By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

Suppose that A explains B. Do A and B need to be true? Provided that we have metaphysical explanation in mind, orthodoxy answers “yes:” metaphysical explanation is factive. This article introduces and defends a non-factive notion of metaphysical explanation. I argue that we need a non-factive notion of explanation in order to make sense of explanationist arguments where we motivate a view by claiming that it offers better explanations than its competitors. After presenting and rejecting some initially plausible rivals, I (...) account for non-factive metaphysical explanation by drawing on existing applications of structural equation models to metaphysical grounding. (shrink)

It is often thought that metaphysical grounding underwrites a distinctive sort of metaphysical explanation. However, it would be a mistake to think that all metaphysical explanations are underwritten by metaphysical grounding. In service of this claim, I offer a novel kind of metaphysical explanation called metaphysical explanation by constraint, examples of which have been neglected in the literature. I argue that metaphysical explanations by constraint are not well understood as grounding explanations.

Belirli betimlemeler, bir belirli tanımlıkla (Türkçede seslendirilmeyen ancak İngilizcede karşılığı "the" olan) başlayan "İngiltere'nin kralı", "Çin'in başkenti" gibi deyimlerdir. Russell bu yazıda belirli betimlemelerin mantıksal olarak nasıl çözümlenmesi gerektiği ile ilgili kendi betimlemeler kuramını ortaya atar. Russell'ın savı, belirli betimlemeler doğru bir biçimde çözümlenirse bir karşılığı olmayan "Fransa'nın şimdiki kralı" gibi deyimlerin yol açtığı türden birçok felsefi bilmecenin ortadan kalkacağıdır.

Abstract: In this paper we argue that Robert Kane’s theory of free will cannot accommodate the possibility of a sinless individual who faces morally significant choices because a sinless agent cannot voluntarily accord value to an immoral desire, and we argue that Kane’s theory requires this. Since the Jesus of the historic Christian tradition is held to be sinless, we think Christians should reject Kane’s theory because it seems irreconcilable with historic Christian Christology. We consider two objections to our argument (...) and argue that both fail. (shrink)

The survival enhancing propensity (SEP) account has a crucial role to play in the analysis of proper function. However, a central feature of the account, its specification of the proper environment to which functions are relativized, is seriously underdeveloped. In this paper, I argue that existent accounts of proper environment fail because they either allow too many or too few characters to count as proper functions. While SEP accounts retain their promise, they are unworkable because of their inability to specify (...) this important feature. However, I suggest that this problem can be overcome by the application of a new strategy for specifying proper environment that is grounded in the operation of natural selection and I conclude by offering a first approximation of such an account. (shrink)

Some recent psychological studies suggest that the belief that humans matter more than other animals can be strengthened by cognitive dissonance. Jaquet (forthcom- ing) argues that some of these studies also show that the relevant belief is primar- ily caused by cognitive dissonance and is therefore subject to a debunking argument. We offer an alternative hypothesis according to which we are already speciesist but cognitive dissonance merely enhances our speciesism. We argue that our hypothesis explains the results of the studies (...) at least as well as Jaquet’s. We then respond to a series of objections. Along the way, we highlight various respects in which further stud- ies are needed to decide between Jaquet’s hypothesis and ours. (shrink)

Dans son article « L’anarchie en philosophie politique », Francis Dupuis-Déri (2007) tente de réhabiliter l’anarchisme face au silence dont il est victime en philosophie politique. Dans cet article, j’entends accepter l’invitation de Dupuis-Déri à prendre au sérieux l’anarchisme et, plus particulièrement, le modèle général d’organisation politique qu’il propose en tentant de répondre à cette question : l’anarchisme est-il un régime politique moralement défendable ? Je réponds par la négative en montrant que l’anarchisme fait face à un trilemme qu’il ne (...) peut, par définition, résoudre. Ainsi, (1) soit l’anarchisme n’est pas moralement souhaitable, (2) soit il se confronte aux mêmes problèmes que rencontrent (selon les anarchistes) la démocratie ainsi que les autres régimes politiques concernant l’autorité et la coercition, (3) soit son application, dans sa version « pragmatique », se réduit à des communautés, ce qui permet en quelque sorte d’évacuer les problèmes soulevés dans les deux autres branches du trilemme, mais ne les résout pas pour autant. (shrink)

An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand’s chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, that is (...) unique to the maximum entropy principle. (shrink)

Brentano never published on Bertrand’s paradox but claimed to have a solution. Adrian Maître has recovered from the Franz Brentano Archive Brentano’s remarks on his solution. They do not give us a worked demonstration of his solution but only an incomplete and in places obscure justification of it. Here I attempt to identify his solution, to explain what seem to me the clearly discernible parts of his justification and to discuss the extent to which the justification succeeds in the (...) light of current work on Bertrand’s paradox. (shrink)

Bertrand Russell was a meta-ethical pioneer, the original inventor of both emotivism and the error theory. Why, having abandoned emotivism for the error theory, did he switch back to emotivism in the 1920s? Perhaps he did not relish the thought that as a moralist he was a professional hypocrite. In addition, Russell's version of the error theory suffers from severe defects. He commits the naturalistic fallacy and runs afoul of his own and Moore's arguments against subjectivism. These defects could (...) be repaired, but only by abandoning Russell's semantics.Russell preferred to revert to emotivism. (shrink)

Revealed that Bertrand Russell's Wisdom of the West was most likely actually written by its "editor", Paul Foulkes, in view of the prominence in the text of the ideas of Foulkes' teacher, John Anderson. That suspicion later turned out to be true.

The principle of indifference is supposed to suffice for the rational assignation of probabilities to possibilities. Bertrand advances a probability problem, now known as his paradox, to which the principle is supposed to apply; yet, just because the problem is ill‐posed in a technical sense, applying it leads to a contradiction. Examining an ambiguity in the notion of an ill‐posed problem shows that there are precisely two strategies for resolving the paradox: the distinction strategy and the well‐posing strategy. The (...) main contenders for resolving the paradox, Marinoff and Jaynes, offer solutions which exemplify these two strategies. I show that Marinoff’s attempt at the distinction strategy fails, and I offer a general refutation of this strategy. The situation for the well‐posing strategy is more complex. Careful formulation of the paradox within measure theory shows that one of Bertrand’s original three options can be ruled out but also shows that piecemeal attempts at the well‐posing strategy will not succeed. What is required is an appeal to general principle. I show that Jaynes’s use of such a principle, the symmetry requirement, fails to resolve the paradox; that a notion of metaindifference also fails; and that, while the well‐posing strategy may not be conclusively refutable, there is no reason to think that it can succeed. So the current situation is this. The failure of Marinoff’s and Jaynes’s solutions means that the paradox remains unresolved, and of the only two strategies for resolution, one is refuted and we have no reason to think the other will succeed. Consequently, Bertrand’s paradox continues to stand in refutation of the principle of indifference. (shrink)

The notion of logical construction was used by Bertrand Russell in the early 20th century, which originally comes from A. N. Whitehead. Russell said that matter as a mind-independent thing can only be known by description. He also argued that matter is a logical construction of sense-data. However, this leads to an incoherent view of the direct or indirect connection between a mind and the external world. The problem examining is whether a collapsing house is a logical construction of (...) the sense-data of rumbling sounds and collapsing shapes. Using Russell's writings between 1911 and 1918, I will analyze how Russell characterized logical constructions. Finally, I will show Russell’s view about the relation of logical constructions to matter and sense-data. A careful interpretation of Russell's thoughts shows that the contents of the statements of the physical world are not constructions being equivalent to the contents of the sense-datum statements. (shrink)

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same (...) time, the philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability. The book finishes with the author’s proposed solution—a solution in the spirit of Bertrand’s, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference. (shrink)

Until very recently the received wisdom on Russell’s moral philosophy was that it is uninspired and derivative, from Moore in its first phase and from Hume and the emotivists in its second. In my view this is a consensus of error. In the latter part of this essay I contend: 1) that Russell’s ‘work in moral philosophy’ had at least three, and (depending how you look at it) up to six ‘main phases’; 2) that in some of those phases, it (...) was not derivative, but on the contrary, highly original; 3) that Russell was a pioneer of two of the chief forms of ethical anti-realism that have dominated debate in this century, emotivism and the error theory (so that if the theory of Human Society was derived from emotivism, it was derived from a family of theories that Russell himself helped to create); 4) that the revolt against Hegelianism, which led to the birth of Analytic Philosophy, had an ethical dimension to it; and 5) that Russell played an important part in the debates that led up to Moore’s Principia Ethica, so that the view form which his own opinions were derived is one that he helped to develop. -/- I also argue that Russell himself pioneered a rather puritanical conception of philosophy which tended to extrude his own writings on politics and practical ethics as not really philosophical. Since this conception has been largely abandoned, it is time to let them back into the fold. I argue that this views of practical affairs are often backed by interesting philosophical arguments, illustrating this thesis with a reconstruction and critique of Russell’s Hobbesian argument for world government. (shrink)

In this article, the author analyses the relationship between two prominent philosophers of the 20th century in Europe and Great Britain—Ludwig Wittgenstein and Bertrand Russell. According to a lot of correspondence available nowadays we can reconstruct not only the environment of thought in Cambridge in the beginning and the first half of the 20th century but to find out some very personal, subjective grounds for the changes of relationship between thinkers, misunderstandings between them. Such a kind of biographical-historical reconstruction (...) does not interfere but helps to understand better the origin, development, and criticism of philosophical ideas and theories. In this context, the personal relationship between Russell and Wittgenstein, their friendship for more than 30 years, and mutual assistance, both intellectual and business, played a big role in the development and formation of both philosophers as philosophers. Even mutual disagreements and criticism of ideas over time helped them to see the shortcomings and sometimes even complete failure of their theses and statements. First, the author describes in detail the role of Russell in Wittgenstein’s life: first meeting and inspiration to do philosophy, support in studies, assistance in the publication of Wittgenstein’s first book, support, and facilitation in returning to Cambridge in 1929, obtaining PhD degree and receiving Trinity College grant. Second, the author considers the fundamental points of philosophical disagreements between the two philosophers and Wittgenstein’s critique of Russell’s ideas. (shrink)

From 1901 till, at least, 1919, Russell persistently maintained that there are two kinds of logic, between which he sharply discriminated: mathematical logic and philosophical logic. In this paper, we discuss the concept of philosophical logic, as used by Russell. This was only a tentative program that Russell did not clarify in detail, so our task will be to make it explicit. We shall show that there are three (-and-a-half) kinds of Russellian philosophical logic: (i) “pure logic”; (ii) philosophical logic (...) investigating the logical forms of propositions; (iii) philosophical logic exploring the logical forms of facts: in epistemology; and in the external world. In particular, Russell’s program or philosophical logic of the facts of the external world remained less than sketchily outlined. We shall discuss it in some detail in the hope that it can start a new life. (shrink)

The task of this paper is to reconstruct Bertrand Russell project for religion without God and dogma. Russell made two attempts in this direction, first in the essay “Free Man’s Worship” (1903), and then, in theoretical form, in the paper “The Essence of Religion” (1912). Russell’s explorations of religious impulses run in parallel with his work on technical philosophy. According to Russell from 1903–12, religion is an important part of human pursuits. However, whereas the ordinary man believes in God, (...) the freeman embraces a religion without fear and dogma. He strives for a union with the universe achieved in contemplation made from many perspectives through “impartiality of vision”. For this reason freemen renounce the Self and the Will. Russell abandoned his project for religion without God mainly because of Wittgenstein’s criticism. In his later writings he continued to criticize the religion of the ordinary man, without to further develop a positive philosophy of religion, though. (shrink)

Despite its enormous popularity, Russell’s theory of definite descriptions has received various criticisms. Two of the most important objections against this theory are those arising from the Argument from Incompleteness and the Argument from Donnellan’s Distinction. According to the former although a speaker may say something true by assertively uttering a sentence containing an incomplete description , on the Russellian analysis such a sentence expresses a false proposition; so, Russell’s theory cannot adequately deal with such sentences. According to the latter (...) objection a descriptive sentence is actually ambiguous—it expresses a general proposition when the description contained in it is used attributively, and a singular proposition when the description in question is used referentially; Russell’s theory is inadequate as it fails to capture this ambiguity and offers an analysis according to which a descriptive sentence expresses only a general proposition. These objections are examined in the present dissertation. It is shown here that these objections arise from: (i) ignoring the distinction between the meaning of a sentence and the assertions made by using it, (ii) the failure to distinguish between the semantic meaning of a sentence and the pragmatic meaning with which it is used on a particular occasion. To make the distinction mentioned in (i), a significant part of Scott Soames’ theory concerning meaning and assertions has been adopted in this dissertation; and, to make the distinction mentioned in (ii), a test, namely the cancellability test, and two Distinguishing Criteria, namely DC-1 and DC-2, have been developed here. It has been argued here that if we properly make the relevant distinctions, then we will find that: (a) the phenomenon cited by the Argument from Incompleteness can be well explained keeping the Russellian analysis of descriptive sentences intact, (b) the phenomenon arising from the Argument from Donnellan’s Distinction raises an issue of pragmatics and is irrelevant to Russell’s semantic analysis of descriptive sentences. So, none of the above criticisms poses a genuine threat to Russell’s theory of definite descriptions; his theory actually provides, to a large extent, a correct semantic analysis of descriptive sentences. (shrink)

Review of BERTRAND RUSSELL: THE SPIRIT OF SOLITUDE, the first volume of Ray Monk's biography of Russell.

Review of a reissue of Russell's My Philosophical Development.

‘Poor Bertie’ Beatrice Webb wrote after receiving a visit from Bertrand Russell in 1931, ‘he has made a mess of his life and he knows it’. In the 1931 version of his Autobiography, Russell himself seemed to share Webb’s estimate of his achievements. Emotionally, intellectually and politically, he wrote, his life had been a failure. This sense of failure pervades the second volume of Ray Monk’s engrossing and insightful biography. At its heart is the failure of Russell’s marriages to (...) Dora Black and Patricia (Peter) Spence, his poor relationships with his children John and Kate, and the decline in his reputation as a philosopher. Russell, who had changed the direction of philosophy irrevocably, was in later years unable to find permanent academic employment in Britain, ousted from his professorship at the City College of New York because of his views on sex and marriage, and was reduced to giving nonspecialist lectures at a foundation established by the Philadelphia philanthropist Albert C. Barnes. Eventually in 1944 he returned to Cambridge, but by then the philosophical world was in the grip of Ludwig Wittgenstein’s ideas, and Russell was largely ignored. (shrink)

CORCORAN RECOMMENDS COCCHIARELLA ON TYPE THEORY. The 1983 review in Mathematical Reviews 83e:03005 of: Cocchiarella, Nino “The development of the theory of logical types and the notion of a logical subject in Russell's early philosophy: Bertrand Russell's early philosophy, Part I”. Synthese 45 (1980), no. 1, 71-115 .

Exposed in 1948, within his masterpiece on the scope and limits of human knowledge, the epistemological tenets that Bertrand Russell regarded as fundamental elements in the construction of scientific knowledge, are still worthy of a detailed discussion today. Given the excellence of the author, it will not be surprising to see that Russell's gnoseologic postulates, even for the present scientific view, address some of the most controversial questions still to be solved in the theory of knowledge.

I present an answer to the title question which relates Russell’s writings to a remark by C.D. Broad. Russell shared the same concerns as Broad about the new postgraduate students at the University of Cambridge but instead of voicing them, his writings left a problem.

Russell identifies the conflict between the ego of self and the greater universe causes internal strife that can only be resolved by truly open questioning. Through this, we are enriching our lives and our minds, while becoming closer to our universal truths.

Review of The Cambridge Companion to Bertrand Russell.

Russell’s initial project in philosophy (1898) was to make mathematics rigorous reducing it to logic. Before August 1900, however, Russell’s logic was nothing but mereology. First, his acquaintance with Peano’s ideas in August 1900 led him to discard the part-whole logic and accept a kind of intensional predicate logic instead. Among other things, the predicate logic helped Russell embrace a technique of treating the paradox of infinite numbers with the help of a singular concept, which he called ‘denoting phrase’. Unfortunately, (...) a new paradox emerged soon: that of classes. The main contention of this paper is that Russell’s new conception only transferred the paradox of infinity from the realm of infinite numbers to that of class-inclusion. Russell’s long-elaborated solution to his paradox developed between 1905 and 1908 was nothing but to set aside of some of the ideas he adopted with his turn of August 1900: (i) With the Theory of Descriptions, he reintroduced the complexes we are acquainted with in logic. In this way, he partly restored the pre-August 1900 mereology of complexes and simples. (ii) The elimination of classes, with the help of the ‘substitutional theory’, and of propositions, by means of the Multiple Relation Theory of Judgment, completed this process. (shrink)

Marathi Translation of Bertrand Russell's Preface of History of Western Philosophy.

Economists use various models to explain why it is that firms are capable of pricing above marginal cost. In this paper, we will examine two of them: the Cournot and Bertrand duopoly models. Economists generally accept both models as good explanations of the phenomenon, but the two models contradict each other in various important ways. The puzzle is that two inconsistent explanations are both regarded as good explanations for the same phenomenon. This becomes especially worrisome when the two models (...) are offering divergent policy recommendations. This report presents that puzzle by laying out how the two models contradict each other in a myriad of ways and then offers five possible solutions to that puzzle from various economists, philosophers of science, and philosophers of economics. (shrink)

Despite of the fact that Reichenbach clearly acknowledged his indebtedness to Hilbert, the influence of this leading mathematician of the time on him is grossly neglected. The present paper demonstrates that the decisive years of the development of Reichenbach as a philosopher of science coincide with, and also partly followed the “philosophical” turn of Hilbert’s mathematics after 1917 that was fixed in the so called “Hilbert’s program”. The paper specifically addresses the fact that after 1917, Hilbert saw the axiomatic method (...) as an instrument for providing the foundations not only of mathematics but also of other sciences. In particular, Hilbert’s axiomatic program was closely connected with the theoretical physics and arguably helped Einstein to discover the general theory of relativity. In this context, one can see Reichenbach’s project to axiomatize Einstein’s theory of relativity as a continuation of this project. Under Russell’s influence, after 1914 Hilbert also developed an interest in mathematical logic. Reichenbach experienced similar transition from axiomatics to logic which went together with turn of his interest from Hilbert to Russell. Reichenbach’s rapprochement to Russell also supported the transition of his interests from epistemology to ontology. (shrink)

I take a dim view of this absurdly overpraised book, marred as it is is by errors of fact, interpretation and method and surprisingly uniformed (as it appears to be) about Russian history. It shows what can go wrong with Skinnerite intellectual history in the hands of somebody less gifted than Skinner himself.

Logicism is the thesis that all or, at least parts, of mathematics is reducible to deductive logic in at least two senses: (A) that mathematical lexis can be defined by sole recourse to logical constants [a definition thesis]; and, (B) that mathematical theorems are derivable from solely logical axioms [a derivation thesis]. The principal proponents of this thesis are: Frege, Dedekind, and Russell. The central question that I raise in this paper is the following: ‘How did Russell construe the philosophical (...) worth of logicism?’ The argument that I build in response to this is that Russell perceived an inverse proportion between a logical reduction of mathematics and the certitude of non-novel mathematical theorems—such that the more we reduce mathematics to logic, the more certain we become of our mathematical theorems; this was portrayed through a presentation of mathematical knowledge as coherent. Therefore, I set out to sketch Russell’s coherence theory and appraise it in relation to the presence discourse: i.e., in relation to logicism and mathematical certainty. (shrink)

Moore and Russell’s philosophical and personal paths through the early years of the twentieth century make a fascinating chronicle. Some of this story is familiar; but material from the unpublished Moore papers adds new and forceful detail to the account. It is a commonplace by now that Russell and Moore were not friends, although they maintained a long professional association. Their most intellectually intimate phase came early on, reaching a peak in 1897–99. But I show that during this period Moore (...) developed an indisputable antagonism toward Russell, which I argue was motivated by a form of intellectual self-preservation from the Russellian juggernaut. This paper examines aspects of the development of their views and their relationship between 1894 and 1901. (shrink)

Bertrand Russell [1912] argued that we are acquainted with our experiences. Although this conclusion has generated a lot of discussion, very little has been said about Russell's actual arguments for it. This paper aims to remedy that. I start by spelling out two Russellian arguments for acquaintance. Then I show that these arguments cannot both succeed. For if one is sound, the other isn't. Finally, I weigh our options with respect to these arguments, and defend one option in particular. (...) I argue that we have good reason to believe that we can be, and sometimes are, acquainted with our experiences. (shrink)

This paper presents a history of Bertrand Russell's evolving views on the nature of truth. It begins with his brief defense of a primitivist view of truth, followed by his critical accounts of both the coherence and pragmatic theories of truth. Then the paper discusses Russell's shift to the correspondence theory, and the variations of it he defended throughout his career.

Bertrand Russell famously argued that causation is not part of the fundamental physical description of the world, describing the notion of cause as “a relic of a bygone age”. This paper assesses one of Russell’s arguments for this conclusion: the ‘Directionality Argument’, which holds that the time symmetry of fundamental physics is inconsistent with the time asymmetry of causation. We claim that the coherence and success of the Directionality Argument crucially depends on the proper interpretation of the ‘ time (...) symmetry’ of fundamental physics as it appears in the argument, and offer two alternative interpretations. We argue that: if ‘ time symmetry’ is understood as the time -reversal invariance of physical theories, then the crucial premise of the Directionality Argument should be rejected; and if ‘ time symmetry’ is understood as the temporally bidirectional nomic dependence relations of physical laws, then the crucial premise of the Directionality Argument is far more plausible. We defend the second reading as continuous with Russell’s writings, and consider the consequences of the bidirectionality of nomic dependence relations in physics for the metaphysics of causation. (shrink)

This chapter examines Bertrand Russell's developing views--roughly from 1911 to 1918--on the nature of introspective knowledge and subjects' most basic knowledge of themselves as themselves. It argues that Russell's theory of introspection distinguishes between direct awareness of individual psychological objects and features, the presentation of psychological complexes involving those objects and features, and introspective judgments which aim to correspond with them. It also explores his transition from believing that subjects enjoy introspective self-acquaintance, to believing that they only know themselves (...) by self-description, and eventually to believing that self-knowledge is a logical construction. It concludes by sketching how Russell's views about introspection and self-knowledge change as a result of his adoption of neutral monism. Along the way, it sheds additional light on his acquaintance-based theory of knowledge, preference for logical constructions over inferred entities, and gradual progression towards neutral monism. (shrink)

In Bertrand Russell's 1903 Principles of Mathematics, he offers an apparently devastating criticism of the neo-Kantian Hermann Cohen's Principle of the Infinitesimal Method and its History (PIM). Russell's criticism is motivated by his concern that Cohen's account of the foundations of calculus saddles mathematics with the paradoxes of the infinitesimal and continuum, and thus threatens the very idea of mathematical truth. This paper defends Cohen against that objection of Russell's, and argues that properly understood, Cohen's views of limits and (...) infinitesimals do not entail the paradoxes of the infinitesimal and continuum. Essential to that defense is an interpretation, developed in the paper, of Cohen's positions in the PIM as deeply rationalist. The interest in developing this interpretation is not just that it reveals how Cohen's views in the PIM avoid the paradoxes of the infinitesimal and continuum. It also reveals some of what is at stake, both historically and philosophically, in Russell's criticism of Cohen. (shrink)

The thesis that in order to genuinely think about a particular object one must be (in some sense) acquainted with that object has been thoroughly explored since it was put forward by Bertrand Russell. Recently, the thesis has come in for mounting criticism. The aim of this paper is to point out that neither the exploration nor the criticism have been sensitive to the fact that the thesis can be interpreted in two different ways, yielding two different principles of (...) acquaintance. One principle uses the notion of content in distinguishing genuine thinking-about things from a merely derivative kind of thinking-about things. The other principle is quiet about content, focusing instead on a distinction between satisfactional and non-satisfactional means of bringing things into thought. Most work has focused on the first, content-based principle of acquaintance. But criticisms of this principle do not apply straightforwardly to the non-content-based principle. I shall argue that the latter principle merits independent assessment as part of the broader effort to account for genuine thinking about particular objects. In the final section of the paper, I will sketch a roadmap for this assessment. (shrink)

The goal of this note is to bring into wider attention the often neglected important work by Bertrand Russell on the foundations of physics published in the late 1920s. In particular, we emphasize how the book The Analysis of Matter can be considered the earliest systematic attempt to unify the modern quantum theory, just emerging by that time, with general relativity. More importantly, it is argued that the idea of what I call Russell space, introduced in Part III of (...) that book, is more fundamental than quantum theory, general relativity, and quantum gravity since the topological ordinal space proposed by Russell would naturally incorporate into its very fabric the emergent nature of spacetime by deploying event assemblages, and not spacetime or particles, as the fundamental building blocks of the world. (shrink)

In The Problems of Philosophy, Bertrand Russell presents a justification of induction based on a principle he refers to as “the principle of induction”. Owing to the ambiguity of the notion of probability, the principle of induction may be interpreted in two different ways. If interpreted in terms of the subjective interpretation of probability, the principle of induction may be known a priori to be true. But it is unclear how this should give us any confidence in our use (...) of induction, since induction is applied to the external world outside our minds. If the principle is interpreted in light of the objective interpretation of induction, it cannot be known to be true a priori, since it applies to frequencies that occur in the world outside the mind, and these cannot be known without recourse to experience. Russell’s principle of induction therefore fails to provide a satisfactory justification of induction. (shrink)