In this note, we review paradoxes like Russell’s, the Liar, and Curry’s in the context of intuitionistic logic. One may observe that one cannot blame the underlying logic for the paradoxes, but has to take into account the particular concept formations. For proof-theoretic semantics, however, this comes with the challenge to block some forms of direct axiomatizations of the Liar. A proper answer to this challenge might be given by Schroeder-Heister’s definitional freedom.

From 1895, the year he published his first signed article, to four days before his death in 1970 when he wrote his last, Bertrand Russell was a powerful force in the world of mathematics, philosophy, human rights and the struggle for peace. During those years he published 70 books, almost as many pamphlets and over 2,000 articles, he also contributed pieces to some 200 books. The availability of the Bertrand Russell Archives at McMaster University since 1968 has made (...) it possible for the first time to compile a full, descriptive bibliography of his writings. The Collected Papers are based on it. Fully annotated, the Bibliography is textually oriented and will guide the scholar, collector and general reader to the authoritative editions of Russell's works. It includes references to the locations of all known speeches and interviews, and reproductions of the dust-jackets of Russell's books. Blackwell, Ruja and Turcon have cooperated for nearly 20 years on the new Bibliography. Lord Russell saw the extensive additions for it near the end of his life and declared: `I am impressed.'. (shrink)

Three polemical exchanges between Bertrand Russell and F. H. Bradley, F. C. S. Schiller, and the prosecutor in Russell's trial for violating the Defence of the Realm Act in 1916 are examined in order to bring to light some paradigms of informal reasoning, with a view to encouraging research into the logic of natural language. Ten such paradigms are expressed, e.g., Agree with the contention but not for the reasons given; Agree that the criticism is valid and report (...) that one has modified the criticized doctrine but not in the manner suggested. (shrink)

James A. Harris's biography of David Hume is the first such study to appear since Ernest Mossner's The Life of David Hume (1954). Unlike Mossner, Harris aims to write a specifically "intellectual biography", one that gives "a complete picture of Hume's ideas" and "relates Hume's works to the circumstances in which they were conceived and written" (vii). Harris's study turns on four central theses or claims about the character of Hume's thought and how it is structured and developed. The claims (...) are: (1) Hume's Treatise has no claim to any sort of "privileged" status in relation to Hume's other major works -- which include his Essays and his History of England. -/- (2) There is no system, doctrine, or fundamental aims or ambitions that serve to unify Hume's thought. -/- (3) Irreligious aims and interests are not of any particular or unique importance for Hume's thought. Moreover, whatever irreligious aims and objectives Hume may have had, they reflect his moderate, neutral and detached attitude to this and all other subjects -- there is no underlying animus or hostility against religion that motivates his contributions to this subject. (4) Hume's thought should be understood and explained not in terms of his concern with some specific subject matter or body of doctrine but rather in terms of his style and his identity as a "philosophical man of letters". -/- The general picture of Hume that emerges from this study, as constructed around these four core theses, is, as I will explain, incomplete, unconvincing and, in important respects, seriously flawed and misleading. -/- . (shrink)

The Silk Route from Europe to China. Harry Holcroft. Pavilion, London 1999. 88 pp. £14.99. ISBN 1 86205 322 7.

_'Every man would like to be God, if it were possible; some few find it difficult to admit the impossibility.'_ - _Bertrand Russell_ From 1931-1935 Bertrand Russell was one of the regular contributors to the literary pages of the _New York American_, together with other distinguished authors, such as Aldous Huxley and Vita Sackville-West. _Mortals and Others Volume II_ presents a further selection of his essays, ranging from the politically correct, to the perfectly obscure: from _The Prospects of Democracy_ (...) to _Men Versus Insects_. Even though written in the politically heated climate of the 1930s, these essays are surprisingly topical and engaging for the present day reader. Volume II of _Mortals and Others_ serves as a splendid, fresh introduction to the compassionate eclecticism of Bertrand Russell's mind. (shrink)

Donald Russell, Emeritus Professor of Classical Literature at the University of Oxford, has been a leading figure in several fields of classical scholarship over the last few decades. The present volume collects essays written in his honour by scholars who have all worked closely with him. They fall into three sections, corresponding to Donald Russell's main work: Latin literature, Greek imperial literature, and ancient literary criticism. They are unified by two of Russell's own pervasive concerns: ethics, the (...) concern of classical literature with moral conduct, and rhetoric, the techniques of effective persuasion. (shrink)

Solutions to Russell’s paradox of propositions and to Kaplan’s paradox are proposed based on an extension of von Neumann’s method of avoiding paradox. It is shown that Russell’s ‘anti-Cantorian’ mappings can be preserved using this method, but Kaplan’s mapping cannot. In addition, several versions of the Epimenides paradox are discussed in light of von Neumann’s method.

In the end, Harris provides a compelling argument for selective intolerance toward harsh moral traditions. He argues via a kind of moral realism, linked to a form of utilitarian ethic, but I submit that these are not doing the real work. To reach a similar conclusion, we can rely on much weaker premises. It’s enough that we have a non-arbitrary conception of what morality is for, and what sorts of things we can rationally and realistically want moral traditions to do. (...) Where they divert from that conception, moral traditions merit our critique and opposition. These should be every bit as severe, absolutely as passionate, as Harris evidently wants, but that does not commit us to his total picture of morality's landscape. Like it or not, morality is a much trickier phenomenon. (shrink)

For me personally the year 1945 is significant because it marked the beginning of my own academic career. In that year I matriculated at Oxford as a candidate for the B.A. in Literae Humaniores. For Hegel studies it is significant for a different reason. It is the year in which Popper’s Open Society and Its Enemies appeared. Popper’s book contributed nothing to the understanding of Hegel - M. B. Foster’s Political Philosophy of Plato and Hegel, which appeared ten years earlier, (...) is much more important in that respect - but it sealed in amber, so to speak, the image of Hegel which had become canonical for the liberal generation whose public conscience was Bertrand Russell. It marked the nadir of Hegel’s reputation in the Anglo-Saxon world.. (shrink)

At least since Martin Heidegger’s influential reading of Thomas Aquinas’s account of truth as a precursor to modern philosophy’s unfortunate “forgetfulness of being,” it has been popular to classify the Angelic Doctor as one of the fore­runners of the modern “correspondence theory” of truth. In what follows, I attempt to answer the question of whether or not this is a correct assessment. I want to suggest that Aquinas’s account of truth has superficial concord but deep conflict with modern correspondence theories. (...) The argument proceeds in two major segments: First, I attempt to establish a working definition of correspondence theory by tracing its development in the work of John Locke, John Stuart Mill and Bertrand Russell. Next, in light of these fundamental features of correspondence theory, I sketch out the way in which Aquinas’s own account is in superficial concord but deep conflict with it. (shrink)

This book explores contributions by some of the most influential women in the history of philosophy, science, and literature. Ranging from Sappho and Sophie Germain to Stebbing and Evelyn Fox Keller, this work ultimately demonstrates the impact these non-canonical, sometimes unknown or hidden, sources had, or may have had, on the recognized male leaders in their fields, from Aristotle to Pascal, Kant, Whitehead, and Russell. Chapters reflect philosophical pluralism, both analytic and continental themes, and cover figures reaching across the (...) entire history of ideas in the West, from pre-historic times to the twentieth century. Anyone interested in coming to know or in preparing to teach women in the history of philosophy, science, and literature will appreciate this collection and its myriad insights into the still unrecognized voices of non-canonical sources across these disciplines. (shrink)

Broad, C. D. Leibniz's predicate-in-notion principle and some of its alleged consequences.--Couturat, L. On Leibniz's metaphysics.--Friedrich, C. J. Philosophical reflections of Leibniz on law, politics, and the state.--Curley, E. M. The root of contingency. Furth, M. Monadology.--Hacking, I. Individual substance.--Hintikka, J. Leibniz on plenitude, relations, and the "reign of law."--Ishiguro, H. Leibniz's theory of the ideality of relations.--Kneale, M. Leibniz and Spinoza on activity.--Koyré, A. Leibniz and Newton.--Lovejoy, A. O. Plenitude and sufficient reason in Leibniz and Spinoza.--Mates, B. Leibniz on (...) possible worlds.--Russell, B. Recent work on the philosophy of Leibniz.--Wilson, M. D. On Leibniz's explication of "necessary truth.". (shrink)

Leibniz's predicate-in-notion principle and some of its alleged consequences, by C. D. Broad.--On Leibniz's metaphysics, by L. Couturat.--Philosophical reflections of Leibniz on law, politics, and the state, by C. J. Friedrich.--The root of contingency, by E. M. Curley.--Monadology, by M. Furth.--Individual substance, by I. Hacking.--Leibniz on plenitude, relations, and the "reign of the law," by J. Hintikka.--Leibniz's theory of the ideality of relations, by H. Ishiguro.--Leibniz and Spinoza on activity, by M. Kneale.--Leibniz and Newton, by A. Koyré.--Plenitude and sufficient reason (...) in Leibniz and Spinoza, by A. O. Lovejoy.--Leibniz on possible worlds, by B. Mates.--Recent work on the philosophy of Leibniz, by B. Russell.--On Leibniz's explication of "necessary truth," by M. D. Wilson.--Bibliography (p. [421]-425). (shrink)

The A to Z of Logic introduces the central concepts of the field in a series of brief, non-technical, cross-referenced dictionary entries. The 352 alphabetically arranged entries give a clear, basic introduction to a very broad range of logical topics. Entries can be found on deductive systems, such as propositional logic, modal logic, deontic logic, temporal logic, set theory, many-valued logic, mereology, and paraconsistent logic. Similarly, there are entries on topics relating to those previously mentioned such as negation, conditionals, truth (...) tables, and proofs. Historical periods and figures are also covered, including ancient logic, medieval logic, Buddhist logic, Aristotle, Ockham, Boole, Frege, Russell, Gödel, and Quine. (shrink)

Alonzo Church (1903–1995) was a renowned mathematical logician, philosophical logician, philosopher, teacher and editor. He was one of the founders of the discipline of mathematical logic as it developed after Cantor, Frege and Russell. He was also one of the principal founders of the Association for Symbolic Logic and the Journal of Symbolic Logic. The list of his students, mathematical and philosophical, is striking as it contains the names of renowned logicians and philosophers. In this article, we focus primarily (...) on Church’s philosophical contributions. (For an account of his life and academic history see the Introduction to The Collected Works of Alonzo Church (2019).) However, we also discuss his mathematical results when it is desirable to do so in order to pursue a philosophical issue. (shrink)

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov function, which (...) assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)

Most philosophical explorations of responsibility discuss the topic solely in terms of metaphysics and the "free will" problem. By contrast, these essays by leading philosophers view responsibility from a variety of perspectives -- metaphysics, ethics, action theory, and the philosophy of law. After a broad, framing introduction by the volume's editors, the contributors consider such subjects as responsibility as it relates to the "free will" problem; the relation between responsibility and knowledge or ignorance; the relation between causal and moral responsibility; (...) the difference, if any, between responsibility for actions and responsibility for omissions; the metaphysical requirements for making sense of "collective" responsibility; and the relation between moral and legal responsibility. The contributors include such distinguished authors as Alfred R. Mele, John Martin Fischer, George Sher, and Frances Kamm, as well as important rising scholars. Taken together, the essays in _Action, Ethics, and Responsibility_ offer a breadth of perspectives that is unmatched by other treatments of the topic. Contributors: Joseph Keim Campbell, David Chan, Randolph Clarke, E.J. Coffman, John Martin Fischer, Helen Frowe, Todd Jones, Frances Kamm, Antti Kauppinen, Alfred R. Mele, Michael O'Rourke, Paul Russell, Robert F. Schopp, George Sher, Harry S. Silverstein, Saul Smilansky, Donald Smith, Charles T. Wolfe The hardcover edition does not include a dust jacket. (shrink)