Chris Swoyer

In der vorliegenden Arbeit wird Leibniz' wahrscheinlich detailliertestes und ausgefeiltestes System untersucht: ein Kalkül der Einfügung und eine der Konjunktion ähnliche Operation, die er realis abjectio nennt. Das System soll hinreichend detailliert und mit hinreichender Präzision vorgestellt werden, um zu zeigen, daβ es ausgefeilt formal logisch ist und eine Anzahl originärer und wichtiger Züge aufweist. Neben seinem eigenständigen Interesse ist dieses System wichtig wegen seiner Auswirkungen auf andere Aspekte von Leibniz' Logik und Philosophie, und ein weiteres Ziel dieser Arbeit ist, einige dieser Verbindungen aufzuspüren

In this paper I present a formal language in which complex predicates stand for properties and relations, and assignments of denotations to complex predicates and assignments of extensions to the properties and relations they denote are both homomorphisms. This system affords a fresh perspective on several important philosophical topics, highlighting the algebraic features of properties and clarifying the sense in which properties can be represented by their extensions. It also suggests a natural modification of current logics of properties, one in which some complex predicates stand for properties while others do not

That laws of nature play a vital role in explanation, prediction, and inductive inference is far clearer than the nature of the laws themselves. My hope here is to shed some light on the nature of natural laws by developing and defending the view that they involve genuine relations between properties. Such a position is suggested by Plato, and more recent versions have been sketched by several writers.~ But I am not happy with any of these accounts, not so much because they lack detail or engender minor difficulties, though they do, but because they share a quite fundamental defect. My goal here is to make this defect clear and, more importantly, to present a rather different version of this general conception of laws that avoids it. I begin by considering several features of natural laws and argue that these are best explained by the view that laws involve properties, that this involvement takes the form of a genuine relation between properties, and, finally, that the relation is a metaphysically necessary one. In the second section I start at the other end, and by reflecting on the nature of properties arrive at a similar account of natural laws. In the final section I develop this account in more detail, with emphasis on the nature of the relation between properties it invokes. Along the way several natural objections to the account are answered.