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)

F. H. Bradley was the foremost philosopher of the British Idealist school, which came to prominence in the second half of the nineteenth century. Bradley, who was a life fellow of Merton College, Oxford, was influenced by Hegel, and also reacted against utilitarianism. He was recognised during his lifetime as one of the greatest intellectuals of his generation and was the first philosopher to receive the Order of Merit, in 1924. His work is considered to have been important to the (...) formation of analytic philosophy. In metaphysics, he rejected pluralism and realism, and believed that English philosophy needed to deal systematically with first principles. This work, first published in 1893, is divided into two parts: 'Appearance' deals with exposing the contradictions that Bradley believed are hidden in our everyday conceptions of the world; and in 'Reality', he builds his positive account of reality and considers possible objections to it. (shrink)

Do non‐symmetric relations apply to the objects they relate in an order? According to the standard view of relations, the difference between aRb and bRa obtaining, where R is non‐symmetric, corresponds to a difference in the order in which the non‐symmetric relation R applies to a and b. Recently Kit Fine has challenged the standard view in his important paper ‘Neutral Relations’ arguing that non‐symmetric relations are neutral, lacking direction or order. In this paper I argue that Fine cannot account (...) for the application of non‐symmetric relations to their relata; so far from being neutral, these relations are inherently directional. (shrink)

The full-text of this article is not currently available in ORA, but you may be able to access the article via the publisher copy link on this record page. N.B. Prof Williamson is now based at the Faculty of Philosophy, University of Oxford.

This paper first discusses how Russell and Hochberg have addressed some phenomena of relatedness, notably relational order, in a similarly ‘positionalist’ way, yet by appealing to different sorts of formal relations: “positions” in Russell's case and “ordering relations” in Hochberg's. After pointing out some shortcomings of both approaches, the paper then proposes an alternative view based on ‘o-roles’, which are, roughly speaking, ontological counterparts of the thematic roles postulated in linguistics. It is argued that o-roles are sort of middle-of-the-road entities (...) in the sense that they have the virtues of positions and those of ordering relations, without having their respective vices. Some tentative ideas on which o-roles should be acknowledged are also put forward. (shrink)

There are three different degrees to which we may allow a systematic theory of the world to embrace the idea of relatedness—supposing realism about non-symmetric relations as a background requirement. (First Degree) There are multiple ways in which a non-symmetric relation may apply to the things it relates—for the binary case, aRb ≠ bRa. (Second Degree) Every such relation has a distinct converse—for every R such that aRb there is another relation R* such that bR*a. (Third Degree) Each one of (...) them applies in an order to the things it relates—with regard to the state that results from R's applying to a and b, either R applies to a first and b second, or it applies to b first and a second. Whereas the first degree is near-indubitable, embracing the second or third generates unwholesome consequences. The second degree embodies a commitment to the existence of a superfluity of distinct converses and states to which such relations give rise. The third degree embodies commitment to recherché facts of the matter about how the states that arise from the application of one non-symmetric relation compare to any other. It is argued that accounts that purport to offer an analysis of the first degree generate unwelcome second or third degree consequences. This speaks in favour of our adopting an account of the application of relations that's not an analysis at all, an account that takes the first degree as primitive. (shrink)

Is there an explanation of why the state of x's bearing the non-symmetric binary relation R to y is different from its differential opposite, the state of y's bearing R to x? One traditional view has it that the explanation is that non-symmetric relations hold of objects in an essentially directional way, ordering the relevant relata. We call this view ‘directionalism’. Kit Fine has suggested that this approach is subject to significant metaphysical difficulties, sufficient to motivate seeking an alternative analysis. (...) He considers two such alternative explanations, which he labels ‘positionalism’ and ‘anti-positionalism’. Of these he endorses the latter. We argue that anti-positionalism fails to provide a coherent explanation of the distinction between differential opposites, and that one should simply hold the minimalist position that there is no explanation for this metaphysical difference. (shrink)

There is a standard view of relations, held by philosophers and logicians alike, according to which we may meaningfully talk of a relation holding of several objects in a given order. Thus it is supposed that we may meaningfully—indeed, correctly—talk of the relation loves holding of Anthony and Cleopatra or of the relation between holding of New York, Washington, and Boston. But innocuous as this view might appear to be, it cannot be accepted as applying to all relations whatever. For (...) there is an important class of metaphysical and linguistic contexts which call for an alternative conception of relation, one for which the order of the relata plays no role and in which the application of the relation to its relata is achieved by other means. (shrink)

Applying the rules and systems of mathematics and logic to instance ontology, this work argues for the validity and problem-solving capacities of instance ontology, and associates it with a version of the realist position which is named by the author as moderate realism.

Collection of articles on medieval logic and semantics. Introduction by Sten Ebbesen and 24 contributions by scholars in the history of medieval theories of language. The papers in this volume treat several aspects of the history of theories of language from the 12th to the 14th century, aspects that have in a way or another been dealt with by Ebbesen himself.Festschrift in honor of Sten Ebessen in the occasion of his 65th birthday.

First published in 1984 as part of The Collected Papers of Bertrand Russell , Theory of Knowledge represents an important addition to our knowledge of Russell's thought. In this work Russell attempts to flesh out the sketch implicit in The Problems of Philosophy . It was conceived by Russell as his next major project after Principia Mathematica and was intended to provide the epistemological foundations for his work. Russell's subsequent difficulties in presenting his theory of knowledge, brought on by what (...) he considered to be devastating criticisms of Wittgenstein, led to both his abandonment of this work and to a major transformation in his thought. Theory of Knowledge , now available for the first time in paperback, gives us a picture of one of the great minds of the twentieth century at work. It is possible to see the unsolved problems left without disguise or evasion. This second edition has retained the full scholarly introduction. The photographs of the manuscript, appendices, and notes on textual matters have been eliminated to provide a concise and accessible guide to understanding both Russell's own thought and his relationship with Wittgenstein. (shrink)

Scholars have known that a variety of medieval theories on relation existed, but no full-length systematic study has been attempted until now. With this book Henninger fills an important gap in our knowledge of medieval philosophy. Dealing with such varied thinkers as Aquinas, Henry of Ghent, Richard of Mediavilla, John Duns Scotus, Henry of Harclay, William of Ockham, and Peter Aureoli, the book will interest anyone concerned with late medieval philosophy and the transition to the early modern period.