Quantification Theory in *8 of Principia Mathematica and the Empty Domain

The second printing of Principia Mathematica in 1925 offered Russell an occasion to assess some criticisms of the Principia and make some suggestions for possible improvements. In Appendix A, Russell offered *8 as a new quantification theory to replace *9 of the original text. As Russell explained in the new introduction to the second edition, the system of *8 sets out quantification theory without free variables. Unfortunately, the system has not been well understood. This paper shows that Russell successfully antedates Quine's system of quantification theory without free variables. It is shown as well, that as with Quine's system, a slight modification yields a quantification theory inclusive of the empty domain.     

The ontological foundation of Russell's theory of modality

Prominent thinkers such as Kripke and Rescher hold that Russell has no modal logic, even that Russell was indisposed toward modal logic. In Part I, I show that Russell had a modal logic which he repeatedly described and that Russell repeatedly endorsed Leibniz's multiplicity of possible worlds. In Part II, I describe Russell's theory as having three ontological levels. In Part III, I describe six Parmenidean theories of being Russell held, including: literal in 1903; universal in 1912; timeless in 1914; transcendental in 1918–1948. The transcendental theory underlies the primary level of Russell's modal logic. In Part IV, I examine Rescher's view that Russell and modal logic did not mix.The United States Naval Academy Research Council kindly provided a summer 1988 research grant for work on this essay. This essay was presented at the Bertrand Russell Society Meeting during the December 1988 Eastern Division Meeting of the American Philosophical Association in Washington, D.C.     

Some early similarities and later differences between Bertrand Russell and B. F. Skinner

B. F. Skinner credited Bertrand Russell with converting him to behaviorism and with writing one of the books that most influenced him. Particularly in Skinner's early work, there are similarities between Skinner and Russell that extend across mathematics, determinism, positivism, verbal behavior, future communities, evolution, and pragmatism. Later, Skinner's views changed, and he parted company with Russell in most of these areas. Perhaps the most dramatic and fundamental departure came when Skinner embraced pragmatism, which Russell said he "hated." However, there was a time during which Russell wrote favorably of pragmatism as a view for science. Although the similarities between Skinner and Russell may have resulted from common cultural influences, Russell appears to deserve credit for leading Skinner into the stimulus-response behaviorism of two-term necessities; he may also deserve some credit for helping to lead him out of it and into the selectionist behaviorism of three-term contingencies.     

Soames on Russell’s logic: a reply

In “What is History For?,” Scott Soames responds to criticisms of his treatment of Russell’s logic in volume 1 of his Philosophical Analysis in the Twentieth Century. This note rebuts two of Soames’s replies, showing that a first-order presentation of Russell’s logic does not fit the argument of the Introduction to Mathematical Philosophy, and that Soames’s contextual definition of classes does not match Russell’s contextual definition of classes. In consequence, Soames’s presentation of Russell’s logic misrepresents what Russell took to be its technical achievement and its philosophical significance.     

The Definability of the set of natural numbers in the 1925 Principia Mathematica

In his new introduction to the 1925 second edition of Principia Mathematica, Russell maintained that by adopting Wittgenstein's idea that a logically perfect language should be extensional mathematical induction could be rectified for finite cardinals without the axiom of reducibility. In an Appendix B, Russell set forth a proof. Gödel caught a defect in the proof at *89.16, so that the matter of rectification remained open. Myhill later arrived at a negative result: Principia with extensionality principles and without reducibility cannot recover mathematical induction. The finite cardinals are indefinable in it. This paper shows that while Gödel and Myhill are correct, Russell was not wrong. The 1925 system employs a different grammar than the original Principia. A new proof for *89.16 is given and induction is recovered.     

Russell on Negative Judgement

Topoi - This paper concerns Bertrand Russell’s changing views on negative judgement. ‘Negative judgement’ is considered in the context of three theories of judgement that Russell...     

Zeitordnung und Zeitpunkte

In many of his writings Russell developed a theory of time,highly interesting bothfrom a philosophical and from a logical point of view.Strangely enough, this has not acquired generalattention. The most important relational propertiesof the duration and points of time will be presented.In addition, Russell's considerations on the existenceand density of time points will becritically analysed and systematically reconstructed.A. G. Walker's explication of the concept of timepoint is unlike that of Russell. His theory oftime reflects the Dedekindian concept of cut.Walker's constructions will be modified in a suitableway and supplemented so that it becomes possileto prove the continuity of the temporal series.     

Sense data and logical relations: Karin Costelloe-Stephen and Russell’s critique of Bergson

ABSTRACT

Though scholarship has explored Karin Costelloe-Stephen’s contributions to the history of psychoanalysis, as well as her relations to the Bloomsbury Group, her philosophical work has been almost completely ignored. This paper will examine her debate with Bertrand Russell over his criticism of Bergson. Costelloe-Stephen had employed the terminology of early analytic philosophy in presenting a number of arguments in defence of Bergson’s views. Costelloe-Stephen would object, among other things, to Russell’s use of an experiment which, as she points out, was first conducted by Carl Stumpf. Russell appeals to Stumpf's experiment in his attempt to prove that sense data are terms in logical relations, a thesis presupposed by the project of logical analysis outlined in Our Knowledge of the External World. A reformulated version of Costelloe-Stephen's argument put forth by this paper shows that Russell's argument fails to provide adequate proof for his thesis. Further modifications of the argument can also address a reconstruction (based on contemporary reports) of Russell's reply to Costelloe-Stephen. In his reply, Russell would use, already in 1914, the term ‘analytic philosophy’ in contrasting his and Moore’s approach to a continental one, exemplified by Bergson and Costelloe-Stephen.     

The Visual Field in Russell and Wittgenstein

Bertrand Russell developed a conception of the nature of the visual field, and of other sensory fields, as part of his project of explaining the construction of the external world. Wittgenstein's remarks on the visual field in the Tractatus are in part a response to Russell. Wittgenstein, against Russell, analyses the visual field in terms of facts rather than objects. Further, his conception of the field is, in a distinctive sense, depsychologised.     

The early Russell on the metaphysics of substance in Leibniz and Bradley

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.     

The aim of Russell’s early logicism: a reinterpretation

I argue that three main interpretations of the aim of Russell’s early logicism in The Principles of Mathematics (1903) are mistaken, and propose a new interpretation. According to this new interpretation, the aim of Russell’s logicism is to show, in opposition to Kant, that mathematical propositions have a certain sort of complete generality which entails that their truth is independent of space and time. I argue that on this interpretation two often-heard objections to Russell’s logicism, deriving from Gödel’s incompleteness theorem and from the non-logical character of some of the axioms of Principia Mathematica respectively, can be seen to be inconclusive. I then proceed to identify two challenges that Russell’s logicism, as presently construed, faces, but argue that these challenges do not appear unanswerable.     

On Russell's vulnerability to Russell's paradox

Influenced by G. E. Moore, Russell broke with Idealism towards the end of 1898; but in later years he characterized his meeting Peano in August 1900 as ‘the most important event’ in ‘the most important year in my intellectual life’. While Russell discovered his paradox during his post-Peano period, the question arises whether he was already committed, during his pre-Peano Moorean period, to assumptions from which his paradox may be derived. Peter Hylton has argued that the pre-Peano Russell was thus vulnerable to (at least one version of) Russell's paradox and hence that the paradox exposes a pre-existing difficulty in Russell's Moorean philosophy. Contrary to Hylton, I argue that the Moorean Russell adhered to views which insulated him against the paradox. Further, I argue that Russell became vulnerable to his paradox as a result of changes in his Moorean position occasioned, first, by his acceptance of Cantor's theory of the transfinite, and, second, by his correspondence with Frege. I conclude with some general comments regarding Russell's acceptance of naïve set theory.     

Proposed principles for the management of school records: excerpts

We reprint here, with permission of the Russell Sage Foundation, selected excerpts from their Guidelines for the Collection, Maintenance, and Dissemination of Pupil Records, published in 1970. The Guidelines should receive the careful attention of every school and college and all other institutions and agencies which collect personal information about their students and clients. The document is the report of a work conference, convened by the Foundation in May 1969, whose 20 participants included lawyers, a judge, a state senator, a philosopher, sociologists, educators, and the following APGA members: Annette Engel, Leo Goldman, Franklyn A. Graff, John L. Holland, Martin R. Katz, John D. Krumboltz, Roger T. Lennon, and Thomas E. Long. David A. Goslin of Russell Sage chaired the conference and edited the report. The portion reproduced here consists mainly of portions of the Guidelines themselves. The full report, which includes suggestions for implementation, has been widely distributed; additional copies are available from the Russell Sage Foundation, 230 Park Avenue, New York, N.Y. 10017.     

In defense of the mirror thesis

In this journal, Luke Russell defends a sophisticated dispositional account of evil personhood according to which a person is evil just in case she is strongly and highly fixedly disposed to perform evil actions in conditions that favour her autonomy. While I am generally sympathetic with this account, I argue that Russell wrongly dismisses the mirror thesis—roughly, the thesis that evil people are the mirror images of the morally best sort of persons—which I have defended elsewhere. Russell’s rejection of the mirror thesis depends upon an independently implausible account of moral sainthood, one that is implausible for reasons that Russell himself suggests in another context. Indeed, an account of moral sainthood that parallels Russell’s account of evil personhood is plausible for the same reasons that his account of evil personhood is, and that suggests that Russell himself is actually committed to the mirror thesis.     

Reviews

HOW BRAVE A NEW WORLD? by Richard A McCormick.
PERFECT FOOLS: FOLLY FOB CHRIST'S SAKE IN CATHOLIC AND ORTHODOX SPIRITUALITY by John Saward.
THE LIVES OF THE DESERT FATHERS. Introduction by Benedicta Ward S.L.G. translated by Norman Russell.     

A Berry and A Russell Without Self-Reference

In this paper I present two new paradoxes, a definability paradox (related to the paradoxes of Berry, Richard and König), and a paradox about extensions (related to Russell’s paradox). However, unlike the familiar definability paradoxes and Russell’s paradox, these new paradoxes involve no self-reference or circularity.     

BOOK REVIEWS

Book reviewed in this article: Werner Simpfendörfer, Ökumenische Spurensuche Porträts Walter A. Wiest & Elwyn A. Smith, Ethics in Ministry: A Guide for the Professional Russell Chandran: Third World Theologies in Dialogue     

Note on Florensky’s Solution to Carroll’s ‘Barbershop’ Paradox: Reverse Implication for Russell?

Pavel Florensky solves Lewis Carroll??s ??Barbershop?? paradox to support his reasoning in a previous chapter. Our discussion includes a) the problem (which we also refer to as the p paradox), b) Carroll??s solution, c) Bertrand Russell??s solution, d) Florensky??s solution and then e) a material example proffered by Florensky. Both Russell and Florensky disagree with Carroll??s solution, yet, (ostensibly) unbeknownst to themselves they offer the same solution, which is ??p implies not-q??. Given Florensky??s material example, the solution seems to tell us something about the logic of belief. We ask whether Florensky??s example has reverse implications for Russell??s solution.