way, is being; what we are is being, and so is how we are.”35

No experience, no matter how ursprünglich, can disclose an embedding dimension of the distinction horizon/Open because all experience takes place only within and by virtue of the horizon/Open, sense-making, affective/cognitive ‘taking-as.’ Just as authentic and inauthentic existence are only modifications of one another,36 so too are the abyss and the everyday. However much absurdity, so much sense-making.

Apposite here is Nāgārjuna’s statement of the theorem:

“There is no distinction whatsoever between saṃsāra and nirvāṇa. There is no distinction whatsoever between nirvāṇa and saṃsāra. What is the limit [koṭiḥ] of nirvāṇa, that is the limit of saṃsāra. There is not even the finest gap to be found between the two.”37

DCW 7/04/2020


1 Martin Heidegger, The Fundamental Concepts of Metaphysics: World, Finitude, Solitude (tr. William McNeill and Nicholas Walker 1995) 333: das Ursprüngliche und Erste ist und bleibt ständig die volle ungeschiedene Mannigfaltigkeit, aus der heraus . . .

2 Martin Heidegger, Logic: The Question of Truth (tr. Thomas Sheehan 2010) 76-­77

3 Ibid.

4 Heidegger’s Preface to William J. Richardson, S.J., Heidegger: Through Phenomenology to Thought (4th ed. 2003) x.

5 William J. Richardson, “Heidegger and Psychoanalysis?” 5 Natureza Humana 9, 12 (2003).

6 Martin Heidegger, Zollikon Seminars: Protocols—Conversations—Letters (ed. Medard Boss tr. Franz Mayr and Richard Askay 2001) 77.

7 What then is the dimension enabling one respect of difference’s differing from another respect? So Herbert Feigl to Hilary Putnam: “Is the difference between a difference in kind and a difference in degree a difference in kind or a difference in degree?” Hilary Putnam, “Rethinking Mathematical Necessity,” repr. in Words and Life (ed. James Conant 1994) 262 note 10. Cf. Aristotle: “But since we also distinguish white from sweet, and every other perceptible thing from every other, then there is also something by which we perceive that they [color and taste] are different. And this is necessarily perception, since they are perceptible things. . . . but it is [also] necessary that some one thing say that they are different, for sweet is different from white and therefore the same thing says so. And what it says, so too it both grasps by thinking and perceives.” On the Soul (tr. Joe Sachs rev. ed. 2004) 130-­131. Bekker 426b: ἐπεὶ δὲ καὶ τὸ λευκὸν καὶ τὸ γλυκὺ καὶ ἕκαστον τῶν αἰσθητῶν πρὸς ἕκαστον κρίνομεν, τινὶ καὶ αἰσθανόμεθα ὅτι διαφέρει. ἀνάγκη δὴ αἰσθήσει· αἰσθητὰ γάρ ἐστιν. . . . δεῖ δὲ τὸ ἓν λέγειν ὅτι ἕτερον· ἕτερον γὰρ τὸ γλυκὺ τοῦ λευκοῦ· λέγει ἄρα τὸ αὐτό· ὥστε ὡς λέγει, οὕτω καὶ νοεῖ καὶ αἰσθάνεται-­

8 Cf. “Magnitude-­notions are only possible where there is an antecedent general notion which admits of different modes of determination [Grössenbegriffe sind dur da möglich, wo sich ein allgemeiner Begriff vorfindet, der verschiedene Bestimmungsweisen zulässt].” Determinations form a continuous manifold if there is a continuous path from one to another; if there is no such continuous path between them then determinations form a discrete manifold. Determinations in the case of continuous path are called points, in the discrete case elements. Bernhard Riemann, Über die Hypothesen, welche der Geometrie zu Grunde liegen (1854); tr. William Kingdon Clifford, “On the Hypotheses which lie at the Bases of Geometry.” And that is the last we hear from Riemann of “antecedent general notion.” https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/

9 Martin Heidegger, Being and Time (tr. John Macquarrie and Edward Robinson 1962) 71. I.e., two regions and their bridge.

10 Id. 82.

11 “what Heidegger . . . called the ‘narrow’ sense of the ontological difference: the distinction between things and their being.” Thomas Sheehan, Making Sense of Heidegger: A Paradigm Shift (2015) 222.

12 Martin Heidegger, The Basic Problems of Phenomenology (tr. Albert Hofstadter rev. ed. 1988) 319.

13 Fundamental Concepts of Metaphysics 360.

14 Ibid.

15 Basic Problems of Phenomenology 319.

16 Fundamental Concepts of Metaphysics 356.

17‘Seinsfrage’ in Sein und Zeit [ist] der verkürzte Titel für die Frage nach der Herkunft der ontologischen Differenz.” As quoted in Sheehan, Making Sense of Heidegger 222 fn. 131.

18 Fundamental Concepts of Metaphysics 362.

19 William J. Richardson, “Heidegger and God – and Professor Jonas,” 40 Thought: Fordham University Quarterly 13, 28, 29, 31, 35 (1965).

20 Martin Heidegger, Being and Time (tr. Joan Stambaugh 1996) 35 fn.

21 Martin Heidegger, Discourse on Thinking (tr. Hans E. Freund and J. Anderson 1966) 63­‐64.

22 John D. Caputo, “Three Transgressions: Nietzsche, Heidegger, Derrida,” 15 Research in Phenomenology 61, 70 (1985).

23 Making Sense of Heidegger 222.

24 Martin Heidegger, Four Seminars: Le Thor 1966, 1968, 1969; Zähringen 1973 (tr. Andrew Mitchell and François Raffoul 2003) 47; Topologie des Seins.

25 Making Sense of Heidegger 227.

26 Ibid.

27 Four Seminars 22.

28 Making Sense of Heidegger 227.

29 Graham Priest, “Heidegger and the grammar of being” in Beyond the Limits of Thought (2nd ed. 2002) 242.

30 Martin Heidegger, History of the Concept of Time: Prolegomena (tr. Theodore Kisiel 1985) 291.

31 Heidegger’s letter to Sartre, October 28, 1945 (my emphasis); tr. Pete Ferreira here: http://enowning.blogspot.com/2006/06/heres-­my-­translation-­original­‐in.html

32 Making Sense of Heidegger 164.

33 Making Sense of Heidegger 113.

34 Thomas Sheehan, “Heidegger: πάθος as the thing itself”; forthcoming in Philosophers in Depth: Heidegger on Affect edited by Christos Hadjioannou.

35 Being and Time (MR) 26.

36 Id. 168, 224, 312, 365.

37 Nāgārjuna’s Middle Way: Mūlamadhyamakakārikā (tr. Mark Siderits and Shōryū Katsura 2013) 25.19-­20, p. 302. Nietzsche: Wir können nicht um unsre Ecke sehn. Die fröhliche Wissenschaft § 374.