Hegel indicates throughout his writings that the claims most pivotal to his system of philosophical science receive their proof only in logic itself. That ‘the idea is the truth’ (EL: §213A),Footnote 1 that ‘the idea consists in the unity of the subjective, or the concept, and objectivity’ (2007: §437A), that ‘the form of thinking is the absolute form and that the truth appears in it as it is in and for itself’ (EL: §24A3)—all this, he explains, falls to the work of logical science and cannot be proven through any other means.Footnote 2 And yet, given that he acknowledges as ‘a requirement of all scientific knowledge, and especially of philosophy, that nothing should occur in it that has not yet been proved’ (LPR: 113), Hegel has surprisingly little to say in either the Encyclopaedia Logic or the Science of Logic itself about what he means by ‘proof’ or what sort of proof procedure it is that he thinks is suited to meet such a demand. The few comments that can be found in either version of the Logic explicitly concerned with questions relating to proof are suggestive, but brief and indirect.Footnote 3 In his Lectures on the Proofs of the Existence of God, however, Hegel offers an extended discussion of proof that throws considerable light on the Logic’s own proof procedure.Footnote 4 In what follows, I examine Hegel’s otherwise elusive comments on proof contained in his logical writings in view of this contemporaneous discussionFootnote 5 in order to reconstruct Hegel’s theory of rational proof, that is, the proof procedure at work in the Logic supporting the claims of his speculative metaphysics.
In section I, I draw from Hegel’s Lectures on the Proofs of the Existence of God as well as his Lectures on the Philosophy of Religion in order to lay out three basic features of his theory of proving in general: connection, necessity and mediation. While these features are not unique to Hegel’s theory of rational proof, they nevertheless form the backdrop against which this theory takes shape. In section II, I present Hegel’s account of modes of proof where connection is external and necessity is subjective and indicate why these are insufficient for thinking about the specific object with which rational proof is concerned. In sections III and IV, I consider Hegel’s critical treatment of the ontological and cosmological arguments in two parts of his corpus. The focus of section III is Hegel’s discussion of these arguments in the Encyclopaedia Logic, where they are presented in terms of the proof of the understanding in contrast to rational proof. Section IV focuses on Hegel’s Lectures on the Proofs of the Existence of God, showing how Hegel criticizes the traditional existence proofs on the basis of their syllogistic structure. While sections III and IV reveal how, for Hegel, these arguments fail in utilizing a form of mediation that is inadequate to their content, section V brings to light the form of mediation that Hegel thinks is up to this task. Finally, I argue in section VI that the proof procedure of the Logic is best understood in terms of the theory of rational proof and explain how this sheds light on two lingering interpretive issues in Hegel’s metaphysics: its relationship to the ontological argument and its solution to ‘the problem of beginning’.
I. On proving in general
To make Hegel’s theory of rational proof intelligible, it will first be necessary to look to those basic features that he takes to characterize proving as such. Hegel’s most explicit comments along these lines can be found in his 1829 Lectures on the Proofs of the Existence of God as well as his 1827 Lectures on the Philosophy of Religion. These lectures revolve around Hegel’s critique and speculative reconstruction of the traditional proofs of God’s existence, but they also provide valuable insights related to his thoughts on proving in general. In particular, they make clear three features that Hegel takes to be common to any mode of proving whatsoever. These three features will serve as the basis for my own reconstruction of Hegel’s theory of rational proof, which I argue is at work not only in his speculative resuscitation of the traditional proofs of God’s existence, but also, crucially, in the Logic. Regardless of whether one is engaged in the authentication of an historical fact, the demonstration of a geometric theorem, or even the proof of God’s existence, proving, for Hegel, involves: (i) showing a connection among objects or terms, (ii) demonstrating that such a connection is necessary, and (iii) establishing that necessary connection among objects or terms through exhibiting their mediation.
Any mode of proof will, first of all, show a connection among some set of objects or terms. As Hegel writes in the Lectures on the Philosophy of Religion, ‘to show connection [Zusammenhang zeigen] means in general to prove’ (LPR: 417). Thus, a historical proof of the authorship of De Bello Gallico will show the connection between this text and the historical figure of Julius Caesar, while a geometric proof of the Pythagorean Theorem will connect the length of the hypotenuse of a right triangle to the lengths of its other two sides. In the legal context, proving a party’s guilt will involve connecting them to some criminal offense. Since there are, then, several different kinds of proof (e.g., historical, geometric, legal), linking together a wide array of different objects and terms, it is far from apparent that there is a single form of connection common to all three of these cases. Indeed, Hegel suggests that there is not just one form of connection that can be taken to define proving as such. Nevertheless, when we turn to section II, we will see that there is one form of connection in particular that takes precedence in Hegel’s theory of rational proof.
In any mode of proof, what is essential is, secondly, that the connection among objects or terms is portrayed as necessary: ‘for proving as such [Beweisen überhaupt] simply means to become conscious of connection [Zusammenhangs] and thus of necessity’ [Notwendigkeit] (LProofs: 63). This necessity can also come in a variety of forms. In the case of the ontological argument, the necessity by which the being of God is connected to the latter’s concept is evidently metaphysical or logical in character. But Hegel also indicates that this necessity could be of a causal character when the terms joined together in the proof are finite, sensuous objects (as in, for instance, a forensic firearm examination linking the slug of a bullet to the gun from which it was fired). Indeed, a proof may generate nothing more than subjective necessity, with no real bearing on the matter at hand, when it serves simply as an aid to cognition—a point Hegel often raises in relation to geometric proofs. As we shall see, however, these forms of necessity are to be distinguished from the sort that occurs in rational proof.
Finally, Hegel indicates that any mode of proof will establish the connection among objects or terms as necessary by exhibiting their mediation. Thus, he writes in the Science of Logic that ‘proof is, in general, mediated knowledge’ [vermittelte Erkenntnis] (SL: 420/6:125–26)—a kind of knowledge that, in contrast to the indemonstrable and immediate certainty that Jacobi locates in belief,Footnote 6 proceeds along chains of explanatory dependence.Footnote 7 More specifically, it is through presenting the objects or terms under consideration in relations of dependency and conditionality, such that the one is shown to depend on or follow from the other, that a proof will establish the necessity of their connection. Accordingly, Hegel writes: ‘in the superficial sense “proving” means that a content, a proposition, or concept is shown to result from something prior to it. In that way we cognize its necessity’ (LPR: 113). Though a proof will generally establish the necessary connection among its objects or terms through exhibiting their mediation along these lines, I will show in section V that there is a specific form of mediation at work in Hegel’s theory of rational proof that mirrors the logical activity of the concept and that distinguishes the former from modes of proof organized around the reflective determinations of essence. Before turning to this discussion, however, I would first like to examine some remarks where Hegel faults certain modes of proving on account of their externality and subjectivity. For it is here where his theory of rational proof will start to take form.
II. On external connection and subjective necessity
In this section, I examine two models of proof that Hegel discusses in relation to the traditional proofs of God’s existence. I do so in order to foreground the specific form of connection at work in Hegel’s theory of rational proof and the kind of necessity this mode of proof is meant to yield. To this end, I look first to Hegel’s discussion of modes of proof where the connection is ‘wholly external or mechanical’ (LPR: 165). Then, I consider his account of proofs that portray a connection that, though intrinsic to the matter under investigation, permit of only subjective necessity.
Some forms of proof make only an external connection among objects. Hegel finds this to be especially true of proofs pertaining to finite objects such as objects of perception and those of historical reflection. Hegel offers as an example of the former the argument that a house must have a roof. The connection here is an external one, for Hegel. ‘We see that a roof is necessary to the walls’, he writes
because the house has this characteristic protection against weather and the like. The purpose is what links the walls with the roof, and we can therefore say it is proved [es ist bewiesen] that a house must have a roof. These things belong together, they are connected, but we are aware at the same time that this connection [Zusammenhang] does not concern the being of these objects. (LPR: 165)Footnote 8
This sort of proof evidently makes a connection between objects (e.g., between houses and roofs), but, according to Hegel here, such a connection is external, combined through human purpose and action, with no intrinsic relation to the objects themselves. While it may be the case that a house cannot fulfil its characteristic function of providing shelter without a roof, Hegel suggests that this function binds these objects together only externally. A house may or may not have a roof (e.g., if it is undergoing repair), while roofs may also be found atop churches, banks, prisons and cars. In so far as they can exist independently of one another, then, it is we, as purposive beings, that make the connection between such objects in performing the proof.Footnote 9 There is thus no more an intrinsic connection, for Hegel, between houses and roofs than there is between houses and the materials out of which they are ordinarily constructed. Like ‘beams and stones’, they are ‘what they are even without being joined together’ (LPR: 166).
Proofs developed by reflective history also evince an external mode of connection for Hegel. Not only do such proofs link together events that are in themselves separate and external to one another (for instance, the 1817 Wartburg Festival and the introduction of the Carlsbad Decrees two years later). They also draw their material from testimonies that, being external to the events themselves, can be invoked to explain not only these events but others as well. Accordingly, Hegel observes that ‘the course and activity of [historical] knowledge has quite different ingredients than the course of the events themselves’ (LProofs: 47).Footnote 10
If historical proofs make only an external connection among the terms they join together, this should not, however, be taken to impugn their credibility. Hegel is no more interested in contesting the legitimacy of historical knowledge than he is in denying the fact that, throughout most of human civilization, houses have tended to have roofs. Rather, he points to the external connection displayed in certain modes of proving in order to distinguish these from proofs that, by contrast, exhibit a connection that is ‘involved in the thing or the content itself’ (LPR: 165). It is this latter sort of connection that belongs, for Hegel, to proving in the ‘proper sense’, while those proofs hinging on a merely external connection are more appropriately considered forms of indication.Footnote 11 In so far as it concerns connections that are intrinsic to its subject matter, Hegel’s theory of rational proof evidently qualifies as a proof in this specific sense. But it is not the only mode of proof where a connection of this sort can be found. Indeed, it is perhaps best exemplified, for Hegel, in the method of geometric construction.
Proposition I.32 of Euclid’s Elements states that the three interior angles of any triangle are equal to two right angles. Euclid’s demonstration for this consists in drawing a line parallel to that of one of the triangle’s sides, extending the line formed by one of its other two sides, and comparing the magnitude of the angles constructed in this fashion.Footnote 12 In contrast to the modes of proof (or, more precisely, the forms of indication) discussed above, Hegel explains that the connection here is not external to the subject matter but concerns its very nature. Quoting Euclid, he writes: ‘“The three angles in a triangle add up to two right angles”. That is a necessity of the thing itself […]. In the triangle the relation is not of the kind where the connection is external; in this case, rather the one [term] cannot be without the other, for the second is directly posited along with the first’ (LPR: 166). While a house may or may not have a roof, the interior angles of a triangle will alwaysFootnote 13 be equal to two right angles. This is a feature that triangles possess not on account of any connection that I happen to make in constructing the proof, but one that belongs to them necessarily and in virtue of their intrinsic identity.
Nevertheless, even if geometric proofs are capable of portraying a connection that belongs of necessity to their object, Hegel finds that they are still limited by their subjective character. Thus, ‘the necessity that we see in such a proof corresponds indeed to the individual properties of the object itself, these relations of quantity actually belonging to it; but’, he adds, ‘the progression in connecting the one with the other goes on entirely within us’ (LProofs: 46). Geometric proofs are subjective then in that they depend on the activity of the subject performing the proof (i.e., drawing these lines, comparing these angles, arriving at this conclusion).Footnote 14 But Hegel indicates that these proofs are also subjective in so far as they are guided by subjective purposes (e.g., to satisfy my interest in determining the properties of triangles) and would not be initiated otherwise. Accordingly, the method of geometric construction is ‘a process for realizing our purpose of gaining insight’, but one that is quite distinct from the ‘course in which the object arrives at its intrinsic relations and their connections’ (LProofs: 46).Footnote 15 This is why it yields only subjective necessity for Hegel.
To say that geometric proofs permit of only subjective necessity is not to detract, however, from their validity, or to deny the truth of their results. If Hegel insists here on the difference between the process that we follow in conducting the proof and the process through which the object itself derives its identity, it is only to call attention to what is specific to rational proof, and which sets it apart from every other mode of proving. While other proofs are contingent on the activity and purposes provided by the subject conducting the demonstration, the procedure of rational proof is constrained by neither of these factors. This is because it concerns only that sort of object that for Hegel constitutes truth in the highest sense such that there can be no external standard by which it could be proven: the concept or God. Since such an object is ex hypothesi absolute, encompassing everything actual, there is nothing external to it to which it could be contingently connected (unlike forms of indication), nor any subject whose activity or purpose in proving would lie beyond its scope (unlike geometric proofs). Thus, it requires a mode of proof that is capable of exhibiting its internal connections according to their objective necessity. Hegel refers to such a proof procedure in his philosophy of religion as ‘the elevation of the human spirit to God’ (LProofs: 44)Footnote 16 and in the Logic as ‘the manner of proving engaged in by reason’ (EL: §36A). For the sake of clarity, I will refer to both procedures here as Hegel’s theory of rational proof.
But why characterize such a process in terms of proof? If the concept (or God) ‘proves itself in itself’ such that ‘we have only to look to its own process’ (LProofs: 44) to attain insight into its nature, would it not be more accurate to characterize our epistemic stance towards such an infinite, all-encompassing object as one of intuition or faith instead?Footnote 17 Why does self-support count in this instance as a mode of demonstration and not, as elsewhere, an expression of dogmatism?Footnote 18 And in so far as mediation is integral to Hegel’s own theory of proving in general, how does rational proof satisfy the mediation feature that he himself insists upon? Hegel addresses these questions in his discussion of the traditional proofs of God’s existence, as I show next. In identifying what is defective in the cosmological and ontological arguments, Hegel clarifies the form of mediation specific to the procedure of rational proof and explains why this mode of demonstration is not susceptible to these concerns about self-justification.
III. Rational proof versus the proof of the understanding in the Encyclopaedia Logic
Hegel’s only explicit discussion of rational proof in his logical writings occurs in an Addition to his account of natural theology in the ‘Vorbegriff’ to the Encyclopaedia Logic. It appears here as an alternative to the ‘proof of the finite understanding’ (EL: §36R) which Hegel finds at work in the traditional proofs of God’s existence. Though Hegel’s description of rational proof is somewhat abbreviated in this text, his account nevertheless makes clear that he understands this mode of proof to circumvent the metaphysical and theological problems that result when the proof of the understanding is applied to objects of reason (e.g., God). It also offers an important clue as to how Hegel’s theory of rational proof establishes a connection among objects or terms as necessary through exhibiting their mediation. After examining how he distinguishes between rational proof and the proof procedure of the understanding in the Encyclopaedia Logic, I show in section IV how this distinction receives further clarification through Hegel’s critical engagement with the cosmological and ontological arguments in the Religionsphilosophie. Then in section V, I suggest that Hegel’s discussion of the three basic modes of categorial connection in his 1829 lecture course explains how rational proof arguably manages to satisfy the mediation feature of proving in general without falling prey to the same difficulties present in the traditional proofs of God’s existence.
Hegel finds that the traditional arguments of natural theology (i.e., the ontological, cosmological, and teleological proofs of God’s existence) make use of a common proof procedure which he associates with the understanding. He considers this however to be a ‘wrongheaded approach’ that occasions problematic metaphysical and theological consequences. Hegel describes this mode of proof as follows:
The chief point here is that the way of constructing proofs as it is undertaken by the understanding concerns the dependency of one determination on another. With this kind of demonstration [Beweisen], one makes a presupposition, something fixed, from which something else follows. So what is being demonstrated here is the dependency of a determination on a presupposition. Now if the existence of God is supposed to be demonstrated in this way, then this means that the being of God is made to depend on other determinations so that the latter constitute the ground of God’s being. Here one sees immediately that something out of kilter is bound to result, for God is supposed to be the ground absolutely of everything and therefore not dependent on something else. (EL: §36A)
I would like to highlight three important points concerning the proof of the understanding that emerge from this description. First, this mode of proof appears to be consistent with the account of proving in general sketched above in section I, whereby a proof establishes a necessary connection between objects or terms through exhibiting their mediation. Thus, the cosmological argument (to use Hegel’s example) presents the connection between God and some contingent aspect of finite nature (e.g., a series of physical events) as necessary by showing the former to follow from or to be mediated by the presupposition of the latter. Secondly, however, Hegel indicates that certain metaphysical and theological difficulties arise when the proof of the understanding is used to demonstrate God’s existence. His suggestion here is that these difficulties arise precisely on account of its mediation feature. Since this mode of proof is only capable of exhibiting the ‘dependency of one determination on another’, Hegel finds that it cannot but treat God as dependent on or mediated by that other from which the proof proceeds. Accordingly, he suggests in a nearby note that the cosmological argument introduces the spectre of pantheism in grounding God’s existence on finite nature, while the ontological argument, in proceeding on the basis of a merely subjective representation of God’s essence, threatens to further entrench the very concept-object dualism it purports to overcome.Footnote 19 Finally, I would stress that the mediation problems that Hegel voices here echo the complaints that Kant and Jacobi had already raised against the traditional arguments of natural theology.
Let us now turn to the description of rational proof that Hegel puts forward in this text as an alternative to the proof of the understanding:
Reason […] understands by proof something quite different from what the understanding and common sense do. To be sure, the manner of proving engaged in by reason [das Beweisen der Vernunft] equally takes something other than God for its point of departure, and yet in its progression it does not leave this other standing as something immediate and as a being. Rather, by exhibiting this other as something mediated and posited, it leads at the same time to the result that God is to be regarded as that which is truly immediate, primordial, and self-subsistent, containing mediation as sublated within himself. (EL: §36A)
Here we see that what distinguishes rational proof from the proof of the understanding, for Hegel, is not the presence or absence of mediation, but concerns rather the form by which this mediation occurs. More specifically, while the proof of the understanding establishes a necessary connection between objects or terms by showing the one to depend on or to be mediated by the other as its ground, this occurs in rational proof by exhibiting their mutual mediation. This is presumably what leads Hegel to suggest that this mode of proof can be used to demonstrate God’s existence without incurring the same challenges that historically have been brought against the arguments of natural theology—because, that is, he thinks that rational proof is capable of exhibiting God as mediated by some other without thereby treating this other as God’s ground and necessary presupposition.
The contrast that Hegel draws in the ‘Vorbegriff’ to the Encyclopaedia Logic between two alternative modes of proof is instructive: it shows his concern to develop a theory of demonstration that can make good on the traditional aspirations of natural theology, it points toward specific objections that he thinks such a theory must be able to meet, and it suggests that he considers rational proof, in so far as it includes a form of mutual mediation, to provide such a theory. Nevertheless, this discussion is admittedly quite compressed, leaving more than a few questions open. How, for instance, does he propose to account for the unique form of mediation on which his theory of rational proof evidently turns? What range of objects does he think this mode of proof can successfully accommodate? Is it only applicable to natural theology, or does he think its reach extends beyond this domain? Finally, to what extent does Hegel’s account of rational proof describe the proof procedure at work in his Logic? Hegel does not address these questions anywhere in his logical writings. However, the lengthier, more sustained treatment of the cosmological and ontological arguments in his philosophy of religion offers some important points of clarification.Footnote 20 In these lectures, Hegel elaborates on the mediation problems that we saw him touch upon in the ‘Vorbegriff’ to the Encyclopaedia Logic. Here, however, he links these problems to the form of the ordinary syllogism and its inability to convey the logical moment of negativity. Since these lectures clarify the problems to which Hegel offers his theory of rational proof as a solution, we turn to them now in order to reconstruct this theory with greater precision.
IV. The formal defect of the traditional existence proofs in the Religionsphilosophie
Hegel’s discussion of the cosmological argument in his Lectures on the Proofs of the Existence of God is by and large consistent with his treatment of the topic in the aforementioned Addition to §36 of the Encyclopaedia Logic. He raises here the same objection as in the Addition, that in proceeding from ‘what is conditioned to its condition’, it makes the absolutely necessary being dependent on some contingent aspect of finite nature. Interestingly, however, Hegel now explicitly attributes this objection to JacobiFootnote 21 and presents it along with this significant qualification:
while this defect must be conceded, it is to be observed on the contrary that no objective significance is to be given to such a relationship of conditionedness and dependence. This relationship is present only in a wholly subjective sense. The proposition does not state, and is not meant to state, that the absolutely necessary [being] has conditions, and indeed is conditioned by the contingent world—quite the contrary. The whole process of the connection exists only in the act of proving. It is only our knowledge of the absolutely necessary being that is conditioned by that starting point. (LProofs: 112)
Hegel grants to Jacobi that the cosmological argument misrepresents God as something grounded and dependent. But he immediately takes the sting out of this objection by reframing the mediation problem on which it is predicated. If the cosmological argument makes a necessary connection between a contingent world and an absolutely necessary being by exhibiting the latter’s dependence on the former, then this dependence can only be subjective in character, bearing solely on our knowledge and the conditions of its emergence.Footnote 22 Otherwise, this dependence obviously conflicts with the conception of God at issue in the argument as an absolutely necessary being. Accordingly, Hegel suggests that the mediation problem present in the cosmological proof does not necessitate pantheism but amounts to a ‘formal defect’ in the argument’s structure.
Hegel describes this defect as follows: ‘The essential and formal defect of the cosmological argument lies in the fact that finite being not only is taken as the mere beginning and starting point but also is maintained and allowed to subsist as something true and affirmative’ (LProofs: 162). The cosmological argument not only misrepresents God as finite and dependent; Hegel points out here that it also bestows an affirmative and enduring reality upon what is essentially transitory and contingent. However, though this evidently conflicts with the conception of finite being from which the proof proceeds, the problem lies, more deeply, in its syllogistic structure. Hegel’s suggestion is that it is on account of this structure that the cosmological argument cannot establish a necessary connection between its terms without mischaracterizing both. Take, for example, the argument that (i) if a contingent world exists, then an absolutely necessary being exists; (ii) a contingent world exists; (iii) therefore, an absolutely necessary being exists. Hegel’s concern with such an argument is that it fails to account for the difference that obtains between the sort of existence belonging to a contingent world and that of an absolutely necessary being, linking these together indifferently through the abstract quality of ‘existence’. This is a problem that, according to Hegel, plagues ordinary syllogistic reasoning in general. The ‘ordinary syllogism’ (gewöhnlicher Schluβ) brings together its objects ‘in such a way that the two determinations thus linked […] constitute an external, finite relationship to each other’ (LProofs: 113). It makes no difference whether these objects are infinite or finite, sensible or intelligible, internally linked or externally joined. The ordinary syllogism can only establish their connection by casting them in relations of externality and finitude.Footnote 23 While this is perfectly valid for certain kinds of objects, like beams and stones, which maintain their identity whether they are joined together or not, Hegel argues that it is not suitable for showing the intrinsic connection which obtains between a finite, contingent world and an infinite, absolutely necessary being. This requires a form of mediation that can capture not only the ‘dependency of a determination on a presupposition’, but also the negation of this same presupposition in the argument’s result. This, however, is something that Hegel finds the ordinary syllogism cannot provide: ‘this moment of the negative is not found in the form taken by the syllogism of the understanding [Form des Verstandes-Schlusses], and therefore the latter is defective in the region of the living reason of spirit—in the region wherein absolute necessity itself is considered as the true result, as something that does indeed mediate itself through an other, but mediates itself with itself by sublating the other’ (LProofs: 114).
Before turning to Hegel’s discussion of this unique form of mediation, let us briefly examine his account of the ontological argument in the Lectures on the Philosophy of Religion. Though it takes the idea of God, rather than finite being, as its foundation and point of departure, Hegel indicates that the ontological proof suffers from the same mediation problem as the cosmological, rendering this argument no more effective than the latter. He describes the problem here as follows:
We have the representation of God. But God is no mere representation, for God is. How then are we to accomplish this passage, how are we to gain the insight that God is not merely something subjective within us? Or, how is the determination of being to be mediated with God? For being and God are two different things. (LPR: 181)
Here, Hegel reiterates the concern raised by Kant (and earlier, by Gaunilo) that a crucial difference obtains between what one merely represents to oneself as existing and what actually is, and that the latter cannot simply be ‘plucked’ out of the former.Footnote 24 However, rather than simply grant this objection and the concept-object dualism evidently informing it, Hegel recasts the problem once again as a defect in the argument’s structure.
The ontological proof represents its objects in such a way that no passage can be made from the one to the other. It characterizes the concept of God, on the one hand, as a mere subjective representation lacking objective reality (hence the need for proof). At the same time, it portrays the objective reality that it predicates of God as something separate from and external to the latter. But this, once again, points to a deeper problem that Hegel locates in the form of the ordinary syllogism. ‘The unity of concept and being’, he explains, ‘is a presupposition, and the deficiency [in the ontological argument] consists in the very fact that it is a mere presupposition, which is not proved but only adopted immediately’ (LPR: 187).Footnote 25 The problem here is not that the proof presupposes the unity of being and concept in defining God, for instance, as ens realissimum. Nor is it that the presupposed unity of being and concept from which the proof proceeds is merely subjective in character. The problem, again, is formal.Footnote 26 Whatever this argument may presuppose, its syllogistic structure ensures that it will remain preserved in the result in this same immediate form.Footnote 27 Since the ordinary syllogism can show the dependency of a determination on a presupposition—but not the negation of this presupposition in the argument’s result—it cannot exhibit the form of mediation that, for Hegel, links the concept and being of God together in objective unity.Footnote 28 It cannot show, therefore, the transition and development that occurs as one advances from an initially one-sided and subjective representation of God’s essence to a fully determinate conceptual comprehension of the latter. Accordingly, Hegel finds that the ontological argument is no better equipped to explain ‘the elevation of the spirit to God’ than the cosmological, since it too obscures ‘the moment of negation that is contained in this elevation’ (EL: §50R). As we will see later, this also disqualifies the ontological argument from serving as a model for the proof procedure of Hegel’s Logic.
If the traditional proofs of God’s existence are vitiated by mediation problems stemming from their syllogistic structure, the question then arises: how does Hegel’s theory of rational proof manage to satisfy the mediation feature of proving in general without succumbing to these same difficulties? How can it show a necessary connection between its terms without casting these in relations of externality and finitude? How, in other words, is this mode of proof able to convey the negative moment by which each term develops into the other? We turn now to Hegel’s discussion of the three basic modes of categorial connection in his 1829 lecture course to consider his answer.
V. Mediation in the Lectures on the Proofs of the Existence of God
In a remarkable passage from the ninth lecture, Hegel explains that there are three basic ways in which the two ‘aspects’ or ‘categories’ at issue in the traditional existence proofs can be connected. Hegel’s description of these three modes of categorial connection will recall for readers the three sections of the Logic:
The first is the passing over of the one category into its other; the second is their relativity or the shining of the one in or to the being of the other; the third modality, however, is that of the concept or the idea, in accord with which [each] category preserves itself in the other in such a way that the resulting unity, which is implicitly the original essence of both, is also posited as their subjective unity. (LProofs: 89)
In accordance with the first mode of connection, that of ‘passing over’ (Übergehen), one category comes as the other’s negation, beginning only where the other ends, and preserving no trace of the other in this passage. This mode of connection is best exemplified in the transition that occurs in the opening of the Logic, where the category of being vanishes into that of nothing, but as Hegel makes clear in the Encyclopaedia Logic (§161A), it belongs to the Doctrine of Being more generally (e.g., in the transition of quality into quantity).
The second basic mode of connection, which Hegel describes in terms of the ‘relativity’ or ‘shining’ of one category in another, applies broadly to those relations of dependency and externality characteristic of the Doctrine of Essence. It can be seen whenever one category is treated as the essence or ground of another, this other in turn possessing no being of its own and counting as no more than the mere appearance of the former. This mode of connection differs from ‘passing over’ in that it expresses not just the negation of one category in the other, but also its preservation (e.g., as the appearance of this essence, the consequence of this ground). Nevertheless, Hegel points out that if one category is taken in this way as the mere appearance of another which is its essence and ground, then this appearance, and so, this preservation must fall to some third factor linking these categories together from a position of externality (LProofs: 89–90).
Finally, in the third mode of connection, which Hegel identifies with the Doctrine of the Concept, the two categories are linked together in such a way that each one is both negated and preserved in the other.Footnote 29 Here, rather than simply vanishing into each other, the two connected categories retain a distinct identity in being joined. This identity is not something that each category possesses independently of its connection but constitutes a revision emerging precisely through its relation. Nor is this identity something simply bestowed upon one category by another—or merely relative to the subject drawing the connection between them as in the case of geometric proof. It is an identity that results only when these categories are grasped, in their dialectical movement, as moments of the concept.
After introducing the three basic modes of categorial connection, Hegel then proceeds on this basis to reformulate the mediation problems vitiating the traditional existence proofs. If we understand the ontological proof in accordance with the first mode of connection, that of passing over, then this argument shows ‘the process of God becoming nature’ (LProofs: 89). In this case, however, the argument invites the charge of pantheism since it requires that God, in vanishing into nature, must relinquish any distinct identity relative to the latter. If we understand the cosmological proof along these same lines, then it shows the passing over of nature into God, raising concerns of acosmism. On the other hand, if we understand the ontological proof in terms of the second mode of connection, such that nature signifies only God’s appearance, then the argument suggests that ‘nature as a transitional process would exist only for a third element, only for us, wherein the unity resides’ (LProofs: 89–90) but would possess no enduring reality otherwise. Similarly, if the cosmological proof construes nature as the essence from which God springs as a mere appearance of the former, then this makes God ‘something merely produced by religion, something represented, postulated, thought, believed, a semblance or show, not something genuinely independent that starts from itself’ (LProofs: 91).
Each of these cases presents us with a version of the mediation problem that Hegel attributes in the Encyclopaedia Logic to the proof of the understanding and to the form of the ordinary syllogism in his Religionsphilosophie. But casting the problem here in terms of the three basic modes of categorial connection allows us to catch sight of the unique mediation feature at the centre of his proposed solution—that is, it allows us to see how his theory of rational proof aims to establish a necessary connection among its terms by exhibiting their mediation without falling prey to these same difficulties. Accordingly, if the traditional proofs of God’s existence obscure the negative moment by which their diverse terms are internally linked because they rely on an inappropriate mode of categorial connection (where this moment can only emerge in the passing over or shining of one term in the other), then Hegel’s theory of rational proof must make use of a mode of connection that can adequately convey this moment unless it is to suffer the same fate. It must therefore employ, beyond the first two modes of categorial connection, the third mode, according to which each category negates and preserves itself in the other, to exhibit the mutual mediation of being and concept.
Understanding that Hegel’s theory of rational proof makes use of the third mode of categorial connection helps explain how it plausibly manages to satisfy the mediation feature of proving in general without generating any of the problems discussed above. Since this mediation is mutual, with each term both negating and preserving the other to which it is linked, there can be no question here of reducing the one to the other. Nor for the same reason can it be charged with joining its terms together only externally, such that they maintain the same fixed identity in being linked that they possess prior to and outside of their relation. It also explains how this theory eludes the charge of self-justification articulated at the end of section II. Though the mediation here is mutual, it is not merely reciprocal. Hegel characterizes the proof procedure of reason in the ‘Vorbegriff’ to the Encyclopaedia Logic as one where ‘what appeared as a consequence shows itself equally as a ground, and what presented itself at first as a ground is demoted to a consequence’ (EL: §36A). However, his description of the third mode of categorial connection in the Lectures on the Proofs of the Existence of God makes it clear that this cannot amount to mere reciprocity, with each category serving in turn as the ground of the other. Since, according to Hegel, the unity emerging through this mode of connection ‘represents the most absolute foundation and result’ (LProofs: 91) of the two otherwise isolated elements, it is not simply that one term is true because the other term is, and that this other term is true in virtue of the first, but rather that each of these signify developmental moments within a single, self-mediating totality.
VI. Hegel’s logic as rational proof
We have seen that Hegel’s theory of rational proof satisfies the basic features of proving in general (i.e., that it establishes a connection among terms as necessary by exhibiting their mediation). We have also seen that this theory departs from the traditional existence proofs to the extent that it draws on the third mode of categorial connection (i.e., ‘the mediation of reason’). In what remains, I would like to present two reasons why this theory offers the best way to understand the proof procedure at work in Hegel’s Logic and conclude by suggesting the relevance of this theory to two enduring questions in Hegel’s metaphysics: its relationship to the ontological argument and its solution to the so-called ‘problem of beginning’.
First, there is a solid textual basis for identifying the proof procedure of the Logic with the theory of rational proof sketched above in reference to the Religionsphilosophie, as Hegel closely associates these projects throughout his writings. For instance, in the Lectures on the Proofs of the Existence of God, he states that logic is ‘metaphysical theology, which treats the evolution of the Idea of God in the aether of pure thought’ (LProofs: 99) and, in a well-known passage from the Science of Logic, that the latter can be understood as ‘the exposition of God as he is in his eternal essence before the creation of nature and of a finite spirit’ (SL: 29/5:44). In these passages and others like them, Hegel indicates that religion and philosophy are concerned with the same object—namely, with truth in the highest and most unreserved sense.Footnote 30 Since this object is absolute, with no external standard to which it might be compared, this means that it can only prove itself on the basis of its own measure. This is however just what the theory of rational proof means to explain. In contrast to modes of proving that make an external connection between objects or terms possessing their own separate and independent status, the proof procedure of reason exhibits the intrinsic connections through which its object constitutes itself as absolute totality. Accordingly, if Hegel’s logical proof consists in ‘showing how the object makes itself—through and out of itself—into what it is’ (EL: §83A), then the theory of rational proof lays out the basic features of this process.
Second, the argument receives further support from the fact that the features of rational proof so closely parallel the Logic’s own structure. We have seen that the proof procedure of reason establishes a necessary connection between terms by exhibiting their mutual (but non-reciprocal) mediation. But this is just what occurs in the Logic. The latter establishes the connection between being and concept as necessary precisely by exhibiting these categories as moments of a single, self-mediating totality. On this point, Hegel is rather explicit: ‘the truth’, he writes, ‘has to prove itself precisely to be the truth, and here, within the logical sphere, the proof consists in the concept demonstrating itself to be mediated through and with itself and thereby what is truly immediate’ (EL: §83A).
It is moreover clear that Hegel conceives of the self-mediating activity by which the concept establishes its truth in the Logic along the lines of the third mode of categorial connection. Though the logical progression proceeds from being to concept, this does not mean that one category is simply the ground or essence of the other. The latter (the concept) is rather the foundation and result of a self-mediating process that sets out from an other (being) that turns out to be its own abstract and immediate self-conception. ‘Anything abstractly immediate’, Hegel writes, ‘is indeed a first; but, as an abstraction, it is rather something mediated, the foundation of which, if it is to be grasped in its truth, must therefore first be sought’ (SL: 508/6:245). The concept is thus the foundation out of which being first emerges. However, it is ‘just as necessary to consider as result that into which the movement returns as to its ground’ (SL: 49/5:70), since the concept proves its foundational status in the Logic by negating and preserving the category with which it begins (in accordance with the third mode of categorial connection).
Having shown that the proof procedure of the Logic is best understood in terms of rational proof, let us consider two implications that this holds for contemporary discussions of Hegel’s metaphysics.
First, this conclusion provides us with reason to rethink the extent to which the proof procedure of the Logic can be conceived along the lines of the ontological proof. If the foundational status of the concept were not proven but merely presupposed (in accordance with the second mode of categorial connection), there would be little to distinguish Hegel’s Logic from the ontological proof with which it is often associated.Footnote 31 While there are good reasons to affirm this association, I nevertheless believe that the proof procedure of the Logic is best understood in terms of the theory of rational proof sketched above. Jacob McNulty (Reference McNulty2023) correctly observes that Hegel expressed admiration for the ontological proof throughout his career, even describing certain parts of the Logic itself as versions of this argument.Footnote 32 There is also much to be said in favour of Robert R. Williams’s suggestion that, in so far as it shows the ‘actualization of rationality from its own resources’ (Reference Williams2017: 130), the Logic can be viewed in its entirety as one ‘extended’ ontological proof. Finally, it must be granted to Dieter Henrich, that the end of the Logic, where, as he puts it, ‘being is a moment of the concept, or: the concept is being’ (Reference Henrich1960: 215), bears a striking resemblance to the conclusion of the ontological argument.Footnote 33 Such connections are valuable for helping to clarify an important point of agreement between Hegel’s Logic and the ontological proof—namely, that both aim to establish the unity of concept and objectivity. What’s more, they serve to remind us of Hegel’s continued interest in the ontological argument even after Kant’s highly influential criticism of it. But since, as we have seen, Hegel criticizes the ontological proof on the same grounds as the cosmologicalFootnote 34—namely, that it suffers from mediation problems arising from its form, it is important for such claims to be tempered. Indeed, if the Logic can be said to express the ‘underlying truth’ contained in the ontological argument stripped of its abstract, syllogistic form, then surely the same can be said about the cosmological.Footnote 35 After all, the Logic not only proves the being of the concept (i.e., the truth of the ontological argument), but does so precisely by exhibiting the negation and preservation of the finite in the infinite (i.e., the truth of the cosmological argument). Instead of construing Hegel’s Logic as a version of the ontological proof, therefore, it should be seen as extracting elements from both of these arguments and incorporating them into a single proof procedure.Footnote 36
Second, I would like to suggest by way of conclusion that the theory of rational proof illuminates one of the Logic’s most notorious difficulties: the problem of beginning. ‘The beginning of philosophy’, Hegel writes, ‘must be either something mediated or something immediate, and it is easy to show that it can be neither the one nor the other; so either way of beginning runs into contradiction’ (SL: 45/5:65). Thus, if we begin with something mediated, something that receives its support only as the result of some prior line of argumentation, this leaves the legitimacy of the beginning in question. If, on the other hand, we begin with something immediate, something merely presupposed without any argument in its favour, this leaves the beginning equally susceptible to concerns of arbitrariness. Now, there is a growing consensus among scholars that Hegel’s solution to this problem involves denying the exclusive opposition on which it is predicated.Footnote 37 The beginning of philosophy is thus neither something immediate nor something mediated, but rather something self-mediating. However, in light of the foregoing analysis I would add that his solution also involves denying the mode of categorial connection that forms its basis. As Hegel’s discussion of the traditional existence proofs shows, the problem of where or with what one begins is only an issue for the sort of proof procedure in which the conclusion depends on the ground from which one starts—that is, for a procedure premised on the second mode of categorial connection. If the logical proof could only establish a necessary connection among terms by exhibiting their relativity or shining, then the problem of beginning would represent a legitimate threat to its success. But if, as I have argued, the logical proof draws upon the third mode of categorial connection, then it resolves this problem as a function of its proof procedure.
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