Ludwig Wittgenstein (1889-1951) was an extraordinarily original thinker, whose influence on twentieth-century thinking far outside the bounds of philosophy alone. In this engaging Introduction, A.C. Grayling makes Wittgenstein's thought accessible to the general reader by explaining the nature and impact of Wittgenstein's views. He describes both his early and later philosophy, the differences and connections between them, and gives a fresh assessment of Wittgenstein's continuing influence on contemporary thought.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

A little while ago I thought the ontological argument dead and buried beyond any possible hope of resurrection and no philosophical event has caused me much greater surprise than its revival by a member of the very linguistic school to whose line of thinking it seemed most alien and who were held to have given it its quietus once for all. I am tempted to welcome any relapse into metaphysics by a member of this school as being some sign of (...) grace, but on this issue I must for once take sides with the prevailing tradition against at least this kind of metaphysics. Let me make clear, however, what it is I am combating. The term ‘ontological argument’ has been used for arguments which its original supporters would certainly not have recognised as theirs. It has been used for instance to stand for the claim that it is an essential presupposition of thought that what we must think is true of the real, a claim which could not be used to prove the existence of God unless we had available another proof that we really must think that God exists. It has been used for kinds of ‘idealist’ arguments which I do not want to discuss here. It has been used for the argument that the idea of a perfect being cannot be explained as derived from any other idea and must therefore be explained as produced in us by a being who really is perfect, an argument which appears in Descartes side by side with the ontological argument but which he carefully distinguishes from it. (shrink)

This six volume backlist collection brings together an assortment of seminal works by highly influential British philosopher A. C. Ewing. This comprehensive and diverse collection encompasses a fantastic selection of his work in the field of moral philosophy and the history of philosophy; ranging from the definition of good, through to his views on punishment and a study on the work of Emmanuel Kant. Spanning more than 30 years in Professor Ewing’s distinguished career, the reissued volumes in this collection, originally (...) published between 1924 and 1959, offer a thorough and engaging insight into Professor Ewing’s work. (shrink)

Our best scientific theories explain a wide range of empirical phenomena, make accurate predictions, and are widely believed. Since many of these theories make ample use of mathematics, it is natural to see them as confirming its truth. Perhaps the use of mathematics in science even gives us reason to believe in the existence of abstract mathematical objects such as numbers and sets. These issues lie at the heart of the Indispensability Argument, to which this Element is devoted. The Element's (...) first half traces the evolution of the Indispensability Argument from its origins in Quine and Putnam's works, taking in naturalism, confirmational holism, Field's program, and the use of idealisations in science along the way. Its second half examines the explanatory version of the Indispensability Argument, and focuses on several more recent versions of easy-road and hard-road fictionalism respectively. (shrink)

Euclid’s Elements inspired a number of foundationalist accounts of mathematics, which dominated the epistemology of the discipline for many centuries in the West. Yet surprisingly little has been written by recent philosophers about this conception of mathematical knowledge. The great exception is Imre Lakatos, whose characterisation of the Euclidean Programme in the philosophy of mathematics counts as one of his central contributions. In this essay, we examine Lakatos’s account of the Euclidean Programme with a critical eye, and suggest an alternative (...) picture which builds on his work, but differs in a number of important respects. (shrink)

The revival of the philosophy of mathematics in the 60s following its post-1931 slump left us with two conflicting positions on arithmetic’s ontological relationship to set theory. W.V. Quine’s view, presented in 'Word and Object' (1960), was that numbers are sets. The opposing view was advanced in another milestone of twentieth-century philosophy of mathematics, Paul Benacerraf’s 'What Numbers Could Not Be' (1965): one of the things numbers could not be, it explained, was sets; the other thing numbers could not be, (...) even more dramatically, was objects. Curiously, although Benacerraf’s article appeared in the heyday of Quine’s influence, it declined to engage the Quinean position squarely, even seemed to think it was not its business to do so. Despite that, in my experience, most philosophers believe that Benacerraf’s article put paid to the reductionist view that numbers are sets (though perhaps not the view that numbers are objects). My chapter will attempt to overturn this orthodoxy. (shrink)

This short article discusses the fact that the word ‘ancestor’ features in certain arguments that a) are apparently logically valid, b) contain infinitely many premises, and c) are such that none of their finite sub-arguments are logically valid. The article's aim is to motivate, within its brief compass, the study of infinitary logics.

In the first and shorter part of this essay I comment on Wittgenstein's general influence on the practice of philosophy since his time. In the second and much longer part I discuss aspects of his work which have had a more particular influence, chiefly on debates about meaning and mind. The aspects in question are Wittgenstein's views about rule-following and private language. This second part is more technical than the first.

Bertrand Russell is one of the most famous and important philosophers of the twentieth century. In this account of his life and work A. C. Grayling introduces both his technical contributions to logic and philosophy, and his wide-ranging views on education, politics, war, and sexual morality.