At its broadest, Clayton Bohnet’s work investigates the relation between logic and first philosophy through a rigorous comparison of Kant and Hegel, whose major publications offer ‘two radically distinct approaches to the subject matter of logic’ and are especially ‘informative for clarifying the disciplinary boundary between logic and philosophy’ (p. 3). Bohnet circumscribes his inquiry by focusing in particular on the logic of quantity, which he justifies by arguing that some of the most significant philosophical arguments in the past 200 years and even the division of ‘20th-century philosophy into analytic and continental’ turn on ‘the problem of quantification’ (p. 5).
Bohnet situates his investigation within the context of Kant’s and Hegel’s larger philosophical commitments, especially the fundamental question: ‘How is the absolute related to human thought’? (p. 11). Naturally, Kant’s and Hegel’s respective answers prove decisive for their accounts of logic. Thus, although ‘Kant’s metaphysical deduction and the transcendental logic of the first Critique opened up the possibility of thinking about logic in a new way’, that account is embedded in the overall project of the first Critique, which demonstrated ‘that the absolute is transcendent of the conditions of objective knowledge’ (pp. 10, 12). Consequently, logic and metaphysics, while related, remain essentially distinct. In contrast, for Hegel, the absolute (or unconditioned) is immanent in thought and the difference between transcendental and formal logic can be understood as sublated in the self-determining movement and unfolding of the absolute idea. Accordingly, throughout the work Bohnet focuses on the interlocking triad of logic, thought and the absolute, ever attentive to how an account of one implies something about the other two.
Bohnet begins by reconstructing Kant’s view of pure and general logic in order to identify the boundary between logic and metaphysics and to distinguish between logic and transcendental logic. While ‘having no direct relation to intuition and the cognition of objects’, pure logic represents ‘the formal conditions for the possibility of objective verification’, i.e. it constitutes ‘a frame in which our picture of the objective world is constructed’ (p. 55). This frame amounts to a negative condition for truth, establishing the formal rules for thought’s self-agreement. Transcendental logic provides a second, positive framing for objective cognition. By delineating the rules that govern ‘the synthesis of a priori representations, a synthesis that is beyond the scope of general logic’, transcendental logic establishes ‘the conditions and principles of material truth’ (pp. 103, 143).
Chapter 2 develops this distinction by clarifying ‘the meaning of quantity for cognition in the context of general and pure logic’ (p. 57). Bohnet notes the counterintuitive nature of the claim that quantity can be treated as part of general logic, since quantity seems to ‘necessarily deal with number and mathematics, as well as objects presented to the mind by intuition’ (p. 58). Nevertheless, Bohnet asserts ‘that there is a purely logical treatment of quantity’ that does not depend on the enumeration of objects within ‘the frame of the world’ (p. 58). Rather Kant’s treatment of quantity in pure logic ‘consists of an extension that is not countable’ (p. 59). Bohnet identifies how extension is operative in: (1) conceptual analysis, by how many concepts are subsumed under another concept; (2) judgement, by the extent to which a predicate subsumes the subject concept; (3) inferences, by ‘the alternation of the quantifiers of a judgment while preserving the truth value’ (p. 92). However, since concepts and judgements presuppose representation and consciousness (and Kant must introduce intuition to account for representation and consciousness), Bohnet’s investigation is led to inquire into ‘the most original basis for our experience and knowledge’ and more specifically ‘into the conditions of possibility of quantity and/or extension’ (p. 93). This shows how the treatment of quantity in general and pure logic is dependent upon transcendental logic. Three important conclusions follow for distinguishing transcendental and pure logic. (a) Transcendental logic governs ‘cognition as a priori related to objects given by intuition. It is the analytic of the form of thought thinking an object’ – not any determinate object, but an object as such (p. 103). Hence its content is universal. (b) The essence of Kant’s doctrine of quantity is that ‘each object of inner or outer sense must be an extensive magnitude’ (p. 123). (c) Since any object of perception or knowledge is the result of a synthesis of homogeneous parts, ‘the doctrine of quantity in the Critique requires that all determinate cognition that is in accordance with the valid use of the categories must have, involved in its object, extensive magnitude’ (p. 125).
Taking up the question of whether transcendental logic’s insistence that any given object of experience must be quantifiable provides a foundation for formal logic’s treatment of quantity, chapter 4 further explores the relation between the two logics. Emphasizing the importance of Kant’s denial of intellectual intuition (and corollary implications for the human epistemic standpoint), Bohnet argues that, although there is no ‘direct route between transcendental logic and general and pure logic’, there is nevertheless an indirect relation which reveals that the two logics are isomorphic: ‘heterogeneous from one perspective, but homogeneous from another’ (p. 125). That is, while the two logics converge in ‘determinate cognition’ and ‘represent collectively the formal and material conditions of objective determinate knowledge’, they nevertheless remain heterogeneous insofar as the grounds of the formal conditions remain distinct from (and cannot be derived from) those of the material (p. 142).
Chapter 5 considers Hegel’s early criticism of Kant. Situating Hegel in relation to post-Kantian thinkers, such as Reinhold, who are too beholden to the mere letter of critical philosophy, and Fichte and Schelling, who recognize the spirit animating Kant’s philosophical endeavour, Bohnet explores Hegel’s distinction between reflection and speculation and the parallel opposition between Verstand and Vernunft. This antithesis is the ground of Hegel’s criticism of Kant’s disciplining of reason’s speculative ambitions. Since the ideas of reason remain purely formal, Kant’s critical philosophy remains (as characterized in Hegel’s Differenzschrift) ‘a philosophy of the understanding consecrated by reason’ (p. 179). Kant retains ‘the dualism of (a) the regulative and the constitutive role of reason, and (b) the dualism of the understanding and reason’ (p. 183). Such dualisms are manifest in Kant’s delineation of the boundary between faith and knowledge, which, for Hegel, is ‘simply the boundary point at which “the work of reflection comes to an end” and the speculative philosophy begins’ (p. 184).
Bohnet’s final chapter explores Hegel’s mature commitment to a method of philosophizing intended to overcome all such dualisms, namely, speculative dialectic, that transforms the status, role and significance of traditional formal logic. Whereas in Kant logic and metaphysics are sharply differentiated, in Hegel’s Science of Logic, traditional formal logic (the science of concepts, judgements and syllogisms) is metaphysical because ‘it is a moment in the unfolding of the absolute idea’ and thus is ‘as essential to metaphysics as ontology’ (p. 188). As Bohnet’s analysis of the judgement of reflection (in Kant, the judgement of quantity) illustrates, Hegel’s innovation consists in taking up ‘the traditional content of logic from within the speculative process: the concept is the immediate, judgment is the mediating function of negative reason, and syllogism is positive reason’ (p. 212).
Bohnet’s account of the movement of Hegel’s subjective logic from concept to judgement to syllogism provides the first context within which he situates the judgement of reflection in relation to the judgement of existence, which precedes it, and the judgement of necessity, which follows it. This contextualization allows Bohnet to trace the unfolding of the dialectic through the different moments that comprise reflective judgement, namely, singularity, particularity and universality. However, since the judgement of reflection as a whole begins and ends with empirically existing individuals, the culmination of reflection is more accurately understood as an ‘allness’ that cannot be a true universality. It is ‘a fraudulent or spurious universality’ (p. 241). The deficiency drives the dialectic onward. True universality is only attainable in the judgement of necessity which requires a ‘transformation at the level of the content of the judgment. The subject now includes the quantification within itself’ (pp. 246–7).
The distinctive feature of Hegel’s logic, exemplified in this transition, is that ‘each particular kind of judgment has its own particular content’ (p. 253). Content and form are codetermining, for ‘the form of the relation between subject and predicate in each type of judgment is specific and developing’ (p. 253). Logic, therefore, is not something independent, but rather appears as a moment in the self-differentiation of the absolute idea – a process in which form and content undergo mutual and correlative determination.
Bohnet should be commended for his careful, painstaking analysis of some of the most challenging texts in the history of philosophy. His detailed study of quantity provides a route into investigating some of the most fundamental epistemological and metaphysical questions. However, although Bohnet’s introduction suggests that such an analysis might illuminate contemporary philosophical questions and offer a perspective for re-evaluating some of analytic philosophy’s deepest theoretical commitments, this gesture remains a promissory note. A great deal of careful ground clearing is undertaken and the book certainly succeeds in its professed task of situating ‘Hegel’s critique of Kant in the context of the philosophy of logic’ (p. 7). Yet, Bohnet does not return to the aforementioned bigger themes, and the reader is left wishing for a little more big-picture payoff for all the intricate textual exegesis.
