This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

Joe Sachs has followed up his brilliant translation of Aristotle's Physics with a new translation of Metaphysics. Sachs's translations bring distinguished new light onto Aristotle's works, which are foundational to history of science. Sachs translates Aristotle with an authenticity that was lost when Aristotle was translated into Latin and abstract Latin words came to stand for concepts Aristotle expressed with phrases in everyday Greek language. When the works began being translated into English, those abstract Latin words or their cognates were (...) used, thus suggesting a level of jargon and abstraction, and in some cases misleading interpretation, which was not Aristotle's language or style. These important new translations open up Aristotle's original thought to readers. (shrink)

According to Peter van Inwagen, visible inanimate objects do not, strictly speaking, exist. In defending this controversial thesis, he offers fresh insights on such topics as personal identity, commonsense belief, existence over time, the phenomenon of vagueness, and the relation between metaphysics and ordinary language.

This book present a unified semantic theory of expressions involving the notions of part and whole. It develops a theory of part structures which differs from traditional (extensional) mereological theories in that the notion of an integrated whole plays a central role and in that the part structure of an entity is allowed to vary across different situations, perspectives, and dimensions. The book presents a great range of empirical generalizations involving plurals, mass nouns, adnominal and adverbial modifiers such as 'whole', (...) 'together', and 'alone', nominal and adverbial quanitfiers ranging over parts, and expressions of completion such as 'completely' and 'partly'. (shrink)

In this paper I wish to argue for a view that, despite its traditional standing, has not yet in any detail been defended. The view is briefly that in the Republic, at the point where Plato is engaged in contrasting the true philosopher with the “lover of sights and sounds”, he characterises sensible particulars — referred to as “the many” — as being bearers of opposite properties in so radical a manner that they can be said neither to be nor (...) not to be: they lie somewhere between being and utter non-being.There are two related reasons why this traditional view should now be closely scrutinised. The first is that, whatever the outcome, the passage of the Republic in question — 475a-480a — is quite crucial to our understanding of the development of Plato's thought about sensible particulars. The second’ is that it has been suggested recently, and ably argued, that Plato is not in fact talking about particulars at all; rather about types or sorts of particulars. (shrink)

This paper is a restatement of my earlier analysis of this argument (1954), Revised in the light of critical comments by other scholars and of closer study of the text. It includes a critical discussion of an alternative formalization of the argument, First offered by wilfrid sellars (1955) and retained (with modifications) by colin strang (1963), Which eliminates successfully the inconsistency of the premises of the argument but has dubious support from plato's text.

Plato was the first philosopher to discover the metaphysical phenomenon of plural-subjects and plural-predication; e.g. you and I are two, but neither you, nor I are two. I argue that Plato devised an ontology for plural-predication through his Theory of Forms, namely, plural-partaking in a Form. Furthermore, I argue that Plato used plural-partaking to offer an ontology of related individuals without reifying relations. My contention is that Plato’s theory of plural-relatives has evaded detection in the exegetical literature because his account (...) of plural-subjects through the Theory of Forms had not been recognised for what it is. I further submit that Plato’s handling of related individuals through plural-predication is not only a “first” in philosophy, but also an “only”, having remained a unique account in the metaphysics of relations. I hope that Plato’s account will introduce a fresh approach to contemporary debates on the subject. (shrink)

I argue that composition as identity is incompatible with the possibility of emergent properties (as characterized in the paper) and so should be rejected.

For the modern set theorist the empty set Ø, the singleton {a}, and the ordered pair 〈x, y〉 are at the beginning of the systematic, axiomatic development of set theory, both as a field of mathematics and as a unifying framework for ongoing mathematics. These notions are the simplest building locks in the abstract, generative conception of sets advanced by the initial axiomatization of Ernst Zermelo [1908a] and are quickly assimilated long before the complexities of Power Set, Replacement, and Choice (...) are broached in the formal elaboration of the ‘set of’f {} operation. So it is surprising that, while these notions are unproblematic today, they were once sources of considerable concern and confusion among leading pioneers of mathematical logic like Frege, Russell, Dedekind, and Peano. In the development of modern mathematical logic out of the turbulence of 19th century logic, the emergence of the empty set, the singleton, and the ordered pair as clear and elementary set-theoretic concepts serves as amotif that reflects and illuminates larger and more significant developments in mathematical logic: the shift from the intensional to the extensional viewpoint, the development of type distinctions, the logical vs. the iterative conception of set, and the emergence of various concepts and principles as distinctively set-theoretic rather than purely logical. Here there is a loose analogy with Tarski's recursive definition of truth for formal languages: The mathematical interest lies mainly in the procedure of recursion and the attendant formal semantics in model theory, whereas the philosophical interest lies mainly in the basis of the recursion, truth and meaning at the level of basic predication. Circling back to the beginning, we shall see how central the empty set, the singleton, and the ordered pair were, after all. (shrink)

What is the relation between a whole and its parts? The metaphysics of structure and composition is much discussed in modern philosophy; now Verity Harte provides the first sustained examination of Plato's rich but neglected discussion of the topic, and shows how it can illuminate current debates. This book is an invaluable resource both for scholars of Plato and for modern metaphysicians.

The problem of the source of necessity is the problem of explaining what makes necessary truths necessarily true. Simon Blackburn has presented a dilemma intended to show that any reductive, realist account of the source of necessity is bound to fail. Although Blackburn's dilemma faces serious problems, reflection on the form of explanations of necessities reveals that a revised dilemma succeeds in defeating any reductive account of the source of necessity. The lesson is that necessity is metaphysically primitive and irreducible.

The Peri ide^on is the only work in which Aristotle systematically sets out and criticizes arguments for the existence of Platonic forms. Gail Fine presents the first full-length treatment in English of this important but neglected work. She asks how, and how well, Aristotle understands Plato's theory of forms, and why and with what justification he favors an alternative metaphysical scheme. She examines the significance of the Peri ide^on for some central questions about Plato's theory of forms--whether, for example, there (...) are forms corresponding to every property or only to some, and if only to some, then to which ones; whether forms are universals, particulars or both; and whether they are meanings, properties or both. Fine also provides a general discussion of Plato's theory of forms, and of our evidence about the Peri ide^on and its date, scope, and aims. While she pays careful attention to the details of the text, she also relates it to contemporary philosophical concerns. The book will be valuable for anyone interested in metaphysics ancient or modern. (shrink)

The main lines of interpretation offered to date of the Third Man Argument in Plato's Parmenides (132a1-b2) are considered and rejected. A new, set-theoretic, reconstruction of the argument is offered. It is concluded that the philosophical point of the argument is different from what it has been generally supposed to be: Plato is pointing out the logical shortcomings in his earlier formulated principle of One-Over-Many.

Self-taught mathematician and father of Boolean algebra, George Boole (1815-1864) published An Investigation of the Laws of Thought in 1854. In this highly original investigation of the fundamental laws of human reasoning, a sequel to ideas he had explored in earlier writings, Boole uses the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities. Boole considers language not just as a mode of expression, but as a (...) system one can use to understand the human mind. In the first 12 chapters, he sets down the rules necessary to represent logic in this unique way. Then he analyses a variety of arguments and propositions of various writers from Aristotle to Spinoza. One of history's most insightful mathematicians, Boole is compelling reading for today's student of intellectual history and the science of the mind. (shrink)