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Subjective Logic and the Unity of Thought and Being: Hegel’s Logical Reconstruction of Aristotle’s Speculative Empiricism

Paul Redding

Preprint: a later version will appear in Internationales Jahrbuch des Deutschen Idealismus, Volume 12, “Logic”, eds. Sally Sedgwick and Dina Edmunts, 2016.

ABSTRACT

Interpreters disagree over whether the categories or “thought determinations” of Hegel’s Objective Logic should be construed as, following Aristotle, fundamentally about being, or, following Kant, fundamentally about thought. Moreover, they disagree over the relation that Objective Logic stands to Subjective Logic, which inturn involves its own transition to “objectivity”.

This paper focuses on Hegel’s Subjective Logic as charting a process in which a logic initially understood as subjective and formal, after the manner of Kant, comes to acquire content, issuing in a type of unity of thought and being of which the earlier Objective Logic was incapable. In particular, Hegel’s account of judgment and syllogism can be read as a critical reinterpretation of the logic governing the passage from experience to “ideas” in Aristotle’s account of epagoge or “induction”.

When one starts to look through the contents of Hegel’s Science of Logic it seems clear that the text is meant to follow an unfolding sequence of categories or “thought determinations” that start with the most abstract, general and indeterminate—“being” (Sein)—and then become progressively more determinate as with the succeeding category, “determinate being” (Dasein).1 Furthermore, it is clear that this sequence is meant to unfold on a number of different, but systematically interconnected, levels and that negation plays a crucial role in the transitions. Thus, internal to each of the parent categories coinciding with the chapter headings of Section 1, “being” “determinate being” and “being-for itself”, are to be found transitions between finer-grained sub-categories that eventually lead into the parent-category of the following chapter. For example, within the chapter devoted to being we find a progression from being though nothing to becoming from whence we eventually transit to the parent category of the second chapter, determinate being. At first glance, then, the contents of Hegel’s Logic appear to be the type of contents found in what are generally termed “category theories”, albeit subject to a style of presentation that is typical of Hegel’s “dialectic”. The question that immediately arises is surely: how are the categories involved meant to be understood?

1 “Dasein” has been something of a term of art in German philosophy. Hegel stresses its etymology as being (Sein) in a certain place, there (da) (Hegel 2010, pp. 83–4; GW 21, p. 97). A thing’s Dasein is thus associated with it being available for the perceptual grasp of its determinate, specific qualities.

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Within current interpretative disputes over the nature of Hegel’s philosophy more generally positions tend to divide along a line that separates interpreters according to the issue of Hegel’s relation to Kant. On one side of this divide are those “post-Kantians” who see Hegel’s philosophy as starting out from the idea of Kant’s critique of traditional metaphysics and subjecting it to a further internal critique (classically, Pippin 1989, Pinkard 1994); on the other are those who give sufficient weight to Hegel’s critique of Kant to take it as a critique of critical philosophy itself, allowing for the restoration of a project much closer to the type of substantive metaphysics that Kant had rejected, especially metaphysical positions leaning towards Aristotle (Stern 2009) or Spinoza (Beiser 2005; Houlgate 2005). Here the situation is no different. Given that Aristotle and Kant are often themselves taken as providing opposing “objective” and “subjective” approaches to the categories within their own category theories (Thompson 1983), it is not surprising then that “Kantian” versus “Aristotelian” models of category theory commonly reappear as general schemas in relation which the thought determinations of Hegel’s Logic are to be understood. Thus we find some interpreters urging a continuity of Hegel’s Logic with Kant’s Transcendental Logic, and seeing Hegel’s categories as fundamentally norms of thought while others insisting that Hegel’s categories are to be understood objectively, construing Hegel’s Logic essentially as a metaphysics or ontology.

As an exemplar of the former categories-as-norms-of-thought view we might take the early proponent of the so-called “non-metaphysical” reading of Hegel, Klaus Hartmann, who had insisted that Hegel’s logic constitutes “an immanence of thought, an overall sphere in which determinations are viewed as from within, from the stance of thought” (Hartmann 1988, p. 271). In Hartmann’s approach a category is “the claim that being matches what thought thinks of it” (Hartmann 1988, p. 272-3) it is not difficult to hear the echo of Kant’s claim that “reason has insight only into what it itself produces according to its own design” (Kant 1998, Bxiii). Hartmann, nevertheless concedes that there is in some sense an “ontological” dimension of the categories (Hartmann 1988, p. 271). It is the systematic determination of the categories that give to them “ontological potential” (Hartmann 1988, p. 272). In particular, it is determinate negation that enables his procedure “to establish the ingredience of being into thought” by considering the “otherness of being to thought as a negating”, allowing being to be thereby reflected into thought (Hartmann 1988, p. 273). But this does not detract from the fundamentally non-metaphysical status of Hegel’s philosophy, a philosophy “devoid of existence claims” (Hartmann 1988, p. 274).

In contrast we might consider the stance of Stephen Houlgate, a leading proponent of the categories-as-features-of-being approach. Like Hartmann, Houlgate makes concessions to the opposed point of view. The fact that Hegel’s categories are generated by pure thought itself and that the categories “permeate our consciousness and language and give structure to all that we perceive” (Houlgate 2005, p. 9), Houlgate points out, can make Hegel’s approach sound very much like the view put forward Kant, in the Critique of Pure Reason. But Hegel must be read as rejecting Kant’s idea “that the categories do not apply to things themselves” (Houlgate 2005, pp. 24–5). The categories are simultaneously about thought and being. Houlgate will, therefore, explicitly oppose Hartmann’s weaker version of the ontological dimension of categories, and his denial that Hegel’s logic includes existence claims (Houlgate 2005, p. 126).

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The attempt to combine “Kantian” and “Aristotelian” readings of the categories, however, can look like that of trying to square the circle. For his part, Hartmann is faced with justifying his talk of any “ontological” potential for the categories. Here the critic will surely ask why, when Hartmann talks of being coming to be established in thought because of the “ontological potential” of the categories (Hartmann 1988, p. 272), we should take this as meaning anything more than some richer concept of being coming to be thereby established. Similar questions face Houlgate. If the categories that “give structure to all that we perceive” are generated by pure thought itself (Houlgate 2005, p. 9), why, the critic will ask, should we think that the resulting structures bear any relation to the structures of anything other than thought, that is, to being itself? Despite its limitations, at least Kant’s “subjective” construal of the categories is accompanied by an intelligible story as to how the categories could be investigated by the mind in such a pure, a priori fashion: for Kant the categories are simply the mind’s products and so the mind does not have to investigate anything beyond itself in order to come to a knowledge of them. Houlgate is surely right in taking Hegel to be critical of such a subjectivistic understanding of the categories, but it nevertheless can seem entirely mysterious as to how the mind can, simply by pure thinking, come up with features of the way the world is “anyway”, entirely independent of its relation to any mind.

My claim in this essay will be that clarification of these issues is unlikely to be made in isolation from attempts to address a topic that is typically circumvented in such discussions: Hegel’s treatment of formal logic in the context of his more general project of a science of logic.2 It need hardly be said that Hegel’s Science of Logic is not what is known in contemporary philosophy as logic considered as science—formal or mathematical logic, but this fact alone does not imply that Hegel’s science can be understood as entirely indifferent to the more general project of logic as a kind of formal discipline first arising in Greece of which modern mathematical logic is one expression. Here my argument will involve a number of basic claims. First, in his reflections upon the history of speculative philosophy in Greece, Hegel had given pride of place to Aristotle as having overcome a structural limitation of Plato’s project of a philosophical knowledge of “ideas”, stressing the advantages of a certain type of empiricism in Aristotle’s approach. Aristotle’s path to a philosophical cognition of ideas and principles proceeded from an empirical basis, making him a type of speculative empiricist, and this, I suggest, should be significant for Hegel’s own thoughts about the mind’s self-consciousness of its own identity with being: we should not bypass the broadly empiricist idea that “being” gets into thought via experience, and that experience plays a necessary role in our capacity to have thoughts that have “being” as their proper content. Next, this quasi-empiricist dimension of Aristotle’s metaphysics had its own problems, however. Importantly, it compromises his own explicit thoughts about the logical processes involved in going from empirical experience to a cognition of ultimate principles or ideas as instantiated in being. We might say, that Aristotle’s speculative empiricism was compromised by his logical empiricism. Finally, I will suggest that the place to look in Hegel’s Science of Logic for his engagement with this are those parts of Volume Two, the Subjective Logic, where Hegel critically reconstructs, in his own terms, Aristotle’s limited formal logic, and does so in a way that shows how thoughts acquire content, and thereby allows the Science of Logic to transition to categories that properly identify being and 2 For a tentative start to such an attempt see Redding 2014.

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1: The Section “Subjectivity” in Hegel’s Subjective Logic

The prima facie problematic significance of the first section of Hegel’s Subjective Logic for standardly “objective” or categories-as-aspects-of-being readings of his category theory might be brought into focus here by a glance at the way in which a number of its advocates state their positions. Hegel’s logic is an “ontological” or “metaphysical” project, it is often asserted, rather than some kind of formal one. Thus Frederick Beiser notes that it is a “common misconception”, that Hegel’s dialectical logic “is some kind of alternative logic, having its own distinctive principles to compete with traditional logic”. Hegel’s dialectic was, he continues, neither “meant to be a formal logic, one that determines the fundamental laws of inference governing all propositions, whatever their content”, nor was it meant to “complete with formal logic”. It is, rather, “a metaphysics whose main task is to determine the general structure of being” (Beiser 2005, p. 161). A similar formulation is to be found in David Grey Carlson who describes Hegel’s logic as a “theory of ‘being’”, and similarly contrasts such a characterization with logic understood formally. “Hegel’s Science of Logic,” he asserts, “is, of course, an ontology – a theory of ‘being’. It is, he goes on, “radically not what Logic is for analytic philosophy – an exercise for clarifying mathematical or linguistic inferences” (Carlson 2005, p. xi). However, Hegel’s apparent engagement with such “formal” issues in the Subjective Logic seems to raise a problem for this stance. Does it not suggest that for Hegel a consideration of formal logic is somehow internal to or a part of the broader project of logic as a whole? And if this is the case, does it not threaten any attempt to define Hegel’s logic in terms of its contrastive opposition to formal logic?

One possible response here on the part of the categories-as-aspects-of-being reading is that of Andre Doz who has described Hegel’s Subjective Logic as simply a continuation of the Objective Logic of Volume One, in which the categorial structures discussed are, like the earlier, to be understood as determinations of being. Thus Hegel’s notions of “concept, judgement, etc.” (with this list presumably meant to include “syllogism”) in the subjective logic “are only [ne sont que] more developed forms or modes of being” like those in the earlier objective logic such as “becoming, finitude, infinite, …” (Doz 1987, p. 22). Such an approach surely faces immediate problems, however. While it is undoubtedly true that Hegel, especially in his Realphilosophie, appeals to categories such as judgment and syllogism in the ontological sense, one might ask whether it is possible to understand what it would mean for something, say a state, to be a “syllogism” independently of understanding what being a syllogism amounts to in the usual logical sense of the term. Syllogisms in the logical sense attempt to show how pairs of premises are linked to conclusions via conceptual relations among major, middle and minor terms, and, moreover, they appeal to particular configurations of terms that allow structures (judgments) to be understood as linked in distinct patterns in terms of the truths of their components. Without thinking of Hegel’s metaphysical/ontological readings of syllogisms as 3 The Science of Logic is divided into two volumes, entitled Objective and Subjective Logic respectively. The former consists of two books, Doctrine of Being and Doctrine of Essence, and the latter of one, Doctrine of the Concept.

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drawing upon considerations of conceptual connection that are found explicitly in syllogisms as traditionally understood, it is hard to see exactly what could be meant to be conveyed by considering an entity such as a state as a syllogism, and hard to understand the nature of the “conceptual” relations binding its parts to the whole.

More specifically, however, it might be argued that while it is true that the Subjective Logic has it’s own internal return to a more “objective” terrain in which judgments and syllogism gain a type of objectual status, this return appears to emerge out of developments within the considerations of these “formal” issues themselves, in particular, out of issues central to Hegel’s treatment of formal syllogisms. Thus it is difficult not to get the impression that, whatever exactly has transpired in Hegel’s treatment of syllogistic inferences, it has been crucial for the purpose of establishing, contra Doz, a discontinuity between the type of ontology that emerges in the latter part of the Subjective Logic and the type of ontology that is coordinate with the categories with which the Objective Logic had concluded. Those earlier categories had predominantly been associated with Spinoza, the modern representative of the type of substance-metaphysics represented in antiquity by Aristotle, and so the Objective Logic ends with a set of conceptual problems faced by Spinoza’s metaphysics. As Hegel famously had put it in the Preface to the Phenomenology of Spirit, “everything turns on grasping and expressing the True, not only as Substance, but equally as Subject” (Hegel 1977, p. 10; GW 9, p. 18), and it is not surprising that the categories articulating the highest form of substance metaphysics will, following this, turn to issues of “subjectivity”, objective logic becoming subjective logic. Would one then not expect the type of objectivity returned to in the second half of the Subjective Logic to represent Hegel’s own metaphysical categories—ones that, in contrast to those of Spinoza, do allow us to understand “the True, not only as Substance, but equally as Subject”? At this point it might help to review just what is found in Volume Two of Hegel’s Science of Logic, “The Science of Subjective Logic”.

After a short two-paragraph foreword in which Hegel describes his project of rejuvenating the existing somewhat dead and “ossified” logic of the concept, Hegel then devotes about twenty pages to a consideration of “the concept”, which is to a large extent taken up with a discussion of Kant. In this context, “the concept” effectively refers to Kantian “I think” that accompanies all representations, a conception of concept that has been arrived at as “the unity of being and essence” (Hegel 2010, p. 526; GW 12, p. 29). This, Hegel tells us, is so far, only “the concept of the concept” which is “only implicitly the truth” (Hegel 2010, p. 526; GW 12, p. 29), the moments of which have the form of “immediate fixed determinations” that “makes of the concept a subjective thinking, a reflection external to the subject matter” (Hegel 2010, p. 527; GW 12, p. 30). It is not until the following section that we learn that what these “moments” are, but here we are told that they will be set in “dialectical movement” such that the “separation of the concept from the subject matter” is sublated, the totality of “objective concept” emerging as their truth. The text then transitions into “Section I, Subjectivity”, which, after a brief introduction, is made up of three chapters, Chapter 1, “Concept”, in which the concept is discussed in terms of its three moments universality, particularity, and singularity, Chapter 2, “Judgment”, with three parts devoted to judgments of determinate being; reflection, and necessity, and Chapter 3, “The Syllogism”, now treating the syllogisms of determinate being, reflection and necessity. The last form of the syllogism of

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necessity, the disjunctive syllogism, leads into Section II, Objectivity, which considers the concept in its now achieved objectivity, and that in turn is followed by the final third section of The Logic of Subjectivity, “The Idea”. We will only be concerned with Section I, and only parts of it, at that.

It should be noted that the plan of the section “Subjectivity” follows a distinctly early modern plan for a logic as set out in the “Port Royal Logic” of Arnauld and Nicole (1996)—effectively, a series of “reflections on “ideas”, judgments” and inferential “reasoning” (the fourth part of Arnauld and Nicole, on method, it might be argued, coincides to Hegel’s Section II, Objectivity). This plan can also be recognized in Kant’s Critique of Pure Reason. A further feature worth commenting on is the comparative modernity of the role played by the conceptual determination of singularity [Einzelheit]. This is a determination conspicuous by its absence as a quantity in Aristotle’s syllogistic, which only gives a place to universally and particularly quantified sentences; the extension of syllogisms to include singular judgments had first occurred in medieval philosophy, associated with the rise of nominalism. Significantly the term is also conspicuous by its absence in Hegel’s Objective Logic, there being only two uses of the term in Doctrine of Being and two in the Doctrine of Essence (both on the last page, signaling the introduction of the Concept-Logic). In contrast, there are then 199 uses in the Subjective Logic.

Arnauld and Nicole are explicit in dividing ideas according to their generality, particularity, and singularity, with singular ideas being described as representing single things and indicated by proper nouns such as “Socrates’, “Rome” and “Bucephalus”, although the first example given is “the idea each person has of himself”. (Arnauld and Nicole 1996, p. 39). Importantly, single things, they point out, can also be referred to by restrictions applied to general ideas, such as when the common name “triangle” can be applied to a single triangle by attaching an indeterminate idea “as when I say ‘some triangle’” (Arnauld and Nicole 1996, p. 40). For his part, Leibniz had interchangeably used singular terms, like “Socrates” and particular terms, like “some man” to refer to the same thing, but in Kant’s Critique of Pure Reason, “singularity” had now become the mark of an empirical intuition, which is “related to the object” (Kant 1998, A320/B377).4 In conformity with traditional syllogistic logic, Kant’s account of judgment provided no real place for singular judgments: judgments being either particular or general,5 reflecting the restriction of singularity to intuitions. But as in Arnauld and Nicole, there is the alternative for reference to individuals by the use of corresponding particular phrases. Hegel, in line with his general critique of Kant’s concept-intuition distinction, has made singularity conceptual, by making it one of its determinate moments, but other than this the starting point for subjective logic is broadly Kantian.

Another related innovation introduced by Arnauld and Nicole had been that between the comprehension and the extension of an idea (now usually referred to as intension and extension), although there is a degree of ambiguity about this distinction in this period, linked to the different uses of singular and particular terms. Thus, 4 Kant is hesitant in applying singularity to the I because of the suggestion of hypostatizing the I as a single thing (Kant 1998, A582/B610).5 In the Jäsche Logic Kant distinguishes universal, particular and singular judgments, but singular judgment can be reduced to universal ones for “in both the predicate holds of the subject without exception” (Kant 1992, pp. 598–9).

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Lanier Anderson (Anderson 2015, p. 50) argues that “extension” (étendu) in the Port Royal Logic is basically an intentional notion, signifying sets of species concepts gathered under an idea, not the individuals the idea characterizes, and distinguishes this as logical extension from non-logical extension. I will suggest below that Hegel diagnoses this confusion as having its origin in Aristotle who similarly plays on an ambiguous analogue to the modern idea of extension. In contrast, Kant, who also uses “Umfang” (extension) in this intensional way (Kant 1992, p. 593), could be said to have a genuinely extensional notion, in that individual objects are given to cognition via the contents of (singular) empirical intuitions.

In short, the intension–extension distinction is a distinctly modern one, first clearly made in Kant. Armed with it, and looking back on the progress of Hegel’s logic from this modern point-of-view characterizing the Subjective Logic, one might say that the categories at the outset had surely been conceived intensionally, and that the dialectic had moved forward via interactions among the contents of the concepts themselves, concepts such as “being”, “nothing”, “becoming” and so on. The critic, however, will respond that this is not how the process could have been understood then as it presupposes the distinction between intension and extension, while the methodology of the logic is supposedly presuppositionless. Without the distinction, it might be said, the unfolding of the categories at the start of the Objective Logic must be understood in a way that mirrors Houlgate’s reading of the logic—that is, the categories would be conceived as categories of thought as well as being. On further reflection, however, this too appears incorrect, since “as well as” also seems to presuppose the intension–extension distinction. Surely it would be more accurate to describe the corresponding set of categories from the start as having been understood as indifferently about either thought or being.6

This, I suggest, is at least closer to the situation that should be thought to obtain at the outset of the Objective Logic—that of a pre-modern philosophical attitude that, from a modern perspective, seems to run subjective and objective considerations together. Thus from the type of “modern” thought reached at the outset of the Subjective Logic, one might expect to find an attitude to the past like that expressed by Kant in his well-known letter to Markus Herz of February 21, 1772 (Kant 1999, p. 133), in which he remarks that hitherto philosophers had just assumed that their thought possessed the intentional features that it, unreflectively, is taken to have—that it is of being. The Kantian attitude at the outset of the Subjective Logic, therefore, should be concerned with how the mind acquires its cognitive content, and the task will be to answer this question with an array of notions meant to provide an account of how the mind acquires rational knowledge of the world. Of course Hegel’s path through this material will not be one that accepts the modern account: it is only at the outset of the process that each of the three moments of the concept, singularity, particularity and universality, are held as understandable in their isolation from the other two. Hegel, in this respect, will be shown to be the paradigmatic critic of the empiricist “given”—the idea that singular mental contents are thought of as supplying the empirical content of judgments that can be known with certainty and play the a foundational role for the subsequent logical “construction” of knowledge. Rather, in 6 Thus Houlgate’s claim that “a fully self-critical philosophy must thus start from the twofold idea that (a) thought is the awareness of being and (b) being is itself simply what thought discloses” (Houlgate 2008, p. 121) seems to read too much into Hegel’s conception of how a self-critical philosophy must start.

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Hegel’s unfolding of the process of judgment formation, singular items will, in contrast, have their role assigned by the functional role they play in judgments. Moreover, and in line with the “inferentialist” semantics recently championed by Robert Brandom (Brandom 1994), the semantic contents of judgments will themselves be subject to the functional role that those judgments play in inferential relations to other judgments. Nevertheless, for Hegel, this type of holism must be shown to emerge from an account of thought in terms of the interactions between concepts, judgments and inferences from which the Subjective Logic starts.

While Hegel was obviously critical of the modern empiricist account of how thought acquires its content, he was not critical in the same way of what might be described as a type of speculative empiricism present in Aristotle. Nevertheless, he was critical of the type of indeterminacy surrounding the question of the relation of thought and being that marked Aristotle’s account. The task facing Hegel, I suggest, was that of reconstructing the logic of Aristotle’s speculative empiricist path from experience of the actual world to a knowledge of the ideas in a way that is armed with the resources that allow this modern explicit separation of thought and being to be properly made. This, on my reading, is what he is doing in the first section of the Subjective Logic.

2: Advantages and Disadvantages of Aristotle’s Speculative Empiricism

In his Lectures on the History of Philosophy, Hegel rejects the commonplace opposing of Plato and Aristotle as representatives of antithetical extremes such as idealism and realism, or rationalism and empiricism (Hegel 1995 vol. 2, pp. 118–9; W 19, p. 132). For Hegel, as for the neo-Platonists, Aristotle was himself clearly a Platonist—a developer of Plato’s speculative philosophy who took Plato’s dialectic beyond the limitations found in Plato himself.

Many readers will undoubtedly find both Plato and Aristotle as presented by Hegel rather unfamiliar figures. For Hegel, the most significant feature of Plato’s philosophy was that Plato, in his masterpiece of dialectic, Parmenides (Hegel 1995 vol.2, p. 56; W 19, p. 79), had touched on the “speculative” unity of being and non-being. This unity had nevertheless remained somewhat implicit and hidden in Plato, who had one-sidedly focused more on the “affirmative principle” concerning the idea’s abstract self-identity, while in contrast, Aristotle had made explicit this hidden moment of negativity (Hegel 1995, vol. 2, p. 140; W 19, p. 154).

In Hegel’s account of this history, the issue of language importantly enters via a consideration of the Sophists who had used dialogue to confound an interlocutor by showing how, on questioning, particular ideas could become transformed into their opposites. What the Sophists had played upon, it would seem, was the egocentric nature of many everyday judgments: as Protagoras put it, “what to one person is bitter, to another is sweet” (Hegel 1995, vol. 2, p. 63; W 19, p. 70). Socrates too had used these apparent contradictions to confound assumptions unreflectively held by his interlocutor, but whereas the Sophists had used this confusion to deny the ultimate distinction between truth and falsity, Socrates used the technique to free the interlocutor from the constraints of the immediate certitudes of empirical

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consciousness so as to bring “the universal in men to consciousness” (Hegel 1995, vol. 2, p. 51; W 19, p. 61).7 But like Socrates, Plato had been too ready to dismiss the empirical from philosophical inquiry and so pass over the imperfect empirical instances of beings to their ideas. In contrast, Aristotle had assigned a more positive place to the consideration of the sensuously presented world, and had come to a more scientific understanding of the world’s categorical structure. “Aristotle, because he looks at all sides of the universe, takes up all those single things [Einzelne] more as a speculative philosopher, and so works [verarbeitet] upon them that the profoundest speculative concept proceeds therefrom” (Hegel 1995, vol. 2, p. 131; W 19, p. 145). But the degree to which Aristotle works on what he takes from the empirical world seems in tension with that aspect of Aristotle’s empiricism that comes to the fore when his logic is contrasted with that of the Stoics—the image of thought passively accepting the forms it finds in things as they are actually experienced.

Despite his generally much higher estimation of the philosophy of Aristotle in relation to the Stoics, it is clear that Hegel treats the Stoics as having progressed beyond Aristotle in the field of logic. The Stoics, he writes, “made abstract thought the principle” and thereby “developed formal logic”, such that with them, logic was “no longer as with Aristotle, at least in regard to the categories, undecided [unentschieden] as to whether the forms of the understanding are not at the same time the essences of things [Wesenheiten der Dinge]; for the forms of thought are set forth as such for themselves [sind als solche für sich gesetzt]” (Hegel 1995, vol. 2, pp. 254–5; W 19, pp. 273–4). Earlier, discussing Aristotle in relation to the Sophists, Hegel writes that “in perception, in ordinary conception, the categories appear: the absolute essence [das Absolute Wesen], the speculative view of these moments, is always expressed in the expression of perceptions. This pure essence in perception [Wahrnehmung] Aristotle takes up [nimmt […] auf” (Hegel 1995, vol. 2, pp. 131-2; W 19, p. 145).8 “Undoubtedly”, he sums up, “this method in one respect appears to be empirical … in the acceptance of objects [Aufnehmens der Gegenstände] as known in mere representation [Vorstellung]” (Hegel 1995, vol. 2, p. 133; W 19, p. 145, emphasis added).

Thus the passive side of Aristotle’s empiricism is expressed in the idea that the categories of thought are equated with the forms of determinately qualitied actual things as encountered in empirical experience. The very forms found in corporeal substances are conceived as accepted into nous in the process of perception, wherein they now exist as forms without matter, simply as the knowledge of those individual substances from whence they came. But this supposes that it was the set of essential qualities, those that the object has in virtue of being a representative of its species, that were accepted into nous. This logical empiricism thus reflects what I have referred to above as the indifference to the question as to whether the categories are regarded as categories of thought or categories of being—they are implicitly accepted as both. Put another way, it is unclear when referring to an object whether one is referring to it as a determinate single thing or as mere representative of the essential features defining its species: that is, in its singularity or as a particular instance of its 7 For a more recent reading of Plato that stresses the role of the dialogue see Gadamer 1991.8 Hegel constantly plays on the etymological connection between taking (nehmen) and taking up (aufnehmen) with perception (Wahrnehmen)—taking to be true.

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kind.9 Contrast this indeterminacy with what Hegel says of the Stoics, who “set forth” the forms of thought as such for themselves—clearly, the forms of thought as opposed to or as abstracted from those things they are about.10 He notes that, “the question respecting the harmony of thought and object” commences with the Stoics (Hegel 1995, vol. 2, p. 255; W 19, p. 274). It is clear that the Stoics represent a philosophical position in antiquity that anticipates the subjectivist thinking of modernity with its clear intensional–extensional separation, especially that of Kant (Gourinat 2004, 537). However, like modern thinkers, the Stoics seemingly cannot combine the idea of the simplicity of the thought with its determinacy (Hegel 1995, vol. 2, p. 255; W 19, p. 274).

In contemporary thought about the history of logic, it is usually said that the Stoics, in contrast to the Peripatetics, anticipated the modern extensionalist turn in with their propositional logic (Bobzien 2003), and that it was the great achievement of Frege to have unified these two forms of logical thought, effectively by reconstructing term logic to conform with the demands of propositional logic. In line with his appreciation of the Stoics, Hegel was, I suggest, appreciative of the shortcomings of Aristotle’s own formal logic, but he also recognized the limitedness of the Stoic alternative. If we are to follow Aristotle’s empiricist path to a speculative knowledge of ideas, that path must be reconstructed in a way that unifies these opposing attitude in a non-reductive way.

In the following section I propose that Hegel’s treatment of judgments and syllogisms in the Subjective Logic can be understood as such a critical reconstruction of the sorts of cognitive processes at the heart of Aristotle’s “thinking empiricist” account of induction or epagoge. There, I suggest, we are meant to appreciate for the first time in the Science of Logic exactly how “being” becomes incorporated into “thought”, leading to knowledge of “the profoundest speculative concept”.

Section 3: First Steps in a Reconstruction of Aristotle’s Logical Ascent to the IdeaIn Posterior Analytics (Aristotle 1960), Book II, ch. 19, Aristotle states that all animals have perception, but in some percepts are retained in the soul, and introduces his celebrated image of a group of soldiers in come to take a stand in the context of a rout in the course of a battle. This common stand comes about, first by being made by one soldier, then another, then the next, and so on, until “the original position is 9 Aristotle’s ambiguity here might be regarded as the origin of the ambiguity between logical and non-logical essence alluded to above.10 The Stoics had, with their notions of incorporeal sayables “leckta” and assertibles “axiomata”, distinguished thought contents or intensions from their extensions of thought (Nuchelmans 1973, Ch. 4). In contrast, Aristotle’s use of “protasis”, while standardly translated as “proposition” or “premise”, does not seem to have the standard modern philosophical sense of the term—that of referring to an abstract content expressed by an utterance (Crivelli and Charles 2012). While the Stoics had insisted that it was the lecta expressed by the logoi, not the logoi themselves that were true or false, in contrast, for Aristotle, it was the protasis as logos, qua complex of significant sounds, that was true or false (Nuchelmans 1973, 77).

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restored” (Aristotle 1960, 100a1–14). The retreating individual soldiers represent the flow of individual percepts in time, and when the stream of percepts comes to make its collective stand in this way “there is the first beginnings of the presence [in the soul] of a universal (because although it is the singular [to kath ekaston] that we perceive, the act of perception involves the universal, e.g., ‘man’ not ‘a man, Callias’” (Aristotle 1960, 100a15–b1).11 One might here pause to wonder how while singular things, like this man Callias, are perceived, perception can, nevertheless, involve universals. Hegel’s account of judgment in the Subjective Logic, I suggest, is meant to provide an explanation.

Hegel contrasts two different approaches to the logical structure of judgment that might be adopted: a term-first approach in which subject and predicate terms are “treated as ready-made, each for itself outside the other … the judgment itself is simply the act that combines the predicate with the subject” (Hegel 2010, p. 552; GW 12, p.55). This is superficial, however, as “it is in judgment that [subject and predicate terms] must first receive their determination (Hegel 2010, p. 553; GW 12, p. 56). The former clearly reflects the approach to judgment in traditional term logics like that of Aristotle, while the latter seems to apply more to modern conceptions of the proposition, in which the meaning of a part is determined by its contribution to a property of the whole, specifically, its truth-value. Something close to this distinction can be found in the ancient world in the contrast between Aristotelian term and Stoic propositional logics. And yet this distinction might be thought to be reflected in the way in which Aristotle himself had characterized predication with the implicit distinction between the imagery of the containment of the predicate in the subject on the one hand, and on the other, a more linguistic imagery by the idea of the predication or saying of the predicate of the subject. But Aristotle equates the two: “for one term to be wholly contained in another is the same as for the latter to be predicated of all the former” (Aristotle 1938, bk. I, 24b27–29).

I have suggested that Aristotle blurs the difference between an object regarded as a singular thing (objects of “non-logical extension”) and objects regarded as exemplars of their species (quasi-objects of “logical extension”). It is only the latter quasi-subsumptive relation that can be considered as “the same as” (or an inversion of) that of intensional containment. Hegel, reflecting Kant’s separation of singular and particular, treats the subsumptive relation as one between concepts and their proper, (“non-logical”) extensions, and so these two relations will not be the same. Predication as inherence is a characteristic of the first form of judgment Hegel treats—the judgment of determinate being, by which he clearly means an immediate perceptually based “de re” judgment about some specific object, his examples including “the rose is red” and “the rose is fragrant” (Hegel 2010, pp. 558, 559; GW 12, pp. 61, 62). Predication as subsumption, in contrast is found in the succeeding judgment of reflection that will have has a more fully propositional content as in a “de dicto” judgment.

An obvious peculiarity of Hegel’s judgment of determinate being lies in the fact that the predicate term is described as singular, singular terms having no real role within Aristotle’s syllogistic logic, but especially no role as the predicate of a 11 While the translators give “particular” here, I follow Whitaker who claims that “Aristotle’s own terms, ‘singular’ [kath ekaston] and ‘partial’ [en merei], are used clearly and consistently” (Whitaker 1996, p. 89).

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judgment. The modern “subjectivist” feature of Hegel’s approach soon becomes explicit in the fact that by the singularity of the “fragrance” or “redness” of the particular rose Hegel clearly intends the specific fragrance or redness of that rose—its way of being fragrant or red. This was the type “singular” and “immediate” subjective content that Arnauld and Nicole had tried to capture with a sensory idea, and that Kant had tried to capture as the content of an empirical intuition. What Hegel has done, then, is to reclassify Kant’s intuitive content as a type of conceptual content: singularity has become a “moment” of “the concept” rather than the mark of something non-conceptual. In contrast, the predicate of Hegel’s judgment of reflection will be a standardly abstract universal, signifying, say, the indeterminate in the sense of phenomenologically non-specific redness that the rose can be said to share with other things such as post-boxes and fire-engines—all things of which “red” could be truly said. Consonant with this, the judgment of reflection clearly is meant to represent inferential judgments rather than non-inferential or immediate perceptual ones, as there would be no peculiar “what it is like” suggested by the predicate, in contrast to forms appropriate for the expression of immediate perceptual judgments. Along with this, such phenomenological indeterminacy might be thought to be an aid in the context of linguistic interaction, and as appropriate for the attribution of content to others on the basis of what they say.

This distinction between judgments characterized by the different inherence and subsumption forms of predication is now repeated at higher and higher levels, generating an array of increasingly complex judgment types, and ultimately types of syllogisms, from this initial duality. Hegel notes that “every judgment is in principle also an abstract judgment” (Hegel 2010, p. 558; GW 12, p. 61), the implication seeming to be that in making a judgment of determinate being such as “the rose is red” one simultaneously commits oneself to a higher-order judgment concerning the categories exemplified by the terms in the initial judgment. Thus to assert that “the rose is red” is to implicitly assert the abstract proposition “the singular is universal”—an identity that is rooted in the ultimate unity of the “moments” of conceptuality—universality, particularity and singularity. This underlying identity of singularity and universality as “moments” of conceptuality will mean that the subject term of the judgment, typically taken as a singular, will also be able to be read as a universal and the predicate term, typically read as a universal, will be able to be read as a singular. With this, the first “resolved” form of the judgment of determinate being actually encountered—the one described above in which the predicate is taken as expressing the determinate phenomenal property of the thing—will have a singular predicate, and, congruent with this, a universal subject. Thus “the rose” will designate an instance of a universal, a particular instance of rosehood. The subject, then, is no mere this, but, a “this such”—a determination of particularity. In sum, in this type of judgment, the property qua singular determination is taken to “inheres” in the object, qua instance of a universal.12 This is effectively the logical structure of what Hegel treats in the Phenomenology of Spirit as an object of perception (Wahrnehmung) (Hegel 1977, pp. 67–79; GW 9, pp. 71–81).

The reapplication of this higher-order rule identifying singularity and 12 Following the reflective judgment it will be the implicit “secondary substance” contained in the subject term of the judgment of Dasein that will become the explicit subject of the next type of judgment, as in “the rose [i.e., the rose as such] is a plant” (Hegel 2010, p. 576; GW 12, p. 78).

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universality qua determinations of conceptuality will now re-establish the original (singular-universal) determinations of subject and predicate resulting in the judgment of reflection in which the predicate, re-established as a universal, is said to subsume the subject, that is once more construed as a singular (in Anglophone philosophical parlance, a “bare particular”), stripped of the sortal universal that allowed the subject term to pick out something qua particular instance of a kind in the earlier judgment of determinate being. The abstractly singular nature of the subject of the reflective judgment allows it to take indefinite quantified forms, there being particular and universal judgments of reflection that can be contrasted with the explicitly singular ones (Hegel 2010, pp. 570–5; GW 12, pp. 72–7).

Hegel’s device of switching between singular, particular and universal construals of both subject and predicate terms may look idiosyncratic, but it can be readily seen to be a variant of a simple device familiar from early analytic philosophy. Treating the normally universal predicate as a singular term and the normally singular subject term as a universal can be understood as simply reversing subject and predicate terms in the judgment in a manner suggested by Frank Ramsey who, in an effort to undermine the metaphysical significance of the traditional subject–predicate relation, had pointed out that “Socrates is wise” and “Wisdom is a characteristic of Socrates” are equivalent propositions (Ramsey 1925, p. 404). On this model we could construe the judgment of determinate being as having the form: “this red colour (the new subject) is in (predication as inherence) this rose (the new predicate)”. Retaining Hegel’s way of portraying the situation, however, the logical relation of predication can be seen as mirroring the ontological relation between a property and a substance: one thinks of the intension of the predicate as in that of the subject just as the rose’s redness is in the rose itself. Furthermore, because other specific properties of the rose, its shape, its colour, etc., can also be said to be in it, the rose as that in which the various properties inhere must now be considered to have the generality typical of a predicate—to have become a universal—a concrete one—to which various particular properties can belong. This logical structure will become explicit in the categorical sub-form of the judgment of the necessity—a judgment about a secondary substance, the rose as such, that succeeds the judgment of reflection and contains features of both the two earlier forms of judgment (Hegel 2010, pp. 575–6; GW 12, pp. 77–8).

This series of increasingly complex judgment forms generated by this mechanism will eventually lead to a judgment form, the apodictic judgment—the final sub-form of the judgment of the concept—that is shown to be an implicit syllogism (Hegel 2010, pp. 585–7; GW 12, pp. 87–9; Redding 2007, pp. 188–9), and Hegel’s treatment of judgments thereby transits to his treatment of inferences or syllogisms. In this new context, the difference between the two conceptions of predication now appears as one between two different conceptions of logical consequence, as both the “containment” and “said of” relations can be considered as transitive. Hegel will aim to show that a conception of syllogistic inference based on the transitivity of the containment relation, found in Aristotle’s perfect, that is, intuitively obvious syllogisms, actually depends on the weaker truth-based “said of” relation found in Aristotle’s conversion rules, resulting in the collapse of the traditional syllogistic and its replacement by the type of abstract mathematical logic introduced by Leibniz, and championed by the Tübingen philosopher–logician, Gottfried Ploucquet—effectively Hegel’s own logic teacher (Redding 2014).

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Hegel proves a close and astute reader of Aristotle’s syllogistic. Early in the Prior Analytics Aristotle defines what it is to be a perfect syllogism: “When three terms are so related to one another that the last is wholly contained in the middle and the middle is wholly contained in or excluded from the first, the extremes must admit of perfect syllogism. By ‘middle term’ I mean that which both is contained in another and contains another in itself, and which is the middle by its position also; and by ‘extremes’ (a) that which is contained in another and (b) that in which another is contained” (Aristotle 1938, bk. I, IV, 25b32-5). With this Aristotle clearly sets out his conception of the consequence relation as based on the transitivity of the relation of containment. Consonant with this, Aristotle is said to have utilized diagrams in his teaching of logic (Netz 1999, p. 15), likening the way one can see diagrammatic containment relations to the way that we can see how the conclusion of a perfect syllogism follows from its two premises. But Aristotle immediately follows this with an account formulated now in the “predicated” or “said” of mode: “For if A is predicated of all B, and B of all C, A must necessarily be predicated of all C”. Remember that for Aristotle, the said of relation is only a pseudo-extensional one, being a mere reflex of the idea of conceptual containment. Hegel recognizes this, quoting this passage with the gloss that Aristotle had thereby “confined himself […] to the mere relation of inherence by defining the nature of the syllogism” (Hegel 2010, p. 591; GW 12, p. 93). But Hegel believes that Aristotle’s account of consequence implicitly depends on the operation of properly extensional relations implicit in the “conversion rules” required for proving imperfect syllogisms by reducing them to perfect ones that are grasped intuitively on the basis of the containment reading of predication. Hegel, of course, will not argue for one form over the other: both must be aufgehoben in such a way that each continues to play a role. It is the oscillation between each form as noted above that is the means of this Aufhebung.

This is not the place to evaluate Hegel’s interpretation of an aspect of Aristotle’s logic, nevertheless, Hegel’s interpretation appears as a not implausible one in the context of recent accounts (Malink 2013). What Hegel is intent on showing is the interdependence of the explicitly intensionally based “containment” account of predication and consequence with the contrary extensional “subsumption” view—a distinction blurred in Aristotle. In short, perceptual experience provides an initial determinate content for judgment, but as fundamentally intensional this cannot be thought of representative of something genuinely independent of those intensionally related concepts wielded by the judging subject. For the independence of a genuinely extensional referent to be accounted for, the judgment has to be transformed into its reflective analogue, now understood as made true by some independent aspect of the world, but at the expense of the judgment’s determinacy. This becomes explicit in Hegel’s treatment of the “mathematical” syllogism of Leibniz and Ploucquet into which the syllogism of determinate being collapses, and which signals the transition to the syllogism of reflection.

The post-Aristotelian fourth-figure syllogism that concludes the sequence of syllogisms of determinate being confounds the understanding of inference on the model of the transitivity of containment or inherence as in it, the major term, which is a predicate in the major premise, becomes a subject of the conclusion, while the minor term, which had been the subject of the minor premise, becomes a predicate of the conclusion (Hegel 2010, pp. 602–8; GW 12, pp. 104–10). Any notion of transitive

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containment relations have disappeared, and the transitivity of subsumption relations reliant on them for determinate contents has also collapsed. Hegel describes a new conception of consequence operating in this syllogism with the idea that “if two things or two determinations are equal to a third, then they are equal to each other. – The relation of inherence or subsumption of terms is done away with”. This “third” is “in general the mediating term” but it “has absolutely no determination as against the extremes” (Hegel 2010, p. 602; GW 12, p. 104). “The third” here refers to an entirely posited abstract entity that is regarded as subsumed by both the predicate and the original subject term, that is now explicitly treated as a predicate (Antognazza 2007, pp. 22–6). What has happened is that the subject term of the original Aristotelian proposition or protasis, which had been indifferently regarded as a singular (an individual substance) or a particular (a representative instance of its class), has been disambiguated. The overt judgment is now explicitly taken as a joining of two intensional predicates, but at a deeper logical level this relation is seen as underpinned by the fact that they are both truly predicated of a range of objects not represented directly in the surface structure. The judgment structure is then held together by properly singular indeterminate posits, the thirds determining the truth of the overt judgment.

This mathematical syllogism claims Hegel “ranks […] as an axiom, as a first self-explanatory proposition which is neither capable nor in need of proof, i.e., of any mediation – which neither presupposes anything else nor can be derived from anything else” (Hegel 2010, p. 602; GW 12, p. 104). Thus the axioms of mathematical syllogisms do not in fact have the type of immediate intuitable “certainty” that had characterized those “perfect” traditional syllogisms. “If we take a closer look at this prerogative that the proposition claims, of being immediately self-evident, we find that it lies in its formalism, in the fact that it abstracts from every qualitative diversity of determinations and admits their quantitative equality or inequality” (Hegel 2010, pp. 602–3; W, GW 12, p. 105, second emphasis added). This mathematical syllogism structure is axiomatic in that it “is neither capable nor in need of proof”, not because it was, like the perfect syllogism, intuitable, but rather that, abstracting “from every qualitative diversity of determinations” it “only admits their quantitative equality or inequality” just as “lines and figures, posited as equal to each other, are understood only according to their magnitude” (Hegel 2010, pp. 603; GW 12, p. 105). Hegel is aware that Leibniz’s project of mathematical formalization had been linked to the idea of the mechanization of thought, an idea he criticizes in Ploucquet (Hegel 2010, p. 608; GW 12, p. 110).13

Negatively, the mathematical syllogism has undermined the assumptions on which the Aristotelian syllogism was built. The intuitive and intensional basis of the consequence relation purportedly at its heart had been shown to rely on extensional and ultimately mechanically applicable principles. The fate of the traditional syllogistic shows that “the customary exposition of the syllogism and of its particular configurations is not a rational cognition, not an exposition of them as forms of reason” (Hegel 2010, p. 605; GW 12, p. 107). The reconstruction is to take place after the downfall of the traditional program brought about by the mathematical syllogism and it will build on the positive features it shares with the negative. Namely, “that in the abstract determinateness its other has been posited and the determinateness has 13 Both Leibniz and Ploucquet are discussed in relation to the history of the project of the mechanization of thought in Marciszewski and Murawski 1995.

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thereby become concrete”. “What is truly present here” Hegel goes on “is not a mediation based on a given immediacy, but a mediation based on mediation … a mediation of reflection” (Hegel 2010, 603; GW 12, p. 105).

The series of syllogisms that build on the collapse of the traditional syllogistic will eventually arrive at the syllogism of necessity that is “full of content”. I have elsewhere argued that this syllogism is understood as concrete in the sense that represents the conceptually mediated (and so “syllogizing”) intersubjective activities of mutually recognizing concrete socially and historically organized human beings (Redding 1996, 156–8). It is this syllogism that then transitions into the “objective” section of the Subjective Logic. As Hegel links the syllogism of necessity to the ontological proof for the existence of God, this genesis of concreteness can seem mysterious, but that the process by which the syllogism has become contentful need not seem mysterious if it is recognized that it has in fact been at work from the start of the Subjective Logic. It has been the alternating “intensional” and “extensional” steps that have brought an independently conceived “being” into thought, and this can only be understood as commencing with empirically given content that is independent of any particular determination because it is always subject to progressive re-determinations in which it becomes linked in conceptually mediated ways to a wider and wider range of other elements. This has initially been conceived as a process holding for a subject, but the collapse of Aristotle’s logic into mechanized thought has produced a type of radically materialist “identity” of thought and being, albeit surely not of a kind that advocates of Hegel’s categories as “ontological” would wish, but an identity all the same. And, of course, Hegel’s reconstruction, does not stop there. The limitations of mechanical thought are not to be regarded as lying in its image of thought as a worldly corporealized process; rather they lay in the limitations of such a mechanical conception of worldly corporeality, the limitations of which are displayed in Chapter 1 of Objectivity, “Mechanism”. As the interrelated substances of the world become progressively more complexly determined, they come to have properties that had initially been understood as properties of the initially atomistically conceived conscious subject for whom these processes held. Towards the end of Objectivity, worldly things are meant to be sufficiently rich that a subject can find itself in such a thing.

In this essay I have suggested that we take seriously Hegel’s allusions to Aristotle in his Lectures on the History of Philosophy and as type empiricist, what I have called a “speculative empiricist”, who offers a serious alternative to the problematic picture of any kind of direct intellectual intuition that is linked to the distinctly anti-empirical attitudes of his teacher Plato. Moreover, I have suggested a reading of Hegel’s subjective logic as a type of critical reconstruction of Aristotle’s formal logic that starts from a modern subjective position which holds thought and being to be separate. It is then meant to show on the model of Aristotle’s original account, the logical transformation of the perceptual knowledge of singular things into a conception of ideas and principles built into the structure of the world. Read in this way, the analyses of Hegel’s subjective logic and his attitudes to formal logic more broadly, might be seen as having a far greater relevance than they have been traditionally accorded.14

14 I am grateful to Michael Beaney, for discussions on logical issues touched on in this essay, and to Dalia Nassar, for discussion about conceptions of empiricism extant in Hegel’s time.

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