First published in 1903, _Principles of Mathematics_ was Bertrand Russell’s first major work in print. It was this title which saw him begin his ascent towards eminence. In this groundbreaking and important work, Bertrand Russell argues that mathematics and logic are, in fact, identical and what is commonly called mathematics is simply later deductions from logical premises. Highly influential and engaging, this important work led to Russell’s dominance of analytical logic on western philosophy in the twentieth century.

We investigate a rst-order predicate logic based on Wittgenstein's suggestion to express identity of object by identity of sign, and difference of objects by difference of signs. Hintikka has shown that predicate logic can indeed be set up in such a way; we show that it can be done nicely. More specically, we provide a perspicuous cut-free sequent calculus, as well as a Hilbert-type calculus, for Wittgensteinian predicate logic and prove soundness and completeness theorems.

Is the assumption of a fundamental distinction between particulars and universals another unsupported dogma of metaphysics? F. P. Ramsey famously rejected the particular – universal distinction but neglected to consider the many different conceptions of the distinction that have been advanced. As a contribution to the piecemeal investigation of this issue three interrelated conceptions of the particular – universal distinction are examined: universals, by contrast to particulars, are unigrade; particulars are related to universals by an asymmetric tie of exemplification; universals (...) are incomplete whereas particulars are complete. It is argued that these conceptions are wanting in several respects. Sometimes they fail to mark a significant division amongst entities. Sometimes they make substantial demands upon the shape of reality; once these demands are understood aright it is no longer obvious that the distinction merits our acceptance. The case is made via a discussion of the possibility of multigrade universals. (shrink)

Possibility and reference have been central topics in metaphysics and the philosophy of language in the past decades. Wolfgang Freitag’s Form and Philosophy provides a novel approach to these notions and their interrelations, based on the concept of form as the key modal concept: form is the possibility space of objects. In its historic dimension, the book analyses the role of form in Ludwig Wittgenstein’s Tractatus Logico-Philosophicus and Immanuel Kant’s Critique of Pure Reason. In its systematic dimension, the book offers (...) an alternative ontological basis to David Armstrong’s combinatorial theory of possibility and rejects David Lewis’ analysis of possibility in terms of possible worlds. Representation is shown to rest on the idea of direct reference as proposed by David Kaplan and Saul Kripke. It is argued that the problem of reference links up with Wittgenstein’s rule-following problem, the nature of which is extensively discussed. It emerges that form and reference are complementary with respect to the notion of representation. Once their individual roles are seen, many metaphysical puzzles appear in a new light or disappear altogether. (shrink)

David Armstrong's book is a contribution to the philosophical discussion about possible worlds. Taking Wittgenstein's Tractatus as his point of departure, Professor Armstrong argues that nonactual possibilities and possible worlds are recombinations of actually existing elements, and as such are useful fictions. There is an extended criticism of the alternative-possible-worlds approach championed by the American philosopher David Lewis. This major work will be read with interest by a wide range of philosophers.