Online research in philosophy

The paper analyses the significance of the modern concept of „symmetry“ for the understanding of the concept of „intuition“ in Kant's philosophy of geometry. A symmetry transformation or automorphism is a structure preserving mapping of the space into itself that leaves all relevant structure intact so that the result is always like the original, in all relevant respects. Hermann Weyl was the first to show that this idea can be drawn on Leibniz's definition of similarity: two figures are similar if they are only distinguishable through the simultaneous perception of them ( comperceptio ): „an automorphism carries a figure into one that in Leibniz's words is ‚indiscernible from it if each of the two figures is considered by itself‘“. The author argues that, under the light of this definition, Leibniz's notion of „comperceptio“ turns out to play a similar role for the notion of „intuition“ in Kant's philosophy of space and time. Both cases are about the „difference between conceptual definition and intuitive exhibition“, as Weyl puts it. This result has on the one hand an exegetical significance: it frees Kant's notion of „intuition“ from every vague reference to the „visualisation“ of geometrical figures; on the other hand a theoretical one: it makes easy to compare Kant's philosophy of space and time with modern developments of sciences, in which as Weyl first showed, the concept of symmetry plays a fundamental role.

That Leibniz finds the philosophy of Spinoza horrifyingly wrong is obvious to anyone who reads Leibniz’s work; that Leibniz finds Spinozism so seductive that his own system is in danger of collapsing into it is less obvious but, I believe, equally true. The difference here is not so much between an exoteric and an esoteric philosophy suggested by Russell2 but between a thorough-going rationalism on the part of Spinoza and Leibniz’s “mitigated rationalism” – mitigated by the exigencies of his orthodox Christianity. In other words, it is Leibniz’s traditional view of the nature of God and his creatures that leads him to abhor Spinoza’s vision, while his own commitment to a number of principles and ideas pushes him to rationalism. And if Kant is right that the mind naturally desires a system, then Leibniz ought to see the Spinozistic consequences of many of his philosophical principles. Of course, there is nothing new in saying that the God of Spinoza and the God of Leibniz are fundamentally different, but I believe that if we focus on Leibniz’s critique of Spinoza’s account of the nature of God and a constellation of related concepts, we can come to a deeper understanding of the thought of both philosophers.

In his lectures, Kant suggested to his students that the freedom of a divine holy will is “easier to comprehend than that of the human will,”(28:609) but this suggestion has remained neglected. After a review of some of Kant’s familiar claims about the will (in general), and about the divine holy will in particular, I consider how these claims give rise to some initial objections to that conception. Then I defend an interpretation of Kant’s conception of the divine will, and of its historical development in relation to Leibniz and Spinoza, that identifies the content, origin, and role of God’s representations in a way that is responsive to some of the historical and contemporary problems. Finally, I trace a few of the implications of this account of the divine will for our understanding Kant’s account of freedom more generally, including human freedom.

Leibniz's predicate-in-notion principle and some of its alleged consequences, by C. D. Broad.--On Leibniz's metaphysics, by L. Couturat.--Philosophical reflections of Leibniz on law, politics, and the state, by C. J. Friedrich.--The root of contingency, by E. M. Curley.--Monadology, by M. Furth.--Individual substance, by I. Hacking.--Leibniz on plenitude, relations, and the "reign of the law," by J. Hintikka.--Leibniz's theory of the ideality of relations, by H. Ishiguro.--Leibniz and Spinoza on activity, by M. Kneale.--Leibniz and Newton, by A. Koyré.--Plenitude and sufficient reason in Leibniz and Spinoza, by A. O. Lovejoy.--Leibniz on possible worlds, by B. Mates.--Recent work on the philosophy of Leibniz, by B. Russell.--On Leibniz's explication of "necessary truth," by M. D. Wilson.--Bibliography (p. [421]-425).

Broad, C. D. Leibniz's predicate-in-notion principle and some of its alleged consequences.--Couturat, L. On Leibniz's metaphysics.--Friedrich, C. J. Philosophical reflections of Leibniz on law, politics, and the state.--Curley, E. M. The root of contingency. Furth, M. Monadology.--Hacking, I. Individual substance.--Hintikka, J. Leibniz on plenitude, relations, and the "reign of law."--Ishiguro, H. Leibniz's theory of the ideality of relations.--Kneale, M. Leibniz and Spinoza on activity.--Koyré, A. Leibniz and Newton.--Lovejoy, A. O. Plenitude and sufficient reason in Leibniz and Spinoza.--Mates, B. Leibniz on possible worlds.--Russell, B. Recent work on the philosophy of Leibniz.--Wilson, M. D. On Leibniz's explication of "necessary truth.".

In his early lecture note Versuch einiger Betrachtungen über den Optimismus (1759) a young supporter of metaphysical optimism called Immanuel Kant tested the Leibnizian optimism by posing some counter-arguments against it only to falsify them. His counter-arguments were very inventive and they feature often in modern scholarship on Leibniz. In this paper I will present Kant’s main arguments and evaluate them. I will argue that Kant’s understanding on Leibnizian optimism is little misguided and for this reason his own positive counter-argument despite its ingeniousness is problematic. His second solution to the problem is comparable to the doctrine of metaphysical optimism, but fails also for the same reason as the first one.

In this paper, the author examines Leibniz inconsistent treatments of the existence predicate in his formulations of the ontological argument and elsewhere. It is shown that, contrary to expectations, Leibniz at times adumbrates insights often attributed to Kant and Frege.

This paper compares Kant’s and Leibniz’s views on the relation between knowing subjects and known objects. Kant discusses Leibniz’s philosophy in the ‘Amphiboly’ section of the first Critique. According to Kant, Leibniz’s main error is mistaking objects in space and time for mind-independent things in themselves, that is, for monads. The paper argues that, pace Kant, Leibniz regards objects in space and time as mind-dependent. A deeper divergence between the two philosophers concerns knowing subjects. For Leibniz, they are substances. For Kant, we cannot know whether they are substances. Kant conceives of knowing subjects as complex systems of cognitive capacities.

Kant’s avowed commitment to the basic principles of Leibniz’s metaphysics is evident throughout the critical project and stated explicitly in the Prize Essay. However, it is not until the Critique of Judgment, wherein Kant recognizes that Judgment operating in its reflective mood can engender synthetic a priori claims, that Kant is fully capable of appropriating the basic tenets of Leibniz’s metaphysics. This paper examines Kant’s treatment of Leibniz from the perspective of the Critique of Judgment. It is argued that from this vantage point the metaphysics of Leibniz is viewed as fundamental for Kant’s critical project. Moreover, it is argued that it is not until the retrieval of Leibniz’s metaphysics that Kant has a basis for seeking the unity of pure and practical reason.