Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

A picture of the world as chiefly one of discrete objects, distributed in space and time, has sometimes seemed compelling. It is however one of the main targets of Henry Laycock's book; for it is seriously incomplete. The picture, he argues, leaves no space for "stuff" like air and water. With discrete objects, we may always ask "how many?," but with stuff the question has to be "how much?" Laycock's fascinating exploration also addresses key logical and linguistic questions about the (...) way we categorize the many and the much. (shrink)

The remainder of thi8 work will have a different object from that of the four preceding books, which were contained in the first volume. ...

This collection of nine papers brings together Many of Geach's thoughts on such wide topics as resurrection, deductive proof of the existence of God, God's role in ethics, materialism, and the relation of time and prayer. The first three papers are concerned with the survival of death and what form such a survival might take. This includes Geach's argument against materialism in "What Do We Think With?" Two further papers are concerned with arguments about existence, and the remaining papers concern (...) natural theology. (shrink)

Peter Geach and others suppose that change in an object's relational properties absent any change in its intrinsic properties is not a genuine change in that object but only a “mere Cambridge change.” I explain and reject two strategies challenging Geach's position. I then present my own argument against Geach which depends on the recognition of entities identified in terms of their emergent properties, i.e. properties not reducible to physical properties. I provide some examples of such entities and address the (...) problem of finding a criterion for distinguishing genuine from nonge‐nuine change. (shrink)

I EXISTENTIAL PROOFS INTRODUCTION Metaphysical problems, like all philosophical problems, arise from a sense of puzzlement. What is puzzling is that the ...

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.