The final two Metaphysical Expositions argue that our original representation of space must be intuitive. I draw some surprising connections between Kant’s discussion and Leibniz’s account of the continuum. These connections indicate that the point of Kant’s analysis of <space> is to show that our original representation of space is infinitely complex in content. Since no discursive representation can be infinitely complex, our concept <space> cannot derive its content from discursive spontaneity. Its content must rather be given to the mind in order to be thought at all and thus originates in receptive intuition. Kant’s argument does not hinge on the singularity or holistic structure of space, as many hold, but on its infinite complexity and consequent givenness. I develop a novel account of the discursivity of conceptual representation that preserves the validity of Kant’s argument, defend Kant’s account of the infinity of space against prominent objections, and finally indicate how Kant’s argument entails the singularity of intuition (rather than presupposing it).

In this chapter, we consider a group of philosophers who formed their views in opposition to voluntarist natural law. Although there are important differences between Spinoza, Cudworth, Shaftesbury, and Leibniz, all four were united by their opposition to voluntarism. For voluntarists, even natural law is a kind of positive law since it is created by God’s discretionary imposition. Against this, Cudworth complained that voluntarism makes morality “positive, arbitrary and factitious only” and unable to explain morality’s “eternal and immutable” character. Leibniz was also a critic of positivist law, and he subversively reinterprets law in terms of love. Justice, he says, is the “charity of the wise.” For his part, Spinoza opposes not just positivist law but law itself. Indeed, although his great metaphysical work is titled Ethics, it constitutes nothing less than a metaphysical reduction of ethical or normative categories. At the same time, he develops a deeply attractive account of human freedom that inspired thinkers to come (including Nietzsche). Shaftesbury draws mostly from Cudworth, but in a way that gives rise to the moral sense tradition of Hutcheson, Hume, and Smith.

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.

This chapter reconstructs Heidegger’s 1955–56 interpretation of the principle of reason as a principle that resonates or sounds variously in the history of philosophy. The principle is first fully formulated by Leibniz as the principle of sufficient reason, which states that there is no true fact or proposition without sufficient reason for it being so and not otherwise. Heidegger takes Leibniz’s principle of sufficient reason to be a historically specific version of the principle of reason, which is a fundamental ontological principle holding that nothing is without a reason or ground, and so that being is ground/reason. Heidegger hears this association between being and ground resonating in the ancient Greek concept of logos, which is taken up but distorted by the Romans in the concept of ratio. From there, the ontological principle develops into the principle articulated by Leibniz and comes to express the distinctive commitments of modern philosophy and technology. While Heidegger’s historical story is not entirely plausible and contains significant omissions, attempting to reconstruct it reveals why this purported history of the principle of reason is relevant to Heidegger’s broader ontological project.

‘The Sea of Language’ is the first chapter of Volume 1 of a two-volume work entitled Quand Freud voit la mer: Freud et la langue allemande (When Freud Sees the Sea: Freud and the German Language). The author, as writer and translator, explores how the founding tenets of Freudian psychoanalysis are not concepts that happen to have been framed in German, but were derived from the way German parts of speech are rooted in the body and thus grounded in the German language itself, which is not a language of abstraction, as French admirers of German philosophy tend to believe, but of the body in space and in motion, a language of the common people going about their everyday life. The author’s study of the essence of German takes him from poetry to philosophy to the ‘ultimate perversity’: the language of the Third Reich, which he briefly envisages as a return of the repressed within the German language, possibly intuited by Freud. Through his analysis of German, he illustrates how the character of a language can lend itself to perverse manipulation and how individuals can find themselves rejected by the Mother tongue that had so far nurtured them.

Chapter 1 examines the relationship between Old and New Mechanism and uses it to illuminate the relations between metaphysical and methodological conceptions of mechanism. This historical examination will directly motivate our new deflationary account of mechanism developed in the subsequent chapters. We start by focusing on the role of mechanistic explanation in seventeenth-century scientific practice, by discussing the views of René Descartes, Christiaan Huygens, Gottfried Wilhelm Leibniz and Robert Boyle, and the attempted mechanical explanations of gravity by Descartes and Ηuygens. We thereby illustrate how the metaphysics of Old Mechanism constrained scientific explanation. We then turn our attention to Isaac Newton’s critique of mechanism. The key point is that Newton introduced a new methodology that freed scientific explanation from the metaphysical constraints of the older mechanical philosophy. Last, we draw analogies between Newton’s critique of Old Mechanism and our critique of New Mechanism. The main point is that causal explanation in the sciences is legitimate even if we bracket the issue of the metaphysics of mechanisms.

In 1713 Newton finally published the second edition of the Principia. Its changes included not only the new Rules of Philosophising discussed in III.1, but also the very famous General Scholium. This chapter provides the fullest ever contextualisation and interpretation of that text. It charts in detail how Newton’s dispute with Leibniz led him to double-down on his anti-metaphysical stance, and to declare many questions – not least concerning causation – to be beyond the boundaries of legitimate natural philosophy (now described as ‘experimental’). Second, it shows that Newton’s talk of the ‘God of Dominion’ was derived from Samuel Clarke’s recent writings – in line with Clarke’s position, Newton had now moved away from his earlier neo-Arianism into a position of trinitarian nescience in which all speculation on the subject, with consubstantialist or Arian, was dismissed as ‘metaphysical’. The role played by the ‘God of Dominion’ was simply the standard refrain of Newtonian natural theology: that the true conception of the divine that could be predicated from nature was not of an impersonal metaphysical first principle, but of a living God. Finally, Newton’s talk of God’s ‘substantial’ omnipresence was again not a concession to metaphysical thinking, but a residue of yet another polemic devised by his friend Samuel Clarke, this time against the freethinker Anthony Collins.

Chapter 7 returns to Kant for a deeper analysis of his views and their relation to the Euclidean mathematical tradition. Chapter 6 revealed that Euclid defined neither magnitude nor homogeneity, so that these notions are at best implicitly defined by the Euclidean-Eudoxian theory of proportions. Kant reworks the Euclidean theory of magnitudes, defining magnitude in terms of his own understanding of homogeneity, which admits of no qualitative difference of the manifold and which I call strict homogeneity. Most importantly, he thinks that intuition is required to represent either a continuous or a discrete manifold without qualitative difference. This role for intuition in Kant’s philosophy of mathematics and experience has not been appreciated, but finds support in various texts, especially Kant’s lectures on metaphysics and his criticisms of Leibniz’s views in the Amphiboly. Given Kant’s understanding of qualities, differences in dimension correspond to qualitative differences, so that Kant’s account corresponds to Euclid’s understanding of homogeneous magnitudes. Understanding the role of intuition allows us to appreciate the role of the categories of quantity and intuition in part–whole relations and the composition of magnitudes. The chapter closes with clarifying the sense in which intuition is required for the representation of magnitudes.

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 normalization of the elect acquired a corresponding theoretical framework. From the late seventeenth century the preferred explanation for physical growth had been ‘preformation’: the theory, starting with Swammerdam, that all living organisms have pre-existed from the Creation and are born as miniature versions which ‘unfold’ through predetermined stages. Leibniz suggested applying preformationism to the human mind. It was in this context that the word itself, ‘development’ (whose first appearances are better translated as ‘unfolding’), was first employed. The pioneering naturalist Charles Bonnet went on to apply the theory of preformationism to what he now expressly termed ‘psychology’. He identified psychology with the stages of regeneration in the elect (the so-called economy of grace); he linked this development of the person to the Enlightenment idea of ‘social progress’, and represented both as a gradual (rather than instantaneous) unfolding of biblical Revelation.

When influential philosophers prior to the Enlightenment such as Leibniz and Malebranche speculate about the interior life of ‘Man’ they presuppose the elect, saved man. This continues to be the case with Pierre Nicole and Jacques-Joseph Duguet, whose writings coincide with Jansenism’s turn towards a movement of political opposition to absolutism that ended up in Jacobinism. The shadows cast by predestination can still be detected even in Locke and Montesquieu, regarded as the founding figures of the Enlightenment. The theory of election would retain a subliminal presence in the history of the human sciences of the eighteenth century. So too would their increasing preoccupation with causality in psychological and social identity; out of the causes for election and reprobation came the imputation of causes for developmental normality and abnormality (‘idiocy’, ‘imbecility’ etc.) in the history of medicine.

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.

This concluding chapter revisits the four main themes of the book and ties them into important theories and ideas that emerged after 1750.