German science and culture of the seventeenth and eighteenth centuries benefited from the enlightened patronage of the Prussian King Frederick the Great. Moreover, the universities of Germany prospered and became centers of excellence in the West, especially in science. Advances in psychology by German philosophers focused primarily on mental activity. Discarding the environmental determinacy of British empiricism, Leibniz defended the active agency of the mind in molding sensory data to provide experience. The active principle of his monadology lent itself to a dynamic view of harmony between independent physical and psychic processes. The rationalism of Wolff was fully elaborated by Kant, who described pure reason as the formation of perceptions innately through time and space, and asserted an elaborate structure of the mind in terms of categories that order the environment. From these formulations, German psychology received a variety of models suggested by Herbart, Beneke, and Lotze. Collectively, the German tradition is diverse but united by the belief in the activity of the mind and its control of environmental influences.

Chapter 8 focuses on Kant’s reaction to the metaphysics of quantity found in Leibnizian and Wolffian rationalism. Leibniz had broad ambitions for a unified theory of all knowledge that subsumed mathematics under metaphysics. Leibniz accordingly sought metaphysical definitions of quality and quantity that in turn supported metaphysical definitions of similarity and equality as identity of quality and quantity, respectively. A criterion of success was that these definitions corresponded to Euclid’s geometrical notions of similarity and equality. This chapter examines Leibniz, Wolff, and Baumgarten’s views of quality and quantity and the contrast between them, which was closely tied to the conditions of their representation and distinct cognition. Kant adopts some of their understanding of the metaphysics of quantity, such as the definitions of similarity and equality as identity of quality and quantity, respectively. At the same time, he radically reforms it. Kant distinguishes between two notions of quantity, quanta and quantitas, and hence draws two contrasts with two corresponding notions of quality: quality versus quantum, and quality versus quantitas. Most importantly, Kant holds that quanta require intuition for their representation. This preserves the general framework of the Leibnizian and Wolffian metaphysics of quantity while radically reforming it at its foundation.

The previous chapters established the centrality and importance of Kant’s theory of magnitudes. Before investigating Kant’s views more deeply, Chapter 6 provides critical background concerning the theory of magnitude, which is rooted in Euclid’s Elements. It describes the organization and deductive structure of the Elements to explain tensions between Euclid’s account of number and continuous spatial magnitude that persisted into the eighteenth century. It then explains the theory of proportions, in particular, the crucial definition of sameness of ratio. It also describes the mathematical nature of the continuous spatial magnitudes implicitly defined by that theory, including their homogeneity. Euclid also covers number and arithmetic and he regards numbers as collections of units. Much of the theory of proportions covers numbers as well as continuous spatial magnitudes, although Euclid gives numbers a separate treatment. This commonality inspired the search for a universal mathematics that covered continuous magnitudes more generally as well as number. The chapter traces the history and development of these themes in the Euclidean mathematical tradition, and describes its influence on three of Kant’s immediate predecessors: Wolff, Kästner, and Euler. It explains why these philosophers and mathematicians regarded mathematics as a science of magnitudes and their measurement.

The debate in 1792-94 between Wilhelm von Humboldt and Karl von Dalberg focuses on the legitimacy and limits of the state’s promotion of welfare for its subjects. It represents a clash between the Kantian school and advocates of the Leibniz-Wolff philosophy. Dalberg advocates a strongly interventionist state, while Humboldt circumscribes narrowly the scope of rightful political action. Humboldt’s post-Kantian perfectionism aims to maximise freedom and its conditions, rather than to promote happiness, as older perfectionisms had done. Dalberg, in contrast, appeals to Wolff’s defence of enlightened absolutism, viewing the state as the agency for eliminating obstacles to individual and social thriving, or the good life. While illustrating the reception of Kant’s critiques of previous ethical systems, and the persistence of Wolffian themes, the debate is also indicative of the diversity of political positions advocated by Kantians in the aftermath of The Groundwork of the Metaphysics of Morals (1785). In conceiving the individual as a spontaneous monad with a unique developmental trajectory, Humboldt shares with Dalberg a revised version of Leibniz. The blending of Leibnizian and Kantian concepts constitutes the central theoretical interest of the political thought of this period.

Chapter 3 addresses the relationship between the various tasks carried out in the Critique of Pure Reason by analyzing Kant’s multifaceted use of the term ‘transcendental.’ Challenging the received view, it maintains that Kant’s seemingly divergent accounts of the subject hinge on his conception of transcendental philosophy proper and transcendental critique as first-order and second-order branches of transcendental cognition, respectively. Drawing on a brief account of the seventeenth- and eighteenth-century history of the term ‘transcendental,’ the chapter seeks to show that Wolffian ontology and transcendental philosophy proper have more in common than is widely assumed: both disciplines can be said to provide a comprehensive account of the cognitive elements presupposed in any cognition of objects. On this account, the novelty of the Critique consists primarily in the second-order investigation into metaphysics that Kant calls transcendental critique. The chapter concludes by examining Kant’s criticism of the way his predecessors and contemporaries understood the terms ‘ontology’ and ‘transcendental philosophy.’

Chapter 1 elaborates on the historical context within which Kant developed his critique of early post-Leibnizian philosophy. It presents the pertinent elements of Wolff’s highly influential metaphysics and theory of cognition as well as the main thrust of Crusius’s critique of Wolff. Since Kant targeted both Wolff, Crusius, and those who followed in their wake, the chapter also discusses the main tenets of Crusius’s own metaphysics and the controversies that resulted from efforts among early post-Wolffian philosophers to reconcile Leibnizian monadology and Newtonian physics.

Chapter 7 analyzes the Appendix to the Transcendental Analytic entitled “On the Amphiboly of the Concepts of Reflection.” Using Leibniz’s monadology as a prism, Kant here seeks to account for the ultimate premises of his critique and intended reform of metaphysics. More specifically, the chapter conceives of this critique as a variety of transcendental reflection that is guided by four pairs of concepts, including sameness and difference. In order to contextualize this account, the chapter briefly discusses Wolff’s and Baumgarten’s treatment of these concepts. Commentators generally assume that the activity called transcendental reflection is carried out in the Critique of Pure Reason alone. The chapter argues, by contrast, that Kant distinguishes the version of transcendental reflection that informs the ontology of his predecessors from the critical version enacted in the Critique. On this basis, it outlines Kant’s understanding of the difference between a Leibnizian employment of the concepts of reflection and his own.

Focusing on its 1781 version, Chapter 5 interprets the transcendental deduction in light of Kant’s overall investigation into the conditions under which metaphysics is possible. Whereas most commentators take the text to be mainly concerned with the conditions of possibility of empirical cognition, it seeks to demonstrate that the various strands of Kant’s investigation primarily aim to identify the conditions under which categories can be used to produce objects of a priori cognition as such. On Kant’s account, categories can contribute to the production of such objects only if they function as a priori rules for the thoroughgoing unification of successive representations, which is not the case if they are used to determine alleged objects such as the soul, the world as such, and God. Thus, I contend that the transcendental deduction passes a balanced judgment on Wolff’s unqualified affirmation of the possibility of a priori cognition of objects and Hume’s unqualified rejection of the same.

The second chapter seeks to clarify how Kant in the late 1760s and early 1770s came to conceive of the aim and main arguments of what was to become the Critique of Pure Reason. It focuses in particular on Kant’s evolving understanding of the act of critique. The heart of the chapter consists in an analysis of the Inaugural Dissertation. Challenging the prevailing view, the chapter highlights the critical impetus of the treatise by arguing that the specific criterion it employs to curb the ambitions of metaphysics – intellectual purity – is directed against an assumption common to Wolff, Crusius, and early post-Leibnizian philosophy in general. Moreover, it puts into perspective the alleged break between the Dissertation and the Critique by arguing that this early instance of critique is preserved in the Critique of Pure Reason. The chapter argues that Kant in this work introduces a new form of critique by arguing that any a priori cognition of objects necessarily rests on pure intuition.