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The Principle of Non-Contradiction Grounded in Human Being in Aristotle’s Metaphysics Γ (IV)

The WS1928/29 Seminar on the Fundamental Ontological Principles

THE SEMINAR FROM THE WINTER SEMESTER OF 1928/1929, titled “The Ontological Principles and the Problem of Categories,” was Heidegger’s first in Freiburg after returning there from Marburg. It also immediately preceded his famous encounter with Ernst Cassirer in Davos. Explicitly described as taken from the protocols (“Aus den Protokollen einzelner abgeschrieben”), with the author of the protocol for each class explicitly identified, the notes of Weiss are detailed and extensive, amounting to 103 handwritten pages.¹ They also date each class, showing the seminar to have been held in eleven sessions from November 9, 1928, to February 22, 1929, with what appears to have been a supplementary session on February 23. Despite the seminar remaining completely unknown and undiscussed in the literature, Heidegger himself refers to it in a published address commemorating the sixtieth birthday of one of the participants: Eugen Fink.² There are a number of things that make this seminar of exceptional importance and worthy of careful study.

First, despite the title, the focus of the seminar is almost entirely on one ontological principle, the principle of non-contradiction, and only briefly addresses the problem of categories. The seminar provides perhaps the most extensive discussion of the principle of non-contradiction by Heidegger, a principle he elsewhere calls, despite its supposed self-evidence, “perhaps what is most puzzling in Western philosophy” (GA83, 395; vielleicht das Rätselhafteste in der abendländischen Philosophie). Another important discussion is a lecture titled “Der Satz vom Widerspruch” that Heideggger delivered on December 16, 1932. At first only some very schematic and opaque notes for this lecture were published in volume 80.1 of the Gesamtausgabe (GA80.1, 519–526). Very recently, however, two extensive drafts of the lecture were published in GA91 along with associated notes.³ All of these notes and drafts are very clearly indebted to the seminar.⁴ The approach of the seminar is signaled at the very start when Heidegger asks if principles such as the principle of non-contradiction are only “rules of thought” (Denkgesätze) with purely logical content or can be characterized as ontological principles. Though Heidegger will first turn to Kant, who will insist on the purely formal and logical character of the principles, the eventual turn to Aristotle, who will occupy most of the seminar, is anticipated when Heidegger notes that with Aristotle the characterization of the principles as ontological proves to be not without justification (WGK, 1). Another reason for the importance of the seminar is therefore the critique it offers of Kant which, if in part much more developed elsewhere (specifically as concerns the charge that the crucial role of the imagination is suppressed in favor of reason), is more developed here with regard to the part that concerns Kant’s interpretation of the principle of non-contradiction.⁵

The final reason, and the one that concerns us most in the context of the present study, is that the turn to Aristotle takes the form of a detailed reading of Metaphysics Γ. A detailed reading of this book, especially as concerns the later chapters, that is, the ones dealing with the principle of non-contradiction, is not to be found elsewhere in Heidegger. What we have seen to be true of the unpublished seminars is true of the published courses as well: it is the Physics rather than the Metaphysics that most occupied Heidegger, with his interest in the latter text limited to Books A, Z, and Θ with passing mentions of the account of “being qua being” in the first two chapters of Book Γ and of divine being in Book Λ. The detailed reading of Metaphysics Γ that attempts to cover the entire book (though the seminar ends before the very last chapters can receive detailed treatment) is thus unprecedented in Heidegger’s engagement with Aristotle. The lecture drafts referred to above contain only brief references to Aristotle’s discussion in Metaphysics Γ that clearly presuppose the much more detailed exegesis in the seminar. While it is this reading of Aristotle that is of main interest here and will therefore be the focus, I will reproduce the trajectory of the seminar as a whole, both because it deserves being better known and because it provides the context necessary for understanding the interpretation of Aristotle.⁶

To help us follow this complex and rich seminar, it might help to begin with an overview. Heidegger’s reading of Aristotle defends a strong thesis, but it also leaves us with an unfulfilled promise. The thesis is not only that the principle of non-contradiction is for Aristotle an ontological principle and therefore to be studied by the science of being qua being, but that it is ontological in a distinctive sense. Heidegger is in fact as much opposed to treating the principle as only a principle of beings, inherent somehow in beings themselves, as he is to treating it as only a principle of thought. What he finds in Metaphysics Γ is the thesis that the principle characterizes our relation to beings and is therefore grounded in human existence. To use Heidegger’s terminology, it is an ontological principle only by being an existential principle. As for the unfulfilled promise, Heidegger raises at the very outset of the seminar the question of the relation between the principle and a certain conception of time. The principle, after all, in its traditional Aristotelian formulation, is that the same thing cannot be and not be at the same time (ἅμα). The question is provoked by Kant’s deliberate exclusion of time from his formulation of the principle in the Critique of Pure Reason, against, as Heidegger shows, his own insistence on its indispensability in the pre-critical writings. When he turns to Metaphysics Γ, however, Heidegger explicitly postpones consideration of the problem of time and never returns to it in the seminar, despite the presence of the hama in Aristotle’s formulation. As we will see, this failure of the seminar is lamented by Helene Weiss herself when some years later she returns to her notes for the seminar while working on her own book on Aristotle. Yet the seminar does not leave us helpless in the face of this unanswered question. If the principle of non-contradiction is grounded in our existence, the hama essential to it would need to be interpreted, not from the perspective of the being-in-time that characterizes beings, but from the perspective of our own temporality and specifically in the mode that Heidegger will elsewhere characterize as Gegenwärtigen. In this way, the present seminar can be seen to continue the project in SS1928 of finding in Aristotle a recognition, however implicit, of the temporality of human Dasein itself. While two very different texts are the focus in the two seminars, they are also complementary texts: the defense of the principle that something cannot be A and not-A at the same time and in the same respect is just the flipside of recognizing that it is only in motion through time that something can be A and not-A in the same respect.

At the very start of the November 9 class, Heidegger, as already noted, raises the question of whether principles such as the principle of non-contradiction are only “principles of thought [Denkgesätze]” with purely logical content or can be characterized as ontological principles. Finding justification for the latter view in Aristotle, Heidegger then outlines three questions: (1) Are precisely these principles (principle of identity, principle of non-contradiction, and so on) the ontological ones in an original sense? (2) In what consists their character of being fundamental principles? In what sense can one say that they ground (begründen)? (3) In what way do they hang together with the problem of the categories? These questions will be only partly and briefly addressed in what follows. This is because the focus of the seminar will immediately become and remain one principle, that of non-contradiction, and the “problem of the categories” will not be addressed at all.

Heidegger turns to Kant’s “System aller Grundsätze des reinen Urteils” (System of all Fundamental Principles of Pure Judgment) in the Critique of Pure Reason (A 148ff., B 187ff.) with the second question in view, considering what is said there concerning what makes the fundamental principles fundamental principles before turning to what Kant says about the principle of non-contradiction in particular. Heidegger explains that in this turn to Kant the interest is not in history as such, but in the extent to which the historically given answer to the above questions can be “immediately contemporary” (unmittelbare Gegenwart). With this proviso he cites Kant’s answer to the second question raised above: “A priori fundamental principles carry this name not merely because they contain within themselves the principles of other judgements, but also because they are not themselves grounded in higher and more universal cognitions” (A148, B188; emphasis in original; my translation). The last phrase conceals an ambiguity that Heidegger goes on to identify explicitly in Leibniz’s notion of primae veritates. One meaning is that these are the highest in the sense of “first truths.” Heidegger already raises questions here. If these truths are first in the sense that they are implied in other truths and must therefore always be thought with them, what does this mean? One must think the lower truths according to the higher ones. But, Heidegger objects, how can one think according to [gemäß] a principle? “Already here everything remains dark” (WGK, 3). The other meaning is that these are highest in the sense of “the most universal truths.” All other truths are special cases of these principles, so that the latter define the very essence of truth. Heidegger clearly sees these two meanings as quite distinct and therefore speaks of an ambiguity that “points to a profound inner questionableness of the matter itself” (WGK, 3). Indeed, it is not hard to see that this ambiguity in the fundamental principles reflects that ambiguity in the nature of being itself that Heidegger calls “ontotheology”: just as “being” can refer to either the highest being or being as such, so the characterization of the fundamental principles reveals an ambiguity in the nature of truth between “highest truth” (or what is “most true”) and “what is true universally.”

As for the first question above, that is, whether the first principles are ontological in character, Heidegger notes that the central theme of the Critique of Pure Reason, which first emerges precisely in the section on the fundamental principles, is how “a nature” is overall possible. What Kant understands here by nature (see A845, B873) is the being of things as such—beings, things present at hand in their totality. Therefore the goal of the Critique of Pure Reason, Heidegger concludes, is an “ontology of nature” in the broadest sense (WGK, 4). Yet, importantly, Heidegger claims that Kant is held back from this goal by the fact that he develops this ontology from the perspective of nature understood narrowly as the object of mathematical physics (WGK, 4).

In turning now to Kant’s account of the principle of non-contradiction, Heidegger focuses on Kant’s insistence that it is a “purely logical principle,” a conviction that leads him to reject the traditional formulation in favor of the following: “no predicate that contradicts a thing can be attributed to it.” Kant’s objection to the standard formulation (A152–153, B191–193), that is, “A thing cannot be at the same time A and not-A,” is that it introduces the condition of time and thereby renders the principle no longer purely formal (WGK, 7). That a profound inner difficulty lies hidden here is suggested, according to Heidegger, by the fact that ten years previously (in his “dissertation”) Kant took the opposite view (WGK, 7–8).⁷ If Kant came to reject time as a condition of the principle, that is because, Heidegger observes, he came to see such a condition as restricting the principle to things existing in time. But this is the case, Heidegger objects, only if “at the same time” (zugleich) refers to time in the sense of existing within time. “Against this it can be objected: does the temporality [Zeitlichkeit] of the ‘at the same time’ necessarily signify ‘existing-within-time’ [Innerzeitigkeit]? Or more generally: can the logical exist simply without time? [kommt das Logische schlechthin ohne Zeit aus?]” (WGK, 9). Heidegger ends this first class by describing as “our task to expound in a concretely phenomenological fashion the meaning of this ‘at once’ [zugleich]: it clearly cannot be identified with the simultaneity of two occurrences taking place at the same temporal point within time; instead, it must have some other meaning, to be discovered by us, so that Kant’s argument is not conclusive” (WGK, 10).

Rather surprisingly, however, the next class of November 16 (protocol attributed to Käte Oltmanns) begins with the announcement that the question of time will be momentarily put aside. The reason is that we must first “make clear for ourselves the problem situation [Problemlage] of the Kantian teaching of the fundamental principles as a whole, and then on this way to show the extent to which they stand in an inner relation to time” (WGK, 10). Yet the seminar will never return to the question of time, as it will not even accomplish what Heidegger describes as the prior task: not only because Heidegger’s discussion of Kant runs out of time, but because the problem of the character of the principle of non-contradiction will lead him away from Kant and back to Aristotle.

Kant introduces the principle of non-contradiction as the highest principle of analytical judgments only to contrast it with the fundamental principle of synthetic judgments which are the ones that truly interest him (WGK, 11). But Heidegger now questions the distinction between analytic and synthetic judgments. An analytic judgement is supposed to be one in which the predicate is contained in the subject. But does that not depend on my perspective, on whether I have posited the predicate within the subject? And must not the predicate be contained in the subject for a judgment to be true? When I say that “this book is brown,” the predicate is contained in my concept of this book (since what I am referring to is “this brown book”) and must be so in order for the judgment to be true. But one will object: “brown” does not belong to the essence of “book” and therefore lies outside the concept. But in this case analytical judgments become the same as essential judgments, whereas the former are supposed to be purely formal while the latter are clearly substantive and therefore supposedly synthetic. “The body is heavy” is an essential judgment but supposedly synthetic (WGK, 12–13). In the end, the only difference between analytic and synthetic judgments appears to be in their manner of grounding: synthetic judgments have their ground and the demonstration of their truth in the object, whereas analytic judgments have this in the concept itself. “The judgments differ through their manner of grounding and not with respect to how I in each case arrived at the judgment” (WGK, 14).⁸

Heidegger then turns to Kant’s formulation of the highest fundamental principle of all synthetic judgments: “each object stands under the necessary determinations of the synthetic unity of the manifold in a possible experience” (A158, B197). Heidegger’s immediate comment is that this sentence is initially incomprehensible, the whole passage is obscure, and Kant is battling here with insurmountable difficulties (WGK, 14) A great source of unclarity is the failure to investigate what sense of “ground” is at issue here. Kant simply introduces a Grundsatz for synthetic judgments to parallel the Grundsatz for analytic judgments as if the sense of “Grund” were the same and clear in both cases.

Heidegger seeks some clarity in putting Kant’s project into its historical context. Against Leibniz, for whom the principle of non-contradiction is the ontological principle, at least as Leibniz has been traditionally interpreted, Kant is reducing this principle to a purely logical function. But then is his highest fundamental principle of synthetic judgments his version of Leibniz’s other fundamental principle, the principle of sufficient reason? (WGK, 16).

The essence of experience is determined for Kant by three things: (1) “pure time” as the pure manifold of intuition, (2) the synthesis thereof in pure productive imagination, and (3) the unity of this synthesis in transcendental apperception (WGK, 17). But then these also determine the essence of truth (WGK, 18). Heidegger reaches the following important conclusion: “The Kantian principle of sufficient reason, that all objects are subject to the conditions of the possibility of experience, therefore says: to truth belong pure time, imagination and transcendental apperception. It is the highest fundamental principle of all synthetic judgments because it is a statement about the essence of truth insofar as it is possible for finite understanding; as . . . the principle of non-contradiction is about correctness [Richtigkeit], that is, a determination of our thinking apart from any relation to an object. The one grounds a logic of truth, the other a logic of correctness” (18). But the question this immediately raises for Heidegger, and which he claims remains open for Kant, is that of the inner relation here between truth and correctness and thus between the two principles. Heidegger then opens up the prospect of understanding this relation within the phenomenon of time, given that time “plays a decisive and yet completely unclarified role in both principles” (WGK, 18). This is also a question of the relation between formal and transcendental logic (WGK, 18–19).

But the other problem here is the unity of the three determinations that are supposed to constitute the one essence of truth. Kant suggests that the sensibility and the understanding have a common root, but one unknown to us (A15). He then places the imagination simply on a level with them, between them. But Heidegger goes further, admittedly beyond Kant, in suggesting the following: “But it can be shown that with the discovery of what he calls productive imagination the root of spontaneity and receptivity is already exposed; from it spring time, that is, as Kant defines it, as pure succession, and the transcendental apperception, and indeed in such a way that we must address the transcendental imagination as the original temporality of Dasein” (20). This suggestion, Heidegger acknowledges, goes not only beyond Kant but against traditional Kantian interpretation, which is concerned with saving the primacy of reason. This traditional interpretation, Heidegger notes, is not arbitrary but has its origin in Kant himself. Kant’s Copernican revolution has the effect of displacing the primacy of reason in favor of the imagination, but Kant works against this in seeking to bring the imagination under the understanding and thus preserve the primacy of reason. “Through the so-called Copernican revolution the imagination assumes in Kant the central position previously occupied by reason. The concept of reason is in reality already exploded in the central investigations of the Critique of Pure Reason, the object of which does not at all remain reason; Kant therefore banishes this consequence. Already in the B edition a shifting of the emphasis toward logic shows itself. The imagination as an independent function is in B generally struck out” (21–22).⁹ An interesting illustration offered by Heidegger concerns a text in A78 that also appears in B103: “The synthesis in general . . . is the mere effect of the imagination, of a blind, though indispensable function of the soul.” In his own exemplar, as Heidegger notes, Kant corrected this to “function of the understanding.”¹⁰ What Heidegger does not explicitly mention is that this correction does not even make sense in the context, since the next sentence is the following: “Only, bringing the synthesis to concepts, that is a function that belongs to the understanding [Allein, die Synthesis auf Begriffe zu bringen, das ist eine Funktion, die dem Verstande zukommt].” If the function of the understanding is bringing the synthesis to concepts, then the prior production of the synthesis in the first place is not the function of the understanding.¹¹

The turn from Kant to Aristotle occurs toward the end of this class. But why this turn? Heidegger makes the following pronouncement regarding Kant’s failure to overcome dogmatic metaphysics: “It is therefore to be said that the overcoming of dogmatic metaphysics in the Critique of Pure Reason does not succeed and could not succeed insofar as there is a failure to see that this overcoming cannot exhaust itself in a critique of the ontological use of pure reason, but rather must ground a radical transformation of the meaning and essence of logic overall” (WGK, 23). For this, presumably, we must return to Aristotle, where we can approach “the dimension in which the principle of non-contradiction has its genuine meaning.” “We will see that the principle is not restricted here to a logical function, but rather points back to something else. It will further be shown, that that which the principle formulates is not at all the essential meaning and that what is meant is itself not at all a principle” (23). What this appears to suggest is that Heidegger will find in Aristotle the “existential,” and implicitly temporal grounding, that is missed in Kant with the suppression of the imagination.

But how can we go beyond Kant’s failure to overcome dogmatic metaphysics in returning to Aristotle? Is not Aristotle the origin of the metaphysics to be overcome? Heidegger immediately asserts that there is no talk of “metaphysics” in the whole of Aristotle’s so-called Metaphysics (WGK, 23–24). Instead, Aristotle speaks of a science of “beings as beings.” Heidegger discusses the meaning of this phrase, noting that “being” is not to be restricted here to essentia or existentia, but must somehow include both, though the “and” that unites them as well as why they must belong to every being remain unclarified (WGK, 25). Turning then to Γ.2 and the claim that “being is said in many ways” (τὸ ὄν λέγεται πολλαχῶς), Heidegger notes that the relation “toward one” (πρὸς ἕν), this peculiar middle between univocity and equivocity, is not further clarified but only illustrated with the health example. He also notes that Aristotle presents four fundamental meanings of being—that is, being in the sense of the categories, accidental being, being as truth, and being in the sense of dunamis and energeia—“without making into a problem how they have come together and if and why there are precisely these four” (WGK, 26).

The class of November 23 (protocol attributed to Max Müller) is prevented from continuing with the interpretation of Metaphysics Γ by what is described in the notes themselves as a “wide-ranging and general digression to which Kant instigated us” (WGK, 34). Heidegger returns to some of the claims made about Kant in the previous class with further evidence and argumentation. Thus, Kant’s discussion of Leibniz’s principle of sufficient reason in his polemic against Eberhard¹² is cited in relation to the question of whether his highest fundamental principle of synthetic a priori judgments is an extension of this principle (WGK, 27). Also, more evidence is given to show the tendency of the second edition of the Critique of Pure Reason to eliminate the imagination as an independent phenomenon, namely B151, where Kant divides imagination between sensibility and understanding, characterizing it as in some respect the work of the former and in another respect the work of the latter, thus ridding it, as Heidegger would note, of any autonomy. The conclusion is that “The temporality of transcendental apperception and time is hardly touched upon” (WGK, 28).¹³ The problem of transcendental subjectivity is a problem of all metaphysics going back to Plato’s “conversation of the soul with itself” (WGK, 29). As for Kant’s stance toward metaphysics, Heidegger cites a letter to M. Herz in 1781¹⁴ in which Kant describes his goal in the Critique of Pure Reason as that of providing a “metaphysics of metaphysics” (WGK, 29).

Heidegger then turns to a discussion of the notion Kant inherits of metaphysics or “ontology” (WGK, 30; a term, Heidegger notes, coined by J. Clausberg only in the seventeenth century [Clausberg 1647]). Kant’s project of laying the groundwork for metaphysics is instigated by the ambiguity of ontology before Kant: the ambivalence (Zwiespältigkeit) already noted above between ens commune (common or universal being) and summum ens (32, highest being). Heidegger traces this back to Aristotle (but also to Plato and Parmenides) and claims that Natorp drew attention to it for the first time (Natorp 1888). Jaeger thoroughly examined the question of the relation between theology and ontology in his Aristotle book “but not philosophically, rather philologically, that is, he makes a ‘development’ out of it” (WGK, 33). Heidegger emphatically rejects the thesis of development: “one can find the most developed ontology right in the earliest writings of Aristotle” (WGK, 33). Against the thesis of development, Heidegger also notes that the transition from katholou to theion, universal being to divine being, can be found in Metaphysics E.1 and the parallel K.7.

Heidegger concludes that the question of the inner unity of metaphysical knowledge, and thus the problem of the possibility of ontology, was not even raised before Kant and that it is the merit of Kant’s “metaphysics of metaphysics” to have raised it. The kind of unity achieved in Scholastic philosophy, and Thomas in particular, is what Heidegger calls only a “unity of results”: the summum ens is the creator of beings as beings (ens commune). Here the question of “the inner unity of metaphysical knowledge” is not even posed.

The class of November 30 (protocol attributed to Günther Siewerth) turns to a reading of Metaphysics Γ.2. Heidegger identifies in this chapter two arguments for the unity of “being insofar as being” (ὄν ᾗ ὄν) and of the science that corresponds to it:

1. The determinations of being and the idea of being as such hang together in some way. The example of health is used to show this.

2. For each genos there is one “perception” (αἴσθησις) and one “knowledge” (ἐπιστήμη).

3. Heidegger insists that aisthêsis here is not physical perception but “noetic intuition” in Husserl’s sense. Heidegger appeals to De Anima Γ.8, 432a, and Metaphysics Θ.10, 1051b21, (for the terms ἁφή, θιγεῖν) and what he calls “Aristotle’s fundamental thesis concerning αἴσθησις, that is, that no distinction is to be found in it between truth and falsehood, as in judgment, but it simply either hits upon or misses its object.” But such a notion of intuition is already to be found in Plato since it is that from which “the Platonic terms ἰδέα, εἶδος for the realm of the ὄντως ὄν are to be interpreted: the ὄντως ὄν is object of an ἰδεῖν” (WGK, 36).

We are then told that in translating the text the class focused on the expressions “some nature” (1003a34; φύσις τις), “being naturally well disposed” (1003b2–3; τῷ εὐφυὲς εἶναι), “in relation to one principle” (1003b6; πρὸς μίαν ἀρχήν). This leads to discussion of Aristotle’s health example: health primarily signifies a condition of the body and then is extended to things like weather or complexion that have a relation to this condition (weather as contributing to or endangering a healthy bodily condition, complexion as a sign of it or of its opposite). This in turn leads to a digression (WGK, 37–39) on the scholastic treatment of analogy (nomina analoga), specifically, the distinction between “analogy of attribution” (a name common to all the meanings, but a plurality of relations to this name) and “analogy of proportion” (a correspondence of relations within the diversity of meanings named by the analogous name). Heidegger claims that the analogy of being can be understood in both ways: (1) ousia is the central term and the other categories relate to it in different ways; (2) all the categories, as the highest “kinds of being” (γένη τοῦ ὄντος), have the same relation to the things under them (WGK, 39).

Returning to Aristotle’s text, Heidegger claims that the example of health illustrates an analogy of attribution, though he adds that the analogy of proportion is not unknown to Aristotle but is mentioned in the Nicomachean Ethics: the reference is presumably to the passage Heidegger discussed in the SS1923 seminar on Book I of the Ethics in which Aristotle mentions analogy of proportion as one of the possible ways, in addition to analogy of attribution, in which the different meanings of the word “good” are related (1096b28–29). Heidegger claims that it is with justification that Aristotle’s mode of demonstration here has been called rather primitive for seeking to determine something about the object of the first philosophy (πρώτη φιλοσοφία) with an example taken from medicine, though he also notes that medicine at the time ranked with mathematics as having the highest scientific validity and as an anthropological science stood much closer to Aristotle’s sought discipline than does today’s empirical medicine (WGK, 40). It is a claim we saw Heidegger make already in the SS1923 seminar on Nicomachean Ethics VI in discussing Aristotle’s comparison there of phro-nêsis and sophia to medicine (1144a4–5).

So that which is being in the original sense, that which is primarily being, is ousia. But what is the meaning of this term? Heidegger notes that we cannot fully capture its meaning with the translation “simply being present-at-hand” (einfach Vorhandensein) nor, therefore, with the Aristotelian hupokeimenon. Instead, he suggests the following characterization: “a thing as it is present in itself and for itself and from out of itself” (WGK, 40; the “for-itself,” he adds, is not any kind of relation but an inner achievement of the respective being). The interpretation of ousia, Heidegger adds, is made easier for us by consideration of the meaning the word had in ordinary language at the time of Aristotle: “means,” “household goods,” thus “what at each moment stands of itself ready for use” (WGK, 41). Aristotle recognizes two kinds of ousia: (1) first ousia, the “this here” (τόδε τι), and (2) second ousia, the “form” (εἶδος): the latter is ousia because the first and original question when we come across a thing in a knowing way (erkennend) is “What is it?”

The interpretation of Γ.2 continues with the class of December 7 (protocol attributed to Kurt Risch). Heidegger notes something remarkable: when it comes to expounding what belongs to the unitary field of the sought science, Aristotle “does so on the basis of the ἕν [one] and not the ὄν [being] itself! He gives only an indirect exposition of the ὄν” (WGK, 42). To the extent that it is the study of the one, the study of being must include study of “ταυτὸν, ὅμοιον, ἴσον [same, similar, equal], with the πλῆθος [many] of ἕτερον, ἀνόμοιον, ἄνισον [other, dissimilar, unequal]” (WGK, 42). The justification is provided by the claim at 1003b23 that the one and being are the same and one nature through [following? grounding? ἀκολουθεῖν] each other. Heidegger asks about the meaning of the verb here and suggests as a translation/interpretation “Fundierung” (founding). Here we see introduced the fundamental problem of the relation between being (ὄν) and unity (ἕν) that runs through the whole history of metaphysics (WGK, 42–43).

A brief overview of the treatment of this problem from the Middle Ages to Leibniz follows (WGK, 43). Heidegger’s main observation is that the unum was distinguished from the “one” in the sense of the unity by which we count. The “one” applies only to what can be counted, that is, number, whereas the unum belongs to everything insofar as it is something. The unum indeed produces a multitudo in combination with its other, but not every multitude has the character of being countable: the “and” is not the same as the plus sign. Heidegger also refers to Leibniz’s monadology, which quite explicitly places the problem of substance under the problem of unity (the μονάς). He finally notes that the problem is already seen in the Platonic dialogues (specifically, Sophist, Philebus, and Parmenides).

Returning to the line-by-line commentary on Γ.2, Heidegger notes that genos and eidê at 1003b21–22¹⁵ should not be understood as “genus” and “species”: neither being nor the one is a genus nor are its eidê species. Among these eidê are specified the “same” (ταὐτόν) and the “similar” (ὅμοιον) starting at 1003b33. “Sameness presupposes unity but is not a species of it” (WGK, 44). On the point that being (and the one) is not a genos, Heidegger cites Metaphysics B.3, 998b22,¹⁶ where Aristotle defends this claim with the argument that there could be no specific differences outside of being and the one that could divide them into species. Heidegger therefore suggests translating eidê here, as in Plato, as “Anblick, Bild,” noting and wanting to preserve the ambiguity of the verbs Bilden, Ausbilden between “developing” (entwickeln) and “making visible” (anschaubar machen). The suggestion therefore appears to be that we understand the eidê of being and the one as both the different ways in which they show themselves and the different ways in which they are realized or developed.

Heidegger continues with the line-by-line commentary of the text following 1003b21–22. I will highlight only what appears especially important (in the sense of making a significant and controversial interpretative claim). 1003b26–27 receives special attention: “For they are all the same: one human being, being a human being, and human being” (ταυτὸ γὰρ εἱς ἄνθρωπος καὶ ὤν ἄνθρωπος καὶ ἄνθρωπος).¹⁷ According to Heidegger, “Aristotle wishes to show that ἕν follows upon ὄν by showing that it is superfluous” (WGK, 47). He then asks: “What is the meaning of ὤν?” He argues that it cannot mean simply existence or essence but must be understood very generally: “ὤν must have the most general meaning possible, its meaning should not be restricted to ‘presence at hand’ [Vorhandenheit]” (WGK, 47). Heidegger’s own suggestion of understanding ôn as “factically existing” (faktisch existierend) anticipates what will be the focus of the seminar on precisely this mode of being that belongs to the human being. As for the meaning of hen, “To repeat: ἕν is not number, does not refer to the individual in contrast to the genus, is also not identity, which is not possible when determinations like ὅμοιον belong to it” (WGK, 48). But the important initial observation Heidegger makes here is as follows: “How do difficulties arise here from the very outset? An ontical relation is taken to be a fundamental ontological determination” (WGK, 47). The point is that the ontic equivalence of “human being,” “one human being,” “being a human being,” tells us nothing about what “being” and “being one” mean here.

Heidegger now traces the central role played by unity in Leibniz’s monadology, Kant’s unity of apperception, and Hegel’s “the essence of the substance is the subject” (WGK, 48–50). An important point he makes regarding Leibniz is that the problem of unity is not for him a formal problem: the unity in question is not simply a transcendental that applies to every possible and merely formal “something.” Rather, the one for Leibniz is unifying (Einigung), not post hoc, but “anticipatory and simple unifying and at one therewith individuating unity” (WGK, 49). This unifying is the vis itself of the monad and not merely its result. From here we can draw a clear line to Kant’s unity of apperception (the unity of the I-think that lies in every category) and to Hegel’s “the subject as the essence of substance.” What is striking in all cases is how the unity that characterizes being is taken back to the unity of the understanding of being. Heidegger therefore asks if we can succeed in the interpretation of the fundamental ontological categories of “being” and “one” in grasping them simply in their ontological content and relation or whether “we must immediately introduce unity; in another formulation: whether we have the Noema in correlation to the Noesis. Does this lie in the essence of being? Is it more than a correlation? More than a relation: that we necessarily always speak of the understanding of being in speaking of being?” (WGK, 50). Heidegger notes that speaking of subjectivity versus objectivity, idealism versus realism contributes nothing to this problem.

No clarification can be gained here without raising the question of the relation between being and beings. This means that “We must at first recognize the entire problem that lies in the ᾗ [in beings qua or as beings]. One always already understands the ᾗ in some way and is tempted to pass it by; but precisely this awakens the suspicion that there is something decisive here” (WGK, 51). Noting the many senses that “being” must include in Aristotle, Heidegger suggests: “Such universality of being forced itself on Aristotle as a problem. And in order to see this in an original way, we should not take all the named forms of being merely as in a formal presentation; they are in Aristotle much more substantial, without being represented as things. . . . If we interpret Aristotle in the sense of formal ontology, how can we come to understand that the principle of non-contradiction is meant to be a principle of being?” (51). It is indeed at this point that Heidegger decides to turn to an interpretation of the principle of non-contradiction “in order, through the clarification of this relatively clear principle, to throw some light on this general problematic” (WGK, 52). That Aristotle is not concerned with formal ontology is shown, according the Heidegger, by his critique of the sophists and the dialecticians: the former for the ethos of their philosophizing and the latter for not taking philosophy far enough (WGK, 53). The interpretation of the principle will be ontological “in the sense that we already encounter the ‘not’ and ‘none’ in being in an elemental way, the problem of negation acquires the same central position as the ὄν” (54). The class concludes with a reference to Hegel as another who built a logic that is also a metaphysics on the ontological basis of contradiction.

The discussion in the class of December 14 (protocol attributed to Anton Kröger) begins with the end of Γ.2 and the restatement of the thesis that there exists one science of being qua being. Heidegger is puzzled by a new addition to its subject matter that does not appear to follow from anything previously said: in studying not only ousiai but also what belongs to them, the science, in addition to the things already mentioned, will be “about the first and the last, genus and species, whole and part, and all other things of this sort” (1005a15–18; περὶ προτέρου καὶ ὑστέρου, καὶ γένους καὶ εἴδους, καὶ ὅλου καὶ μέρους, καὶ τῶν ἄλλων τῶν τοιοὐτων). Heidegger speculates that this represents a later addition by someone referring back to the list of philosophical terms in Book Δ (WGK, 55). But the focus of the class is the third chapter, in which Aristotle turns to the axioms, with special emphasis on the principle of non-contradiction as being by nature the principle of all the other axioms (1005b33–34). Heidegger (WGK, 56) divides the chapter into two parts: the first in which it is shown that it belongs to the same science to study ousia and the axioms (1005a19–b8); the second in which the nature of the axioms is clarified, without immediate discussion of how they ground other things (1005b8–19).¹⁸

Aristotle’s central argument in the first part is that the axioms apply to all beings and therefore cannot be the subject of study for any science dealing with only a part of beings. All the special sciences employ the axioms, but none of them for this very reason can make the axioms its one special object of study (1005a23–25). If the physical philosophers can claim to deal with these axioms, this is only because they pretend to deal with all being, even though they do not (1005a32–33). Aristotle also refers to others who speak about the truth (1005b2–3; τῶν λεγόντων τινὲς περὶ τῆς ἀληθείας), but who are ignorant of the “analytics.” Heidegger interprets the reference as being to sophists and eristics who, in seeking for a demonstration of these principles, show their ignorance of the Posterior Analytics, in particular, where Aristotle shows that first premises of a demonstration cannot be themselves demonstrated (WGK, 58).

Turning to the second part of the chapter, in which Aristotle describes the essential characteristics of the first principles, Heidegger notes the reference to the axioms as “the most stable principles of things” (1005b9–10; βεβαιοτάτας ἀρχὰς τοῦ πράγματος) and takes this as evidence that they are not for Aristotle merely logical principles of thought (WGK, 60). Indeed, Heidegger sees the ultimate grounding of thinking in being, as Aristotle understands it, as bringing into question the very distinction between Denklogik and Gegenstandslogik: even the most formal thinking is still oriented toward a “something,” all thinking is thinking of something, every noêsis has its noêma, as Husserl saw (WGK, 61). Though he does not explicitly note this, Heidegger’s questioning of this distinction clearly parallels his earlier questioning of the distinction between analytic and synthetic judgments.

Heidegger also discusses three different characteristics Aristotle ascribes to a principle by virtue of its being bebaiotatê, a term he interprets as meaning “what lies at the ground of all beings as their foundation” (WGK, 61):

1. It is “impossible to be deceived about” (1005b13; διαψευσθῆναι ἄδύνατον). As lying at the ground of all beings, it lies in a dimension prior to “truth” and “deception”: taking a being as another being (or indeed as itself) presupposes an understanding of being (WGK, 61).

2. It is “most knowable” (1005b13; γνωριμωτάτη): not, Heidegger insists, “What can most easily be known,” but “What is least foreign to us, what we are so familiar with that we normally do not think of making it an explicit theme of discussion” (WGK, 62).

3. It is “unhypothetical” (1005b14; ἀνυπόθετον) in the sense of not requiring presuppositions or conditions.

Heidegger brings together these three characteristics as follows: “So does the ἀρχή βεβαιοτάτη truly lie at the ground of all beings and is given to us as familiar self-evidence prior to all possibility of deception and without any other presupposition” (WGK, 63). But then it is to be studied by that science that makes known being as being and by the person most at home in this science, in other words, the philosopher. Finally, asking what kind of an archê is primarily meant here, Heidegger asserts that it is the principle of non-contradiction.

It is therefore with Aristotle’s formulation of this principle that the next class of January 11, 1929, (protocol attributed to Lisebette Richter) opens: “For it is impossible for the same thing at the same time to belong and not to belong to the same thing in the same respect” (1005b19; τὸ γὰρ αὐτὸ ἅμα ὑπάρχειν τε καὶ μὴ ὑπάρχειν ἀδύνατον τῷ αὐτῷ καὶ κατὰ τὸ αὐτο). Heidegger first considers worth noting the negative character of the formulation.¹⁹ Then he articulates what he considers the double character of the belonging (ὑπάρχειν). On the one hand, he insists that the phrase “impossible at the same time to belong” (ἀδύνατον ἅμα ὑπάρχειν) does not refer to the impossibility of a positing or saying but rather to the impossibility of being in the sense of the belonging of a property to something underlying it. A few lines later, Aristotle does refer to the impossibility of holding (ὑπολαμβάνειν) something both to be and not to be (1005b23–24), but Heidegger sees this as confirming rather than invalidating his reading: “That what is at issue is not the impossibility of a positing emerges from the fact that the ἀρχή is discussed in relation to ὑπολαμβάνειν only later” (WGK, 65). When he turns to the later passage, he indeed claims that the holding (ὑπολαμβάνειν) is only a special case (Sonderfall) of the belonging (ὑπάρχειν), explaining that the impossibility of holding contradictory opinions is grounded not in psychology but in the being itself (WGK, 66). Heidegger appears justified in this claim: Aristotle’s argument for why a person cannot hold contradictory beliefs at the same is that it is impossible for contraries to belong to the same thing at the same time. One can also cite here the beginning of chapter 4, where Aristotle’s opponents are described as maintaining that the same thing can both be and not be and that it is possible to hold (ὑπολαμβάνειν) the same thing both to be and not to be (1005b35–1006a2).²⁰ On the other hand, however, Heidegger finds already in the belonging (ὑπάρχειν) “predicative being” or the “is” of the copula, which gives it a relation to logos, though the “is” of the copula itself clearly contains a reference to being (WGK, 65–66). If Heidegger thus emphasizes the ontological, versus the merely logical character of the principle,²¹ we see that his primary concern is showing the inseparability of the ontological and logical senses.²²

Heidegger now turns to Γ.4 with this question: whether the starting point of the discussions in the preceding chapters is already sufficiently radical to show the connection between the principle and the “being insofar as being” (ὄν ᾗ ὄν) or whether a further radicalization is required to show the extent to which the principle of non-contradiction is a metaphysical one (WGK, 67).²³ Heidegger then suggests seeing 1006a28 as a caesura that divides the first part of the chapter as a proemium from the discussions that follow. In this proemium, Aristotle addresses the question of the demonstrability of the principle and claims it can be demonstrated only indirectly via a “demonstrating elenctically” (ἀποδεῖξαι ἐλεγτικῶς). Citing 1006a11, Heidegger emphasizes the condition of this kind of indirect demonstration: that the adversary (ἀμφισβητῶν) must speak and thus engage in a conversation (διαλέγεσθαι). That the verb “to dispute” (ἀμφισβητεῖν) is used here shows that the speaking (λόγος) at issue is living concrete discussion and not a “proposition” (WGK, 70). Indeed, the examining (ἐλέγχειν) by which the indirect demonstration takes place is not the refutation of a proposition, but has the sense, as Heidegger notes, of a shaming or public accusation (WGK, 68–69). Thus, “As in the paradigm of the Platonic dialogue, what is at issue in this suggestion of a refuting demonstration is bringing someone to the correct παιδεία [education] through ἐλέγχειν” (WGK, 69). This condition—and this is the key point Heidegger will emphasize—“pushes the discussion into a close relation to the essence of the human being as ζῷον λόγον ἔχον [living being possessing speech]” (WGK, 69). This again counts against an interpretation of the principle as a mere principle of valid meaning (vom geltenden Sinn), but also, it would appear, against its interpretation as only a principle about being as being. We appear to have here that “fuller radicalization” Heidegger sought in Γ.4. Fully understanding the “metaphysical” character of the principle of non-contradiction requires us to turn back from being to the way of being of that being that understands being, in other words, the human being. That someone unwilling to speak is described by Aristotle as like a plant (1006a14–15) is for Heidegger further indication that “the argumentation in the ἀπόδειξις ἐλεγκτικῶς [elenctic demonstration] must refer back to the essential original determination of the human being” (WGK, 70).

The class of February 1 (protocol attributed to Simon Moser) begins with a clear statement of the objective of the current interpretation: “The main aim of the interpretation of Γ.3 and Γ.4 is to examine the ontological character of the principle of non-contradiction” (WGK, 71). Yet even more important is Heidegger’s clarification that his interpretation is in fact responding to two extremes: one being the purely logical interpretation and the other that sees in the principle “a rule of beings themselves, so that it is thought of as something like a power working within beings themselves” (WGK, 71). If Heidegger opposes this latter extreme despite its being an “ontological” interpretation, this is clearly because it ignores that grounding of the principle in human existence on which he will insist.²⁴

The starting point of the indirect demonstration, as Aristotle says at 1006a18–21, is not that the opponent grant that this or that is the case, but that the opponent mean anything at all that he and others can understand (σημαίνειν γέ τι καὶ αὐτῷ καὶ ἄλλῳ). Heidegger can therefore say that the starting point of the demonstration is not this or that true statement, but rather truth as a characteristic of human existence. “For human being, and thus for the σημαίνειν τι [signifying something], the ontological presupposition is truth, that is, not the truth of a statement, but the unconcealment of what is at hand, of Dasein itself and of the being-with with others” (73). What characterizes the demonstration is not an ascent to ever more general propositions, but a return to the essence of human existence. “Spoken in the terminology we have used on another occasion: the possibility of a demonstration of the principle of non-contradiction rests on an existential-ontological basis” (WGK, 74). Here we have Heidegger’s important qualification of the ontological interpretation of the principle. Yet Heidegger immediately distinguishes his interpretation from any form of “psychologism” or “physics of thought” by noting that it (1) seeks to present the ontological content of the principle, (2) sees in the return to the human being not a return to psychological events but rather to the essence of Dasein, and (3) understands this essence in a way radically different from the way in which it is understood by psychologism (WGK, 74).

The indirect “demonstration” by refutation requires only that the challenger, as a “living being possessing speech” (ζῴον λόγον ἔχον), grant the “signifying structure of discourse” (Bedeutungsstruktur der Rede): in all understanding and signifying, what is intended is something definite and not any arbitrary thing; it is, in other words, this and not that. Heidegger seeks to make the ground of the demonstration even clearer when, commenting on 1006a24 (ἂν δέ τις τοῦτο διδῷ, ἔσται ἀπόδειξις, “if someone grants this, there will be a demonstration”), he insists that translating “διδῷ” as “grant” (zugeben) is too superficial: “Aristotle thereby actually wants to say that the opponent only needs to give himself. He must simply recollect his own essence, understanding and being-in-truth, which he has forgotten in everyday life. But insofar as truth always necessarily brings with it concealment, human beings thereby give themselves in their original negativity and finitude. So being-human is the ultimate ground, the αἴτιος of the demonstration, in which the opponent must simply hold out” (WGK, 75–76).²⁵ Heidegger also notes that the word aitios also has here the negative sense of “guilty” or “responsible”: the opponent must himself be made responsible for the demonstration if the defender of the principle is not to beg the question. The “guilt” also refers to the “negativity” of existence mentioned in the cited passage: that truth is un-concealment, that all speaking is a “meaning this and not that.”

After having addressed the possibility of demonstrating the axiom, Aristotle at 1006a28 (recall this is where Heidegger located the caesura of the chapter) introduces some arguments that further our concrete understanding of the principle. Heidegger claims that the first is of special importance to him and we immediately see why. Every word signifies this and not this being, so that “with every meaning of a word an understanding of being is given at the same time, and completely apart from the truth of the sentence” (WGK, 76). But what understanding of being in particular? An understanding of being as one. The principle of non-contradiction is thereby only the negative formulation of the principle of identity.²⁶ “In general one can express this as follows: the ontological relation, that every ὄν is ἕν, as we encountered it in Γ.1, returns here in the discussion of the ontological fundamental principles” (WGK, 77). Without the intending of something determinate and something one, there would be no signifying and therefore no dialegesthai, no logos, no noein at all. But this means, in short, as Heidegger notes, that “human existence would be impossible” (WGK, 78). Heidegger clearly wants us to see what this implies: that the principle of non-contradiction, as the ground of grounds, must itself be grounded in the possibility of human existence. This is clearly one important lesson Helene Weiss learned from her notes on the seminar, since in her own 1942 book she writes, “The being-one and being-the-same with itself of every ὄν is designated there [that is, Metaphysics Γ.3, 1005b9ff.] as the securest and unshakeable ground on which rests all διαλέγεσθαι and thereby the being of human beings as such.”²⁷

Given that the crucial phenomenon here is that of intending something determinate, Heidegger encounters and addresses what he sees as a textual difficulty at 1006b4. Here Aristotle says that while a name can signify more than one thing, these significations must be “limited with respect to number” (ὡρισμνένοι δὲ τὸν ἀριθμόν). Heidegger’s problem is that he wishes to take “limited” (ὡρισμένα), just a few lines earlier at 1006b1, as meaning not that what is signified must be “limited in number,” but rather that it must be “determinate”; likewise, he takes the contrasting “unlimited” (ἄπειρα) at b6 to mean not “unlimited in number” but “indeterminate” (WGK, 78–79). The problem, in short, is that the qualification “with respect to number” (τὸν ἀριθμόν) seems not only unnecessary, but misleading. It is hard, however, to see much of a real issue here. If the word “human” has several meanings and these meanings are all determinate, then they must also be a definite number.²⁸ In contrast, if the word can mean anything whatever, then the possible meanings would be unlimited in number.

At the start of the next class of February 8 (protocol attributed to Adolf Hänle), Heidegger divides chapter 4’s argumentation for the principle of non-contradiction into three parts, all taking their starting point from the fact that being and the one “follow one another” (ἀκολουθεῖν): (1) up to 1006b34; (2) 1006b34–1007a20; (3) 1007a20–b18. He says he will engage in particular with the first, which he sees as itself divided into a positive and a negative part. These divisions seem rather forced and arbitrary and it is not clear why Heidegger insists on them. In any case, in the context of discussing the first part, where Heidegger notes that the example is the concrete determination of the being of human beings, he returns again to the point raised at the end of the last class: that “limited” (ὡρισνένον) refers not to a numerical limitation of the possibilities of determination but that “ὡρισμένοι are determinations of the ὄν with regard to their meaning for its unity and sameness” (WGK, 82). Similarly, “the unlimited” (ἄπειρα) are determinations not unlimited in number, but rather not corresponding to the unity of the being in question. The word “number” (ἀριθμόν) at 1006b4 again poses a problem for Heidegger (WGK, 83), who adds here that the text does not fit into the surrounding argument since that argument does not speak of “one” (ἕν) in its contrast to “many” (πολλά). Heidegger suggests the possibility of a later interpolation, but prefers the suggestion that it responds to a possible sophistic objection, that is, that there may be a number of possible determinations of the human being that are not yet named. The response is that even these must presuppose the unity of what is named. “Therefore a speaking about the ὄν in preservation of its character of sameness is possible without the sum total of its possible determinations having been in fact presented” (WGK, 83).

Starting at 1006b7, the clarification of the sameness of the “one” (ἕν) is pursued negatively. Signifying something that is not one is signifying nothing (τὸ γὰρ μὴ ἕν τι σημαίνειν οὐθὲν σημαινεῖν ἐστί). Aristotle considers a possible objection: since “musical,” “pale,” and “human” can all name the same person, do they then signify one and the same thing? The idea that these words are “synonyms” (1006b18; συνώνομα) in the sense of having the same meaning²⁹ is of course rejected by Aristotle. He therefore makes a distinction between “signifying one thing” (τὸ ἓν σημαίνειν) and “signifying about one thing” (1006b15–16; τὸ καθ᾽ ἑνός). While what the names “musical,” “pale,” and “human” signify are said of one thing, they signify not one thing but different things, each one and determinate.³⁰ Heidegger explains, “In their predicative function they only bring to expression a pre-givenness of the ἕν, but do not first constitute it. Thus they do not as predicates constitute the first actualization of the ἕν, not even in a full enumeration conceived of as ideal as possible, but they are first possible in their predicative function if the ἕν is already given beforehand” (WGK, 86). What Heidegger earlier identified as the second part of the chapter’s argument, 1006b35–1007a20, provides a further clarification of the “structure of sameness.” Heidegger suggests that in the background of this argument is a conception of logos he finds expressed in Book Z, 1029b19–23: “The logos in which the thing expressed by the logos is not itself present is the logos of what-it-was-for-each-to-be” (ἐν ᾧ ἄρα μὴ ἐνέσται λόγῳ αὐτὸ, λέγοντι αὐτὸ, οὗτος ὁ λόγος τοῦ τί ἦν εἶναι ἑκάστῳ). This is a passage Heidegger already turned to in the 1922/23 seminar, finding expressed in it an “exceptional logos” that does not presuppose a particular determination of what it seeks to determine. Here his interpretation stresses the point that the thing itself in its unity is not contained in the determination of the logos but is presupposed by it. Thus, we have here a continuation of the point insisted on earlier. “It does not first become ἕν in being determined, but makes the determination at all possible and is its normative principle. The fulfilling determination acquires from it its meaning and existential sense: truth” (WGK, 87).

In the next class of February 15 (protocol attributed to Ludwig Landgrebe), Heidegger returns to the notion of “signifying about one” (σημαίνειν καθ᾽ ἑνός). Heidegger appears to think, wrongly, that “pale” “musical,” and “human being” are being called synonyms by Aristotle and asks how this can be. His answer is the following: “What then constitutes their synonymity is not the substantive meaning of the ὀνόματα in each case, but their common apophantic function” (WGK, 89). In notes that are appended to the seminar transcript, apparently written by Helene Weiss and dated August 26, 1932, she rightly objects to Heidegger’s reading here: “H[eidegger]: they are συνώνομα insofar as they all have the same categorial function (when, namely, one disregards the ἕν of the content peculiar to each). Me: they would, so understood, namely as ἕν, be turned into συνώνομα, as if each did not have its own peculiar content, as if the categorial ‘is’ were no longer understood categorially, but as an identical ἕν.” Thus on the reading of Weiss, Aristotle is not claiming that they are synonyms but, on the contrary, is using the evident absurdity of their being considered synonyms as an argument against collapsing the distinction between their content and what they refer to. But the difference in interpretation is not so significant given that in either case the crucial point is recognized: the difference between the being-one of that of which the names are predicated and the being-one directly signified by each name. Thus, in a later note, dated August 28, 1932, Weiss writes, “When I now read the text of the seminar again, it seems to me that with ‘categorial function’ Heidegger means the same thing as what I see. Perhaps expressed in a shortened and abstract way (perhaps also awkwardly expressed by the writers of the protocols). But our two opinions agree well in what is essential.” Heidegger takes the outcome of the argument to be that if there is to be a “signifying of one” (ἕν σημαίνειν) there must be such a thing as Wassein (WGK, 90; what-being). To “signify one thing” does not mean to refer to the same thing but rather to signify a determinate “what.” What “pale” signifies is something one and determinate and other than what “musical” signifies. But if Heidegger insists on the common “apophantic function,” it is presumably to insist that the predications, each signifying one distinct and determinate thing, presuppose an already given unity to which they refer.

Now Heidegger addresses (WGK, 91) the argument at 1007a21, which he in the last class identified as the third part of the chapter’s argument, that those who say “simultaneously and not” (ἅμα καὶ οὐκ), completely destroy “being and the what-it-was-to-be” (οὐσίαν καὶ τὸ τὶ ἦν εἶναι). Signifying something presupposes what-being and the two negations that accompany it: not being something other and not being nothing. These two negations, for example, not-being not-human and not being nothing, refer to some one thing which we must understand as ousia versus what is “coincidental” or “accidental” (συμβεβηκός). “In other words, when I grant what-being, I thereby grant ousia and indeed on the ground of the negations which are already posited with what-being” (WGK, 92). Heidegger cites the important sentence at 1007a26–27, which he translates as follows: “the meaning of οὐσία is, that the in-itself-being of something (the what-being) is not something other” (τὸ δε οὐσίαν συμαίνειν ἐστὶν ὅτι οὐκ ἄλλο τι τὸ εἶναι αὐτῷ). He then explains: “In other words: if a what-being is granted, it is clear that one necessarily, in thinking to the end what it means to say ‘there is a what-being,’ comes to the distinction between οὐσία and συμβεβηκός” (92). Thereby we see that “signifying one” (ἕν σημαίνειν) is “signifying being” (οὐσίαν σημαίνειν). Heidegger accordingly takes the “καὶ” in the phrase “οὐσίαν καὶ τὸ τὶ ἦν εἶναι” as explicative (WGK, 93). Heidegger also takes the essential part played by the negations above as showing the close coupling of the problem of essence here with logos. Indeed, we see that without the presupposition of “being something” (and not nothing and not something else) there can be no speaking and no conversing.

Notes for the next and final class on February 22 are preceded by a reference to two student presentations. These are puzzlingly dated February 23 and address the chapters of Book Γ the seminar itself does not get to: namely, those following chapter 4. First there is a reference to a Referat on Γ.5 that Weiss judges not worth preserving (nicht abschreibenswert).³¹ A second Referat on Γ.6–8 is attributed to Käte Oltmanns, and here, in contrast, Weiss provides notes on the presentation itself and on the ensuing discussion. Chapters 6–8 deal with, we are told, the absurd consequences of denying the principle of non-contradiction (WGK, 94). Yet while the argumentation in these chapters might appear simply to combat sophistic with sophistic, we are told that Aristotle’s intention is something else. The point is not to go through Aristotle’s individual elenctic demonstrations and show that he is right in this fight, but to recognize as his true intention exposing the opponent “as someone who with his words means nothing at all, whose words are therefore not at all genuine λόγοι or concepts in which alone a διαλέγεσθαι can be carried out” (WGK, 95). The axioms, including the principle of “excluded middle” discussed in chapter 7, are grounded in the determinateness and signifying function of the concept, in the very structure of logos as intending and understanding something. Thus we arrive at the conclusion toward which Heidegger steered discussion of the presentation: “What is therefore presupposed for their grounding is in a peculiar way [in eigentümlicher Weise] this situation of understanding and mutual comprehension [Verständigung]; what is presupposed is the truth of human existence, but not in the sense that the fact of there being truth must be presupposed by means of some decision—rather, truth antecedes Dasein in the sense that it grounds it in its possibility” (WGK, 96). It is precisely this that Heidegger finds in Metaphysics Γ: the recognition that the ultimate principles that ground the truth of all statements, and therefore logic itself, are themselves grounded in the truth of human existence. As noted at the end of the discussion, the truth that grounds the axioms of logic is not primarily the determination of a proposition—that would be logic grounding logic!—but rather “belongs to the transcendence of Dasein” (WGK, 97).

Given the dating to February 23, we must assume that the above was said during a special session that followed immediately upon what was supposed to be the last class of the seminar, suggesting that that last class ended before Heidegger could arrive at the important conclusion he was aiming for. That class of February 22³² continued with the interpretation of 1007a20–b10: what Heidegger earlier designated as the third part of the argument in Γ.4. Yet the focus here too is on the argument’s connection to the problem of Verständigung (mutual comprehension). Points already made are first recapitulated. Then the line-by-line analysis continues with, for example, the important distinction at 1007a31–32 between ousia and sumbebêkos: “being pale” is coincidental to being-human because a human being is pale without being what it is to be pale. On the reference to the negative consequence of proceeding with predication “without limit” (εἰς ἀπειρόν) at 1007b1, Heidegger notes the importance of the notions of peras and telos (understood as limit, end, and not as aim) in the structure of ousia (WGK, 100–101). Commenting on lines 1007b1–3, Heidegger notes the distinction between the genuine combination (συμπλοκή) that grounds the accident (συμβεβηκός) in the unity of the ousia and the secondary combination (συμπλοκή) that joins one accident (συμβεβηκός) with another on the basis of their common, immediate relation to one ousia (WGK, 102): for example, “pale” and “musical” are combined on the basis of the combination of each with the person who is musical and pale. Heidegger also notes that this structure is “closed” both from below and above (1007b9; ἐπὶ τὸ ἄνω): there is no third term unifying an ousia with its accidents nor an additional layer of accidents (so that there would be accidents of accidents). All of this serves to further elucidate the ontology expressed by the principle of non-contradiction: specifically, how being is defined in opposition to the indefinite and accidental.

Before the seminar comes to an end, however, Heidegger skips ahead to 1008b10–13, still in Γ.4, in order to emphasize once again the way in which the principle, and therefore the conception of being it expresses, is grounded in the possibility of human existence (WGK, 103). Here Aristotle is arguing that anyone who denied the principle of non-contradiction could have no reason to walk to Megara or do or avoid anything else. What Heidegger considers significant in this argumentation is how it transcends the prior frame of a possible conversing (διαλέγεσθαι) toward the broader one of the possibility of existence as such. He sees this suggestion as supported by the word diakeisthai when Aristotle, referring to someone who says at the same time this and also not this (ἅμα γὰρ ταῦτά τε καὶ οὐ ταῦτα λέγει), claims that no one is in fact disposed in this way (1008b9–13; οὐδεὶς οὕτω διάκειται). In claiming that not following the principle of non-contradiction is an impossible disposition for a human being, Aristotle is defending the principle as an essential disposition for a human being. Heidegger notes, furthermore, that the impossibility is shown by reference to actions rather than merely speech, as with the example of walking to Megara. We cannot be disposed in such a way as to deny the principle of non-contradiction because such a disposition would prevent us from acting in any way at all.³³ As Heidegger has insisted, what is at stake in the principle is the possibility of human existence as such. The final words recorded in the notes are therefore the following: “διακεῖσθαι, correctly translated with a specific ‘being in the position or able’ [in der Lage sein] (situation), shows in what sphere the argument moves beyond the parameters of a possible διαλέγεσθαι, in that of the possibility of existence as such” (WGK, 103).

The seminar thus reaches a conclusion that we could characterize as holding that the principle of non-contradiction is neither a purely logical nor a purely ontological one, but an existential one in Heidegger’s sense of that term. Yet, as already noted, the seminar never returns to the question of the role that time plays in the principle as indicated by the qualification hama (at the same time), a qualification that Kant’s reformulation of the principle in the Critique of Pure Reason sought to eliminate. It has also been noted that attached to the protocols of the seminar are notes apparently written by Helene Weiss herself several years later in which she reacts to claims recorded in the protocols. On the first page of these notes with the heading “Zum Seminar W. 1928/29,” we read the following: “The problem of the ἅμα is dropped entirely in the continuation of the seminar!” We can only share Weiss’s surprise and disappointment. We also can know no more than she apparently did about the reason for this neglect. Was it simply a question of time? Or a deeper problem? It is striking that many years later, in the seminar of 1944, on Metaphysics Γ and Ζ, Heidegger gives us the same promissory note, and it is again unfulfilled. In a “Nachtrag” for the class of May 16 we read, “Why Aristotle in his formulation of the principle of non-contradiction must include the ἅμα that Kant will not include, considering it unnecessary and counter to the intention of the principle, is something we will see in the continuation of the questioning concerning the ὂν ᾗ ὄν” (GA83, 401). Yet again, the seminar does not return to the question of the hama and turns for an understanding of the “being insofar as being” (ὄν ᾗ ὄν) to the initial chapters of Book Ζ that occupy it to the end. Even more striking, however, is that both in the notes published in GA80.1 (519–526) for his 1932 lecture on the principle of non-contradiction and in the more than 150 pages of further material for the lecture published in GA91 (189–346), Heidegger not once even addresses the temporal condition of the hama as a problem. Indeed, in the lecture drafts and the associated notes Heidegger makes no distinction on this point between the Kantian and Aristotelian formulations of the principle, despite this distinction receiving so much attention in the seminar. He writes throughout as if Kant were right, that is, as if the temporal qualification of the hama were of no significance. This shows that the problem of the principle’s relation to time did not at all receive his attention in the immediate aftermath of the seminar.³⁴

In any case, it is possible to draw from the seminar of 1928/29 some implications for how we are to understand the hama. If the principle of non-contradiction is grounded in the possibility of human existence and expresses its essential disposition, then the hama must express not only the being-in-time of beings but the temporality of human existence itself. We have already seen Heidegger maintain that the hama does not mean the existing of two things at the same point in time. A passage in Γ.5 not addressed in the seminar, while seeming at first to contradict this claim, arguably supports it. Aristotle says of the senses that “each in the same time never says about the same thing that it simultaneously is thus and not thus” (1010b18–19; ἑκάστη ἐν τῷ αὐτῷ χρόνῳ περὶ τὸ αὐτὸ οὐδέποτε φησιν ἅμα οὕτω καὶ οὐκ οὕτως ἔχειν). This appears to count against Heidegger’s interpretation since the temporal condition is here explicitly formulated as “being in the same time.” On the other hand, we find in addition the term hama, which, if it meant the same as “in the same time,” would be redundant. Aristotle could have written simply that “each never says about the same thing in the same time that it is thus and not thus”; what, then, is added with the inclusion of the hama, translated above as “simultaneously”? The condition “in the same time” qualifies the sense and the object; the sensing of the same object occurs in one and the same time. But what the hama appears to qualify is the being of what the sense “says” to be, where this saying must presumably be understood as the disclosing and making-present of the object. The sense cannot disclose the same object as simultaneously thus and not thus; it cannot make the same object present as thus and not thus in the same making-present. Thus, the temporal meaning of the hama appears to be that of presencing or making-present. We should recall that the word hama also has the meaning of “together-with,” and this meaning is not completely foreign to the temporal sense of the principle, as can be seen if we formulate “the sense never says about the same thing in the same time being-thus together with not-being-thus.” (Note how the hama thus appears both temporal and spatial in meaning.) Reflecting the ambiguous logical/ontological character of the principle itself, the hama expresses a “holding-together” that characterizes both the making-present of what is and the self-same presence of what is, a holding-together that the principle maintains to be impossible in the case of being A and being not-A. We can see here why Heidegger, in commenting on Aristotle’s claim that “being a human being” and “one human being” are the same thing, suggested that we understand “one” here, with Leibniz, as qualifying the human being not as a unit but as a unifying, and that we not understand “being” as meaning “being-at-hand.”

We have seen that, according to Aristotle’s defense of the principle of non-contradiction, the very possibility of human existence depends on being able to disclose what it signifies in speech and action as one in the sense of a determinate what that negates being-other and negates indeterminacy. A thing must be made fully present as what it is and in no way as what it is not. The temporality of human existence in which the principle is grounded therefore appears to be what Heidegger elsewhere, at around the same period, calls Gegenwärtigen. A simple definition of this term is provided in the Grundprobleme der Phänomenologie: “This comportment toward what is present in the sense of a having-there of something present, a comportment that expresses itself in the Now, we call the making-present of something.”³⁵ It is only in and through such a Gegenwärtigen that beings can be present and present in the way required by the principle of non-contradiction. The hama then would mean not “being present in the same time” as a qualification of beings but rather self-same making-present as a temporal determination of human existence and self-same being-present as a determination of being itself. In this case, in response to Kant’s concern, the hama would not be a condition restricted to what exists within time, but would condition all our signifying and disclosing, whether or not the object exists “in time.”³⁶

This suggestion receives important confirmation in Kant und das Problem der Metaphysik, where Heidegger, after repeating the assertion that the “zugleich” (ἅμα) need not express “being-in-time” (Innerzeitigkeit), goes on to give a brief indication of what it does express: “The ‘at-the-same-time’ expresses rather that temporal character that, as antecedent ‘recognition’ (‘pre-figuration’), originally belongs to all identification as such. This lies at the ground, as a foundation, of as much the possibility as also the impossibility of contradiction.”³⁷ Heidegger is referring here to Kant’s “synthesis of recognition,” and what he has in mind is expressed more clearly a few pages earlier when he speaks of “a unifying of a being with regard to its sameness. This synthesis toward the self-same, that is, the holding-before-one of a being as something self-same [ein Einigen (Synthesis) des Seienden im Hinblick auf seine Selbigkeit. Diese Synthesis auf das Selbige, d.h. das Vorhalten des Seienden als eines Selbigen]” (GA3, 185). We can say that the qualification “at-the-same-time” refers not to a self-same point in time but to a self-same act of making-present (unifying, synthesis) in which a being appears as self-same and therefore as incapable of being both A and not-A.

Note that nowhere in the 1928/29 seminar, nor in any of the other discussions cited, does Heidegger criticize or question the validity of the principle of noncontradiction. Indeed, he appears to do the exact opposite: to legitimize it by grounding it in the being and temporality of human existence itself. Of course, such a grounding could destabilize the kind of self-evidence the principle has traditionally been taken to have, making it genuinely question-worthy for the first time. Heidegger certainly saw the principle in its traditional formulations as presupposing a naïve and inadequate understanding of being and time and therefore as in need of “destruction.” Specifically, the principle can be seen to presuppose an identification of being with “presence” and a conception of time also exclusively oriented toward the present. Thus, in the 1938/39 text Besinnung, Heidegger can characterize it as the fundamental principle of metaphysics, that is, “of the interpretation of beingness as constant presence and objectivity for a re-presenting [der Auslegung der Seiendheit als beständiger Anwesenheit und Gegenständlichkeit des Vor-stellens]” (GA66, 396). The “destruction” of such an interpretation is not incompatible, however, with the positive appropriation of the principle we see instead in the 1928/29 seminar and that is carried through to at least the 1933 course Die Grundfrage der Philosophie, in which Heidegger asserts, emphatically and seemingly without reservation, that the principle is “a fundamental enduring element of the existential structure of our being overall [ein Grundbestand des Existenzgefüges unseres Daseins überhaupt]” (GA36/37, 59). The 1928/29 seminar shows in detail what makes this positive appropriation of the principle possible: a reading of Metaphysics Γ that interprets the principle as an expression of Aristotle’s ontological thesis that being and being-one “follow upon one another.” As an imperative demanding the unity of being, the principle can be characterized in 1928/29 as a condition of all speaking and acting and therefore of human existence as such. There is also a clear trajectory from the interpretation of the principle of non-contradiction as a negative formulation of the principle of identity in 1928/29 to Heidegger’s attempt in 1957 to locate in the principle of identity that belonging-together (Zusammengehören) of human being and being that he then names with the word Ereignis.³⁸ It is also important in this context to recall that in 1928/29 Heidegger turns to Aristotle to find what, in the same seminar itself and more widely throughout this period, he was claiming Kant shrank from in suppressing the central role of the transcendental imagination: a grounding of human reason and its principles in the being of Dasein, identified in the 1928 seminar with an absolute being-in-motion, and in its distinctive temporality.³⁹