Kristina Engelhard

Metaphysics, traditionally conceived, has often been defined as the inquiry into what lies beyond or is independent of experience, but which nonetheless pertains to the fundamental structure of reality. Thus understood, metaphysics produces claims that are not empirically testable. The 20th century logical empiricists famously—and ferociously—criticised metaphysics on these grounds as being devoid of cognitive content. Despite logical empiricism’s seminal role in the genesis and propagation of the analytic tradition in academic philosophy, metaphysics has made a remarkable comeback during the second half of the 20th century. Contemporary analytic metaphysicians unabashedly refer to intuitions, conceptual analysis, and other genuinely philosophical, speculative methods in their search for insights into the fundamental nature of reality. Or so it seems.

The main thesis of this article is that in Christian Wolff’s Deutsche Metaphysik, empirical sources of knowledge play important if not foundational roles and that inductive methods of reasoning are extensively applied. It is argued that experiential self-awareness plays a foundational role and that empirical evidence, phenomena, and scientific theories from the empirical sciences of Wolff’s time are used for inferential purposes. Wolff also makes use of inductive reasoning, i.e., abduction to hidden causes of empirical phenomena, and inferences to the best or to the only possible explanation. Wolff’s Deutsche Metaphysik is therefore a prefiguration and an interesting case of inductive metaphysics in the contemporary sense. From this contemporary perspective, Wolff draws the distinction between valid and speculative abductions in a different way – but it is also different from that of his more empirically oriented contemporaries.

Kant's theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant's theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in Kant's theory of arithmetic can be picked up, improved by reconstruction and defended under a contemporary perspective: the theory of numbers as products of rule following construction presupposing successive synthesis in time and the theory of arithmetic equations, sentences or "formulas"—as Kant says—as synthetic a priori. In order to do so, two calculi in terms of modern mathematics are introduced which formalise Kant's theory of addition as a form of synthetic operation.

Immanuel Kant is among the most pivotal thinkers in the history of philosophy. His transcendental idealism claims to overcome the skepticism of David Hume, resolve the impasse between empiricism and rationalism, and establish the reality of human freedom and moral agency. A thorough understanding of Kant is indispensable to any philosopher today. The significance of Kant's thought is matched by its complexity. His revolutionary ideas are systematically interconnected and he presents them using a forbidding technical vocabulary. A careful investigation of the key concepts that structure Kant's work is essential to the comprehension of his philosophical project. This book provides an accessible introduction to Kant by explaining each of the key concepts of his philosophy. The book is organized into three parts, which correspond to the main areas of Kant's transcendental idealism: Theoretical Philosophy; Practical Philosophy; and, Aesthetics, Teleology, and Religion. Each chapter presents an overview of a particular topic, while the whole provides a clear and comprehensive account of Kant's philosophical system.