In this important study D. M. Armstrong offers a comprehensive system of analytical metaphysics that synthesises but also develops his thinking over the last twenty years. Armstrong's analysis, which acknowledges the 'logical atomism' of Russell and Wittgenstein, makes facts the fundamental constituents of the world, examining properties, relations, numbers, classes, possibility and necessity, dispositions, causes and laws. All these, it is argued, find their place and can be understood inside a scheme of states of affairs. This is a comprehensive and (...) rigorously this-worldly account of the most general features of reality, argued from a distinctive philosophical perspective, and it will appeal to a wide readership in analytical philosophy. (shrink)

Lewis has objected to Armstrong's notion of a structural universal on the grounds that it violates the Principle of Uniqueness of Composition (PUC), which says that given some parts, there is only one whole that they compose. This paper reviews Armstrong's case for structural universals, and then attempts to reconcile structural universals with PUC by arguing for the existence of arrangement universals. The latter are not only a key to defending structural universals against Lewis' objection, but are in fact essential (...) to Armstrong's conception of structural universals in general. Three objections to my proposal are deflected, and two alternative proposals are shown to be inferior to it. (shrink)

In this important study D. M. Armstrong offers a comprehensive system of analytical metaphysics that synthesises but also develops his thinking over the last twenty years. Armstrong's analysis, which acknowledges the 'logical atomism' of Russell and Wittgenstein, makes facts the fundamental constituents of the world, examining properties, relations, numbers, classes, possibility and necessity, dispositions, causes and laws. All these, it is argued, find their place and can be understood inside a scheme of states of affairs. This is a comprehensive and (...) rigorously this-worldly account of the most general features of reality, argued from a distinctive philosophical perspective, and it will appeal to a wide readership in analytical philosophy. (shrink)

Although the relationship of part to whole is one of the most fundamental there is, this is the first full-length study of this key concept. Showing that mereology, or the formal theory of part and whole, is essential to ontology, Simons surveys and critiques previous theories--especially the standard extensional view--and proposes a new account that encompasses both temporal and modal considerations. Simons's revised theory not only allows him to offer fresh solutions to long-standing problems, but also has far-reaching consequences for (...) our understanding of a host of classical philosophical concepts. (shrink)

The aim of this paper is to introduce a new approach to the modal operators of necessity and possibility. This approach is based on the existence of two negations in certain lattices that we call bi-Heyting algebras. Modal operators are obtained by iterating certain combinations of these negations and going to the limit. Examples of these operators are given by means of graphs.

I will consider Armstrong's problems in trying to account for structural universals, i.e., a kind of complex universal whose instantiation by particulars involves different parts of those particulars instantiating several basic properties and relations, such as the property of being a molecule of methane. I present and criticise Armstrong's most recent attempt to explain structural properties by means of the identification of universals with types of states of affairs and I state my own solution to the problem by appealing to (...) formal relations holding between particulars. (shrink)

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is (...) of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures. (shrink)

David Lewis famously argued against structural universals since they allegedly required what he called a composition “sui generis” that differed from standard mereological com¬position. In this paper it is shown that, although traditional Boolean mereology does not describe parthood and composition in its full generality, a better and more comprehensive theory is provided by the foundational theory of categories. In this category-theoretical framework a theory of structural universals can be formulated that overcomes the conceptual difficulties that Lewis and his followers (...) regarded as unsurmountable. As a concrete example of structural universals groups are considered in some detail. (shrink)

Lewis has objected to Armstrong's notion of a structural universal on the grounds that it violates the Principle of Uniqueness of Composition, which says that given some parts, there is only one whole that they compose. This paper reviews Armstrong's case for structural universals, and then attempts to reconcile structural universals with PUC by arguing for the existence of arrangement universals. The latter are not only a key to defending structural universals against Lewis' objection, but are in fact essential to (...) Armstrong's conception of structural universals in general. Three objections to my proposal are deflected, and two alternative proposals are shown to be inferior to it. (shrink)