The discipline of mathematics has not been spared the sweeping critique of postmodernism. Is mathematical theory true for all time, or are mathematical constructs in fact fallible? This fascinating book examines the tensions that have arisen between modern and postmodern views of mathematics, explores alternative theories of mathematical truth, explains why the issues are important, and shows how a Christian perspective makes a difference. Contributors: W. James Bradley William Dembski Russell W. Howell Calvin Jongsma David Klanderman Christopher Menzel (...) Glen VanBrummelen Scott VanderStoep Michael Veatch Paul Zwier. (shrink)

The current revival of interest in Bradley has included a long-neglected aspect of his thought, namely his philosophy of history. There has been a new edition of The Presuppositions of Critical History with an introduction by Stock, a new essay by Rubinoff, and a recent number of Bradley Studies largely devoted to The Presuppositions of Critical History. All of these essays and articles related Bradley’s work to Collingwood’s, which has been the subject of an even bigger revival. (...) Holdcroft made the point that, though The Presuppositions often contains “embryonic versions of positions he developed in greater detail later”, he did not return to the subject of history ; this is, of course, true of his major works, and history ceased to be a major interest for him. However, on one occasion he was drawn back into the field. The occasion was one of the spats that he had with Bertrand Russell, who had taken over from Pragmatism as Bradley’s main concern, if three articles in Mind in 1909 and 1910 and new pieces prepared for publication in 1914 are anything to go by. These were reprinted or published for the first time as part of Essays on Truth and Reality. One of the new pieces, published as Chapter XIV, was entitled “What is the real Julius Caesar?”. He was responding to an article in Proceedings of the Aristotelian Society, xi, “Knowledge by Acquaintance and Knowledge by Description.”. (shrink)

The fact of russell's changes of mind over the identity of indiscernibles is not in dispute, but what was his final view? several recent writers have portrayed the late russell as not regarding the identity of indiscernibles as necessary, or at any rate as being indecisive or restrictive about its necessity. the present paper argues that such readings of russell are untenable.

F. H. Bradley (1846-1924) was considered in his day to be the greatest British philosopher since Hume. For modern philosophers he continues to be an important and influential figure. However, the opposition to metaphysical thinking throughout most of the twentieth century has somewhat eclipsed his important place in the history of British thought. Consequently, although there is renewed interest in his ideas and role in the development of Western philosophy, his writings are often hard to find. This collection unites (...) all of his published works, much of which has long been out of print, together with selected notebooks, articles, and correspondence from his previously unpublished remains. The set therefore provides the opportunity to view his entire philosophy, both in the breadth of its scope - from critical history and ethics through logic to metaphysics and epistemology - and in its historical development - from the earliest Hegelian writings to the later more psychological and pragmatic work. In addition the set features introductions to Bradley's writings, life and character, providing the framework to assess his permanent importance in the history of philosophy. --the first ever publication of all Bradley's works --includes 5 volumes of reset material, mostly never before published --a collecton that all serious philosophy libraries should have --extremely comprehensive new editorial matter --volumes 4 & 5 are indexed by subject and name --collects Bradley's correspondence, spanning 50 years, with Russell, Samuel Alexander, Bosanquet, Haldane, William James, Andrew Seth Pringle-Pattison, and many others --includes Bradley's notes on Green's lectures on ethics, selected undergraduate essays, notebooks preparatory of his major works, lists of what Bradley read, essays that never reached publication, inventory of Bradley's papers, and a catalogue of Bradley's personal library. (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 and remained influential into the first half of the twentieth. Bradley, who was educated at Oxford, and spent his life as a fellow of Merton College, 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. This collection of some of Bradley's most important journal articles was first published in 1914. He examines coherence and identity theories of truth, and discusses pragmatism and radical empiricism. The book contains extensive discussion of the work of Bertrand Russell and William James, while other essays cover a range of different subjects such as faith, memory, error and God. (shrink)

Collections demand great care. In any attempt to select, sift, and/or package the literary efforts of a major literary figure, whatever is included will be debated and found wanting. For example, what short stories of Ernest Hemingway or sonnets of William Shakespeare or pithy comments of Winston Churchill would make up a selected collection? The choices and possibilities are numerous, and the possible repercussions mind bending. Arguments are sure to ensue, and even like-minded advocates will fiercely debate the inclusion or (...) exclusion of a specific work.Renowned French mathematician Jules Henri Poincare mused to colleague Lord Bertrand Russell that “Science is built up with facts, as a house is with stones. But a... (shrink)

Using ideas proposed in Aboutness and developed in ‘If-thenism’, Stephen Yablo has tried to improve on classical if-thenism in mathematics, a view initially put forward by Bertrand Russell in his Principles of Mathematics. Yablo’s stated goal is to provide a reading of a sentence like ‘The number of planets is eight’ with a sort of content on which it fails to imply ‘Numbers exist’. After presenting Yablo’s framework, our paper raises a problem with his view that has gone virtually (...) unnoticed in the literature. If we are right, then Yablo’s version of if-thenism cannot succeed. (shrink)

In Process and Reality (1929) and subsequent writings, A.N. Whitehead builds on the success of the Frege-Russell generalization of the mathematical function and develops his philosophy on that basis. He holds that the proper generalization of the meaning of the function shows that it is primarily to be defined in terms of many-to-one mapping activity, which he terms 'creativity'. This allows him to generalize the range of the function, so that it constitutes a universal ontology of construction or 'process'. (...) He analyzes the concept of God in terms of functional mapping to structure, and he defines finite entities as iterative 'occasions' of mapping activity. He thus challenges the widespread logical-analytical view that the connectives and variables of a function in its different instantiations are merely numerically different, and he develops a fallibilist theory of activity as essentially serial in nature. (shrink)

Mathematics from a Christian perspective With respect for the history and ever-changing applications of mathematical principles, James Bradley and Russell Howell, along with a team of fellow scholars, invite readers to consider the rich intersection of mathematics and Christian belief. Citizens of the twenty-first century generally believe that mathematics is all about numbers and formulas, with no religious significance— an attitude that belies the faith-based work of thinkers from Plato to Newton. It is time to reawaken our sensitivity (...) to the vital spiritual matters raised by the study of mathematics, a discipline that demands profound thought and helps us understand the beauty and the order of our physical world. Mathematics Through the Eyes of Faith explores questions such as: What is the relationship between chance and divine providence? Do concepts like infinity point beyond themselves to a higher reality? Is mathematics discovered or invented, and why is it effective in the sciences? This comprehensive work, one in a series of cosponsored by the Council for Christian Colleges & Universities, is designed to help students and teachers understand how mathematics has evolved and how the interplay of mathematics and Christian belief can enrich the study of both. (shrink)

The Liar Paradox is an argument that arrives at a contradiction by reasoning about a Liar Sentence. The classical Liar Sentence is the self-referential sentence “This sentence is false.”.

1. The Down Under Logical Disproof of the Theist's God 1.1 Plantinga's Attempted Refutation of the Logical Disproof 1.2 Plantinga Refuted and God Disproved: A Preview 2. Plantinga's Formal Presentation of his Free Will Defense 3. First Formal Flaw: A Non Sequitur Regarding the Consistency of (3) with (1) 4. Further Flaws Regarding the Joint Conditions of Consistency and Entailment 4.1 A Non Sequitur Regarding the Entailment Condition 4.2 Telling the Full Story in Order to Satisfy the Entailment Condition 4.3 (...) Two Non Sequiturs Involving the Consistency Condition 4.4 The Russell Scenario: A Refutation by Logical Analogy 5. Plantinga's Leibnizian Definition of Omnipotence 5.1 Logical Consequences of the Definition 5.2 Why Leibniz Didn't Lapse 5.3 A Fatal Equivocation Over the Scope of Transworld Depravity 5.4 It Was All "Up to God" 5.5 The Distinction Between Absolute and Consequential Modalities 5.6 Plantinga's Ploy 5.7 Plantinga's Modal Muddle 5.8 Interlude on the Prevalence of the Modal Muddle 5.9 Back to Plantinga's Modal Muddle 5.10 Interim Verdict 6. Judgment Day: God Almighty and All Knowing Not Morally Perfect.. (shrink)

In this article I describe the contributions made by Samuel Alexander to the issue of relations which so vexed Bertrand Russell and F. H. Bradley in the late nineteenth and early twentieth centuries. I provide a novel understanding of Alexander’s position concerning relations and describe the way in which he viewed his position as superior to those of Bradley and Russell. I offer, therefore, a more complete picture of a philosophical debate central to the relevant period, (...) through the introduction of a third character whose views have been largely omitted from available narratives. (shrink)

In writings prior to the publication of The Principles of Mathematics (PoM), Russell denies that relations “in the abstract” ever relate and holds instead that only particularized relations, or relational tropes, do so; however, in PoM section 55, he argues against his former view and adopts the view that relations “in the abstract” are capable of a “twofold use” – either as “relations in themselves” or as “actually relating”. I argue that while Russell rightly came to recognize that (...) rejecting his earlier view is necessary for avoiding the Bradleyan view that complex wholes are unanalyzable, his later view can appear as an ad hoc means of avoiding Bradley's argument against “relational thought”. (shrink)

In the early twentieth century an apparently obscure philosophical debate took place between F. H. Bradley and Bertrand Russell. The historical outcome was momentous: the demise of the movement known as British Idealism, and its eventual replacement by the various forms of analytic philosophy. Since then, a conception of this debate and its rights and wrongs has become entrenched in English-language philosophy. Stewart Candlish examines afresh the events of this formative period in twentieth-century thought and comes to some (...) surprising conclusions. (shrink)

In this paper, I will give a presentation of Bradley's two main arguments against the reality of relations. Whereas one of his arguments is highly specific to Bradley's metaphysical background, his famous regress argument seems to pose a serious threat not only for ontological pluralism, but especially for states of affairs as an ontological category. Amongst the proponents of states-of-affairs ontologies two groups can be distinguished: One group holds states of affairs to be complexes consisting of their particular (...) and universal constituents alone, the other holds that there has to be a "unifying relation" of some sort to establish the unity of a given state of affairs. Bradley's regress is often conceived to be a compelling argument against the first and for the latter. I will argue that the latter approaches have no real advantage over the simpler theories—neither in the light of Bradley's regress nor in other respects. (shrink)

A coherent theory of relations was a critical part of Russell’s metaphysics. In Appearance and Reality Bradley posed a problem that sits squarely in the way of any doctrine of “external” relations. Russell, determined to advance such a doctrine, tried several times to find a way around the paradox and apparently believed he had succeeded by making use of one of his inventions, the theory of logical types.Gilbert Ryle and Alan Donagan have advanced an argument that I (...) read, over the objections of its authors, as a special case of Bradley’s. In this paper I argue that the ad hoc solution suggested by Donagan to the special problem is one that Russell had already indicated a willingness to accept but that the general problem of the paradox remains.What finally prevents Russell from solving the paradox is a combination of his refusal to abandon the claim that relations are constituents of facts and the necessity of distinguishing a relational fact from its converse. Following some hints that Russell left, I do some reconstruction, showing how the theory of types would (and should) have been applied had Russell followed through on his own insights. The result, I suggest, is a truly Russellian theory that escapes Bradley’s paradox. (shrink)

The present paper is an extract from a thesis concerning the debate between bradley and russell on the nature of relations. it concerns only the most general points of interaction - the positive influence of bradley upon russell with respect to psychologism, logic, and constructions; the negative influence: russell's work seen as a reaction to bradley. the intention is to show that bradley was an extremely strong influence in russell's development hardly worthy (...) of the disregard which russell showed him. (shrink)

According to Stewart Candlish, Russell and Moore had misunderstood F. H. Bradley’s monism. According to Jonathan Schaffer, they had misunderstood monism more generally. A key thread of the creation narrative of analytic philosophy, according to which Russell and Moore successfully undermined monism to give rise to a new movement is, therefore, in doubt. In this paper, I defend the standard narrative against those who seek to revise it.

In this article I examine the dispute between F. H. Bradley and Bertrand Russell concerning the reality of relations. I show that Bradley’s objections to Russell’s view, that there are such things as relations which serve to effect the unity of complex items, were rooted in a methodological approach which Russell did not share. On Bradley’s view, one must be able to offer reductive analyses of the items one postulates in order that commitment to (...) those items be justified. I argue that Russell expressly rejected this methodological principle of Bradley’s, and instead adopted the view that one may justifiably postulate entities if doing so aids in the illumination of mathematical truths. I show that the postulation of relations does, on Russell’s view, serve to provide that illumination. Russell held that the truths of mathematics constitute fixed data, and that philosophical positions may be judged as successful according to the extent that they possess explanatory power with respect to this data. I argue that Bradley’s and Russell’s exchanges in print, as well as in private correspondence, reflect Russell’s awareness of a fundamental difference in methodological approach. I conclude that Russell elected not to answer Bradley’s objections on their own terms, but rather rejected the methodological assumptions from which those objections emerged. (shrink)

While considerable ink has been spilt over the rejection of idealism by Bertrand Russell and G.E. Moore at the end of the 19th Century, relatively little attention has been directed at Russell’s A Critical Exposition of the Philosophy of Leibniz, a work written in the early stages of Russell’s philosophical struggles with the metaphysics of Bradley, Bosanquet, and others. Though a sustained investigation of that work would be one of considerable scope, here I reconstruct and develop (...) a two-pronged argument from the Philosophy of Leibniz that Russell fancied—as late as 1907—to be the downfall of the traditional category of substance. Here, I suggest, one can begin to see Russell’s own reasons—arguments largely independent of Moore—for the abandonment of idealism. Leibniz, no less than Bradley, adhered to an antiquated variety of logic: what Russell refers to as the subject-predicate doctrine of logic. Uniting this doctrine with a metaphysical principle of independence—that a substance is prior to and distinct from its properties—Russell is able to demonstrate that neither a substance pluralism nor a substance monism can be consistently maintained. As a result, Russell alleges that the metaphysics of both Leibniz and Bradley has been undermined as ultimately incoherent. Russell’s remedy for this incoherence is the postulation of a bundle theory of substance, such that the category of “substance” reduces to the most basic entities—properties. (shrink)

In this article, the Author analyses the Bradleian concept of contradiction and the thesis herewith proposed consists in thinking that the so-called «Russell’s antinomy», one of the most popular and most discussed theoretical points in the modern and contemporary philosophy, is rooted or better is implied in Bradley’s system. The Author argues that, formulating and presenting it at Frege, Russell articulated a question opening a consequent philosophic perspective already conceptually implied by Bradley’s theory of relations.

The type-free property-theoretic system EC, based on the mediation view of predication, is presented. According to the mediation view, the copula or exemplification is a necessary component of every proposition. It is explained how the system EC relates to Bradley's Regress regarding predication. Finally, the system EC is applied to the Meinong-Russell debate on non-existent objects and it is shown how EC allows us to preserve some important intuitions of both Meinong and Russell.

Dans l'Appendice au livre I de The World and the Individual (1898), le philosophe américain Josiah Royce développe, en se fondant sur Was sind und was sollen die Zahlen ? de Dedekind, une critique détaillée du livre de Bradley Appearance and Reality. Se concentrant sur le fameux § 66, Royce maintient que la théorie de Dedekind peut être vue comme l'accomplissement du mouvement de pensée inauguré par Fichte et Hegel : le 'Soi idéal ' est infini et l'arithmétique est (...) la théorie de sa structure formelle. Cet article analyse le contenu de ce texte, en le mettant en relation avec la pensée de Russell et de Lotze. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:January 28, 2009 (12:22 pm) G:\WPData\TYPE2802\russell 28,2 051red.wpd russell: the Journal of Bertrand Russell Studies n.s. 28 (winter 2008–09): 171–90 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631; online 1913-8032 eviews A RELATIONAL DISPUTE Sébastien Gandon iufz/zphier / U. Blaise Pascal 63000 Clermont-Ferrand, France [email protected] Stewart Candlish. The Russell/Bradley Dispute and Its SigniWcance for TwentiethCentury Philosophy. Basingstoke and New York: Palgrave Macmillan, (...) 2007. Pp. xix, 235. isbn 978-0-230-50685-5. £49.99; us$84.95 (hb). Candlish’s book aims at giving a “fair” description of the notorious Russell/ Bradley dispute, that is, a more balanced one than the version that is usually told. The standard account is the one given by Russell, and, as Russell was a party of the debate, it is no surprise that he seriously misconstrued Bradley’s arguments. Attempting to set the historical record straight, Candlish then opposes Russell’s description of the dispute. The author is quite clear, however, on the fact that he does not himself endorse the Idealistic point of view (p. xi). The two Wrst chapters of the book are introductory: the Wrst one is a presentation of the stereotypical picture that the author intends to demolish, while the second is an outline of Bradley’s metaphysics. Chapters 3 and 4 are devoted to a confrontation between Russell and Bradley’s theories of judgment and truth. Chapters 5 and 6 are dedicated to a rehabilitation of Bradley’s writings about relation. In these four chapters, Candlish attempts to show that Russell’s arguments against Bradley were not as devastating as they are supposed to be, and that Bradley’s insights were quite powerful—so much so that they have been rediscovered by some later philosophers, such as Wittgenstein, for instance. The concluding chapter is an attempt to explain the decline of monistic idealism after Bradley. Candlish does not only aim at oTering a “fair” account of the Russell/Bradley dispute. This goal is extended by a more general plea for the introduction of an historical perspective in analytic philosophy. According to Candlish, “our implicit acceptance of a distorted version of philosophy’s recent past has serious consequences ” (p. 19): one of them is that, by misunderstanding our own history, we “misunderstand ourselves and the nature of what we are about” (ibid.); another is that, by being deprived of any way to connect what we do in philosophy January 28, 2009 (12:22 pm) G:\WPData\TYPE2802\russell 28,2 051red.wpd 172 Reviews with what some of the philosophers of the past have done, “we may, as a result, fall under the impression that only we, and those obviously like us, are really doing philosophy, at least as it ought to be done” (ibid.). From this perspective, Russell’s confrontation with Bradley seems to represent a rather good topic: not only does it epitomize a turning-point in Russell’s intellectual evolution and in the emergence of the new tradition, but it also shows how easily the new and victorious analytic philosophy has misconstrued its own history. If I entirely share Candlish’s conviction about the necessity of introducing an historical perspective in analytical philosophy, I am not convinced by Candlish’s own reconstruction of the dispute. In a nutshell, what I Wnd very useful in the book is all that concerns Bradley, and some of the parts devoted to Russell (especially, the analysis of his theory of judgment). What I do not agree with is, Wrst, Candlish’s way of doing history of philosophy; second, his treatment of Russell’s works; and third, his general conception of the use of logic in philosophy. Candlish really succeeds in expounding to the modern eye both the coherence of Bradley’s thought, and the diUculty of grasping it. His analysis of the role Bradley gave to “intellectual satisfaction” (pp. 26–7, 33) and to the “principles of suUcient reason” (pp. 46–7) is very enlightening—it explains why Bradley, while endorsing a kind of methodological scepticism, denied that ultimate contingencies were given in experience (p. 48). Candlish also does a great job of presenting... (shrink)

In Appearance and Reality Bradley has much to say about relations. This is to be found particularly in Chapter 3 and Appendix B, but the whole of the book is on this subject in one way or another. His views aroused immediate opposition and Bertrand Russell, among others, strongly attacked the “doctrine of internal relations,” a phrase which, be it noted, does not occur in Chapter 3 at all and makes its appearance only as part of the controversy. (...) Russell argued that some relations at least are purely external, and that if one does not grant this one is left with no option but to reject pluralism, embrace monism, and regard all truths as analytic. With characteristic honesty Russell admitted that it was aversion to these consequences which stimulated his desire to rebut opinions of the kind that Bradley held. It is the thesis of this essay that while Bradley had something important to say about the “doctrine,” he made a more important point about relations and qualities which has been overlaid by the controversy about “internal relations,” and that this point is an extremely relevant one in the context of much modern philosophizing. I will therefore attempt first of all to draw out Bradley’s most important point about relations and qualities; secondly to consider what connection this has with the “internal relations” controversy; and thirdly to decide whether Russell was right in supposing what he did about pluralism, monism, and analytic truths. (shrink)

Professor Eames explores the development of Russell’s own philosophy in interaction with ten of his contemporaries: Bradley, Joachim, Moore, Frege, Meinong, Whitehead, Wittgenstein, Schiller, James, and Dewey. Her examination of these interactions affords a new historical perspective on 20th century analytic philosophy as well as a deeper understanding of Russell’s philosophy and its influence.

Despite periodic references to F. H. Bradley as a dogmatic metaphysician of the worst sort, or an unreformed, conservative, and nonhistorical Hegelian, one of his logical doctrines is now a commonplace: his analysis of the logical form of affirmative universal categorical statements. In “On Denoting” Russell adopted this analysis without discussion, merely noting that it had been “ably argued” by Bradley. Virtually all philosophers since have followed suit. It is now an accepted truth that statements like “All (...) A’s are B” have the logical form. (shrink)

Different interpretations of Bradley’s regress argument are considered. On the basis of textual evidences, it is argued that the most persuasive is the one that sees the argument as primarily addressing the general issue of unity or connectedness.

Bradley is often described as an Anglo-Hegelian, and hence it is assumed that his doctrines derive from Hegel. It is true that his first two works ‘The Presuppositions of Critical History’ and Ethical Studies are heavily influenced by Hegel. The Principles of Logic is much less so: it certainly contains a number of both laudatory and critical references to Hegel, but the whole design of the book is completely unrelated to his treatment of logic. Appearance and Reality seems to (...) me not to be Hegelian at all. The interesting logical discussions occur in the Principles , and it is here that we can find points of comparison between Bradley and Frege and Russell. This is in part because all three were agreed that it was impossible to account for logic by reference to psychology. Bradley's doctrine of internal relations first emerges in this context, though it is given a more metaphysical interpretation in the subsequent Appearance and Reality . However, most who have talked of internal relations have taken their view from the latter work, and have found the doctrine either confused or silly. This quotation from Appearance and Reality seems to bring out all that is objectionable in the view: And if you could have a perfect relational knowledge of the world, you could go on from the nature of red-hairedness to these other characters which qualify it, and you could from the nature of red-hairedness reconstruct all the red-haired men. In such perfect knowledge you could start internally from any one character in the Universe, and you could from that pass to the rest…For example, a red-haired man who knew himself utterly would and must, starting from within, go on to know everyone else who had red hair, and he would not know himself until he knew them. But, as things are, he does not know how or why he himself has red hair, nor how and why a different man is also the same in that point, and therefore, because he does not know the ground, the how and why, of his relation to other men, it remains for him relatively external, contingent, and fortuitous. But there is really no mere externality except in his ignorance. (shrink)