Bertrand Russell was one of the best-known proponents of logicism: the theory that mathematics reduces to, or is an extension of, logic. Russell argued for this thesis in his 1903 The Principles of Mathematics and attempted to demonstrate it formally in Principia Mathematica (PM 1910–1913; with A. N. Whitehead). Russell later described his work as a further “regressive” step in understanding the foundations of mathematics made possible by the late 19th century “arithmetization” of mathematics and Frege’s logical definitions of (...) arithmetical concepts. The logical system of PM sought to improve on earlier attempts by solving the contradictions found in, e.g., Frege’s system, by employing a theory of types. In this article, I also consider and critically evaluate the most common objections to Russell’s logicism, including the claim that it is undermined by Gödel’s incompleteness results, and Putnam's charge of “if-thenism”. I suggest that if we are willing to accept a slightly revisionist account of what counts as a mathematical truth, these criticisms do not obviously refute Russell’s claim to have established that mathematical truths generally are a species of logical truth. (shrink)

Review of Logic as Universal Science: Russell’s Early Logicism and Its Philosophical Context, by Anssi Korhonen (Palgrave Macmillan 2013).

Certain advocates of the so-called “neo-logicist” movement in the philosophy of mathematics identify themselves as “neo-Fregeans” (e.g., Hale and Wright), presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature and, when it is, often dismissed as not really logicism at all (in light of its assumption of axioms of infinity, reducibility and so on). In this paper I have three aims: firstly, to identify more clearly (...) the primary meta-ontological and methodological differences between Russell’s logicism and the more recent forms; secondly, to argue that Russell’s form of logicism offers more elegant and satisfactory solutions to a variety of problems that continue to plague the neo-logicist movement (the bad company objection, the embarrassment of richness objection, worries about a bloated ontology, etc.); thirdly, to argue that neo-Russellian forms of logicism remain viable positions for current philosophers of mathematics. (shrink)

Logicism is the view that mathematical truths are logical truths. But a logical truth is commonly thought to be one with a universally valid form. The form of “7 > 5” would appear to be the same as “4 > 6”. Yet one is a mathematical truth, and the other not a truth at all. To preserve logicism, we must maintain that the two either are different subforms of the same generic form, or that their forms are not (...) at all what they appear. The historical record shows that Russell pursued both these options, but that the struggle with the logical paradoxes pushed him away from the first kind of response and toward the second. An object cannot itself have a kind of inner logical complexity that makes a proposition have a different logical form merely in virtue of being about it, nor can their representatives in logical forms be single things different for different forms, at least not without postulating too many such objects and thereby creating Cantorian diagonal paradoxes. There are only apparent objects which are actually fragments of logical forms, different in different cases. (shrink)

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)

According to Quine, Charles Parsons, Mark Steiner, and others, Russell’s logicist project is important because, if successful, it would show that mathematical theorems possess desirable epistemic properties often attributed to logical theorems, such as aprioricity, necessity, and certainty. Unfortunately, Russell never attributed such importance to logicism, and such a thesis contradicts Russell’s explicitly stated views on the relationship between logic and mathematics. This raises the question: what did Russell understand to be the philosophical importance of logicism? Building on (...) recent work by Andrew Irvine and Martin Godwyn, I argue that Russell thought a systematic reduction of mathematics increases the certainty of known mathematical theorems (even basic arithmetical facts) by showing mathematical knowledge to be coherently organized. The paper outlines Russell’s theory of coherence, and discusses its relevance to logicism and the certainty attributed to mathematics. (shrink)

In the early 1900s, Russell began to recognize that he, and many other mathematicians, had been using assertions like the Axiom of Choice implicitly, and without explicitly proving them. In working with the Axioms of Choice, Infinity, and Reducibility, and his and Whitehead’s Multiplicative Axiom, Russell came to take the position that some axioms are necessary to recovering certain results of mathematics, but may not be proven to be true absolutely. The essay traces historical roots of, and motivations for, Russell’s (...) method of analysis, which are intended to shed light on his view about the status of mathematical axioms. I describe the position Russell develops in consequence as “immanent logicism,” in contrast to what Irving (1989) describes as “epistemic logicism.” Immanent logicism allows Russell to avoid the logocentric predicament, and to propose a method for discovering structural relationships of dependence within mathematical theories. (shrink)

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...) granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning (...) of Russell's paradox, this position is a natural position for him to have retreated to, when properly understood. (shrink)

In his highly perceptive, if underappreciated introduction to Wittgenstein’s Tractatus, Russell identifies a “lacuna” within Wittgenstein’s theory of number, relating specifically to the topic of transfinite number. The goal of this paper is two-fold. The first is to show that Russell’s concerns cannot be dismissed on the grounds that they are external to the Tractarian project, deriving, perhaps, from logicist ambitions harbored by Russell but not shared by Wittgenstein. The extensibility of Wittgenstein’s theory of number to the case of transfinite (...) cardinalities is, I shall argue, a desideratum generated by concerns intrinsic, and internal to Wittgenstein’s logical and semantic framework. Second, I aim to show that Wittgenstein’s theory of number as espoused in the Tractatus is consistent with Russell’s assessment, in that Wittgenstein meant to leave open the possibility that transfinite numbers could be generated within his system, but did not show explicitly how to construct them. To that end, I show how one could construct a transfinite number line using ingredients inherent in Wittgenstein’s system, and in accordance with his more general theories of number and of operations. (shrink)

The Russell's paradox concerns the foundations of naive set theory. This short short paper is about how it can be interpreted in other contexts and has significance in the world of commands. Understanding the paper assumes that the reader is broadly familiar with the foundations of set theory and its history. The text contains many formulas and therefore the reader should be comfortable in the world of logical formulas. My example is somewhat similar to the barber paradox. There, too, (...) we are puzzled by the feasibility of a task. In the case of the barber paradox there is a solution: the barber is a woman, in my example there is no such escape. (shrink)

Gottlob Frege abandoned his logicist program after Bertrand Russell had discovered that some assumptions of Frege’s system lead to contradiction (so called Russell’s paradox). Nevertheless, he proposed a new attempt for the foundations of mathematics in two last years of his life. According to this new program, the whole of mathematics is based on the geometrical source of knowledge. By the geometrical source of cognition Frege meant intuition which is the source of an infinite number of objects in arithmetic. In (...) this article, I describe this final attempt of Frege to provide the foundations of mathematics. Furthermore, I compare Frege’s views of intuition from The Foundations of Arithmetic (and his later views) with the Kantian conception of pure intuition as the source of geometrical axioms. In the conclusion of the essay, I examine some implications for the debate between Hans Sluga and Michael Dummett concerning the realistic and idealistic interpretations of Frege’s philosophy. (shrink)

Although the economic thought of Marshall and Pigou was united by ethical positions broadly considered utilitarian, differences in their intellectual milieu led to degrees of difference between their respective philosophical visions. This change in milieu includes the influence of the little understood period of transition from the early idealist period in Great Britain, which provided the context to Marshall’s intellectual formation, and the late British Idealist period, which provided the context to Pigou’s intellectual formation. During this latter period, the pervading (...) Hegelianism and influences of naturalism arising from the ideas of Charles Darwin and Herbert Spencer were challenged by Hermann Lotze, a key transitional thinker influencing the Neo-Kantian movement, who recognised significant limits of naturalism, on the one hand, and the metaphysical tenor of absolute idealism, on the other, and attempted to provide a balance between the two. The goal of this paper is to make the provisional case for the argument that Pigou’s views on ethics were not only directly influenced by utilitarian thinkers like Mill and Sidgwick, but they were also indirectly influenced by Hermann Lotze, via the influence of the Neo- Kantian movement on late British idealism. To that end, Pigou’s essays in The Trouble with Theism (1908), including his sympathetic consideration of the ethics of Friedrich Nietzsche, reflect the influence of Lotze indirectly through the impact at Cambridge of: James Ward’s critique of associationist psychology, and consideration of the limits of naturalism including the critique of evolutionary ethics; Bertrand Russell’s rejection of neo-Hegelianism and, together with Alfred North Whitehead, the development of Logicism; and G.E. Moore’s critique of utilitarian ethics on the basis of the naturalistic fallacy and the development of his own intuitionist system of ethics. (shrink)

Bertrand Russell was one of the protagonists of the programme of reducing “disagreeable” concepts to philosophically more respectable ones. Throughout his life he was engaged in eliminating or paraphrasing away a copious variety of allegedly dubious concepts: propositions, definite descriptions, knowing subjects, and points, among others. The critical aim of this paper is to show that Russell’s construction of points, which has been considered as a paradigm of a logical construction überhaupt, fails for principal mathematical reasons. Russell could have known (...) this, if he had taken into account some pertinent results due to Hausdorff or Tarski. Its constructive aim is to show that one can save Russell’s thesis – that points can be defined in terms of events or regions – by using the conceptual resources of modern pointless topology. (shrink)

Throughout his lectures and published writings on anthropology, Kant describes a form of unintentional, unstructured, obscure, and pleasurable imaginative mental activity, which he calls fantasy (Phantasie), where we ‘take pleasure in letting our mind wander about in obscurity.’ In the context of his pragmatic anthropology, Kant was concerned not only to describe this form of mental activity as a fact of human psychology, but more importantly, to criticize and discourage it. But must we share Kant’s negative evaluation? Could fantasy play (...) a positive role in some kinds of experience? In this paper I first reconstruct Kant’s conception of fantasy, and then consider what role fantasy might play in aesthetic experience. Precisely because of his anxieties about fantasy, Kant is careful to distinguish between the lawless freedom of the imagination in fantasy and the ‘free lawfulness’ of the imagination in aesthetic judgment. Departing from Kant, and with help from Susan Sontag, I argue that certain aesthetic objects, especially certain works of modernist art, positively invite fantasy, making fantasy part of proper aesthetic appreciation. I conclude by suggesting that while fantasy can indeed play a positive role in aesthetic appreciation, there is still reason to regard fantasy as ‘normatively ambiguous.’. (shrink)

This paper proves a precisification of Hume’s Law—the thesis that one cannot get an ought from an is—as an instance of a more general theorem which establishes several other philosophically interesting, though less controversial, barriers to logical consequence.

It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other functions as value. (...) Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus. (shrink)

This article is concerned with a central strand of Strawson's well-known and highly influential essay “Freedom and Resentment” Strawson's principal objectives in this work is to refute or discredit the views of the "Pessimist." The Pessimist, as Strawson understands him/ her, claims that the truth of the thesis of determinism would render the attitudes and practices associated with moral responsibility incoherent and unjustified. Given this, the Pessimist claims that if determinism is true, then we must abandon or suspend these attitudes (...) and practices altogether. Against the Pessimist Strawson argues that no reasoning of any sort could lead us to abandon or suspend our "reactive attitudes." That is to say, according to Strawson responsibility is a "given" of human life and society-something which we are inescapably committed to. In this article I argue that Strawson's reply to the Pessimist is seriously flawed. More specifically, I argue that Strawson fails to distinguish two very different forms or modes of naturalism and that he is constrained by the nature of his own objectives (i.e., the refutation of Pessimism) to embrace the stronger and far less plausible form of naturalism. On this basis I conclude that while there is something to be said for Strawson's general approach to these matters, we nevertheless cannot naturalize responsibility along the specific lines that he suggests. (shrink)

JOURNAL OF THE HISTORY OF PHILOSOPHY PRIZE for the best published book in the history of philosophy [Awarded in 2010] _______________ -/- Although it is widely recognized that David Hume's A Treatise of Human Nature (1739-40) belongs among the greatest works of philosophy, there is little agreement about the correct way to interpret his fundamental intentions. It is an established orthodoxy among almost all commentators that skepticism and naturalism are the two dominant themes in this work. The difficulty has been, (...) however, that Hume's skeptical arguments and commitments appear to undermine and discredit his naturalistic ambition to contribute to "the science of man". This schism appears to leave his entire project broken-backed. The solution to this riddle depends on challenging another, closely related, point of orthodoxy: namely, that before Hume published the Treatise he removed almost all material concerned with problems of religion. Russell argues, contrary to this view, that irreligious aims and objectives are fundamental to the Treatise and account for its underlying unity and coherence. It is Hume's basic anti-Christian aims and objectives that serve to shape and direct both his skeptical and naturalistic commitments. When Hume's arguments are viewed from this perspective we can solve, not only puzzles arising from his discussion of various specific issues, we can also explain the intimate and intricate connections that hold his entire project together. This "irreligious" interpretation provides a comprehensive fresh account of the nature of Hume's fundamental aims and ambitions in the Treatise. It also presents a radically different picture of the way in which Hume's project was rooted in the debates and controversies of his own time, placing the Treatise in an irreligious or anti-Chrisitan philosophical tradition that includes Hobbes, Spinoza and freethinking followers. Considered in these terms, Hume's Treatise constitutes the crowning achievement of the Radical Enlightenment. (shrink)

Bernard Williams is widely recognized as belonging among the greatest and most influential moral philosophers of the twentieth-century – and arguably the greatest British moral philosopher of the late twentieth-century. His various contributions over a period of nearly half a century changed the course of the subject and challenged many of its deepest assumptions and prejudices. There are, nevertheless, a number of respects in which the interpretation of his work is neither easy nor straightforward. One reason for this is that (...) both his views and his methods evolved and shifted in significant ways, especially around the time that he wrote and published Ethics and the Limits of Philosophy (i.e. the early 1980s). One way of gauging and assessing these changes in Williams’ views and outlook is to consider his relationship and attitude to other philosophers during this period. Of particular interest is his changing attitude to the moral philosophy of David Hume. This relationship is of considerable importance, not only because it serves as a useful tool for the interpretation of Williams’ views but also because it provides us with some critical insight into the respective strengths and weaknesses of both Hume’s and Williams’ contributions. -/- . (shrink)

In his note 'Paul Russell on Hume's "Reconciling Project"' {Mind, 1984, pp. 587-8) Professor Flew makes two criticisms of my note 'On the Naturalism of Hume's "Reconciling Project"' {Mind, 1983, pp. 593-600). They are: (1) that 'nowhere does Russell take note of the fact that Hume left us two treatments "Of Liberty and Necessity", two treatments which are at least in emphases andtone of presentation very different'; and (2) that I must be 'prepared to offer and to defend some alternative (...) reading' of the first three paragraphs of the first Enquiry discussion 'Of Liberty and Necessity' where Hume suggests that 'the wholecontroversy has hitherto turned merely upon words' {EHU, p. 81—my emphasis: this and later page references are to the Selby-Bigge editions). As regards the first criticism, I refer the reader to my second footnote where I do in fact, quite explicitly, note that Hume left us two treatments 'Of Liberty and Necessity'. In this footnote I point out that my description of Hume's arguments as compattbtltst arguments 'accords somewhat more with the "reconciling" spirit of the Enquiry than with that of the Treatise where Hume tends to identify liberty with liberty of indifference' (p. 593). Obviously in any discussion note there is limited space, and therefore I could not discuss at length complexities which were not of immediate relevance to my alternative interpretation. However, contrary to what Flew claims, I do mention that there are two treatments and that they differ in emphases and tone. (shrink)

In 1911, Bergson visited Britain for a number of lectures which led to his increasing popularity. Russell personally encountered Bergson during his lecture at University College London on the 28th of October, and on the 30th of October Bergson attended one of Russell’s lectures. Russell went on to write a number of critical articles on Bergson, contributing to the hundreds of publications on Bergson which ensued following these lectures. Russell’s critical writings have been seen as part of a history of (...) controversies between so-called ‘Continental’ and ‘Analytic’ philosophers in the twentieth century. Yet Russell’s engagement with Bergson’s thought comes as a response to a particular British form of Bergsonism and is involved with the wider phenomenon of the British import of Bergsonism (by figures connected in different ways to Russell, such as Hulme, Wildon Carr or Eliot). Though this may challenge the view of Russell and Bergson as enacting an early version of the ‘Analytic’-‘Continental’ divide, there are however some particular characterisations of Bergson by Russell which contribute to the subsequent formation of the ‘rotten scene’ (Glendinning 2006: 69) of the divide in the second half of the twentieth century. (shrink)

Kant's most sustained discussion of obscure representations can be found in the first book of his Anthropology from a Pragmatic Point of View. What is puzzling is that in the middle of the section devoted to the topic, Kant asserts that “because this field can only be perceived in his passive side as a play of sensations, the theory of obscure representations belongs only to physiological anthropology, and so it is properly disregarded here.” So, do obscure representations belong to pragmatic (...) anthropology or not? Kant's official position is that they do not, yet the textual evidence—we find discussions of obscure representations in 20 years of his work on pragmatic anthropology—suggests that they do, in fact, belong here. Most of the literature on obscure representations focuses on their contribution to cognition and none has clarified what it would mean to assume a “pragmatic point of view” on obscure representations, and to study them in the context of pragmatic anthropology. My aim in this paper is to provide such clarification, focusing on Kant's discussion of our propensity to “play with” obscure representations and what he calls our “art of obscuring.”. (shrink)

Russell claims that ordinary proper names are eccentric, i.e. that the semantic referent of a name is determined by the descriptive condition that the individual utterer of the name associates with the name. This is deeply puzzling, for the evidence that names are subject to interpersonal coordination seems irrefutable. One way of making sense of Russell’s view would be to claim that he has been systematically misinterpreted and did not, in fact, offer a semantic theory at all. Such a view (...) is put forward in Sainsbury Departing from Frege, Routledge, London, 2002). Sainsbury claims that Russellian descriptivism is not the theory that the thought in the mind of the speaker determines the semantic reference of a name, but simply a theory about the thought in the mind of the speaker using a name. I argue that the truth is subtly different, and points the way towards an intuitive explanation of Russell’s eccentricity. (shrink)

In the replies to my critics that follow I offer a more detailed account of the specific papers that they discuss or examine. The papers that they are especially concerned with are: “The Material World and Natural Religion in Hume’s Treatise” (Ryan) [Essay 3], “Hume’s Skepticism and the Problem of Atheism” (Fosl) [Essay 12], and “Hume’s Philosophy of Irreligion and the Myth of British Empiricism (Gautier) [Essay 16].

The philosophy of Samuel Clarke is of central importance to Hume’s Treatise. Hume’s overall attitude to Clarke’s philosophy may be characterized as one of systematic scepticism. The general significance of this is that it sheds considerable light on Hume’s fundamental “atheistic” or anti-Christian intentions in the Treatise. These are all claims that I have argued for elsewhere.’ In this paper I am concerned to focus on a narrower aspect of this relationship between the philosophies of Clarke and Hume. Specifically, I (...) will consider Hume’s views on the subjects of materialism and necessity in relation to Clarke’s enormously influential debate with Anthony Collins on these topics. I begin by describing the nature and context of this controversy; I then examine how Hume‘s positions on questions of materialism and necessity stand in relation to the positions and arguments taken up by Clarke and Collins; and finally I explain the deeper significance of these specific issues for Hume’s wider “atheistic” or anti-Christian objectives in the Treatise. Hume’s views on the closely related subjects of materialism and necessity, I maintain, constitute core elements of his “atheistic” project in the Treatise, and they manifest his basic antipathy to the theistic metaphysics of the Christian religion in general,and to the Newtonian cosmology of Clarke in particular. (shrink)

In this book, Russell examines Hume's notion of free will and moral responsibility. It is widely held that Hume presents us with a classic statement of a compatibilist position--that freedom and responsibility can be reconciled with causation and, indeed, actually require it. Russell argues that this is a distortion of Hume's view, because it overlooks the crucial role of moral sentiment in Hume's picture of human nature. Hume was concerned to describe the regular mechanisms which generate moral sentiments such as (...) responsibility, and Russell argues that his conception of free will must be interprted within this naturalistic framework. He goes on to discuss Hume's views about the nature and character of moral sentiment; the extent to which we have control over our moral character; and the justification of punishment. Throughout, Russell argues that the naturalistic avenue of interpretation of Hume's thought, far from draining it of its contemporary interest and significance, reveals it to be of great relevance to the ongoing contemporary debate - particuarly in relation to the views of P.F. Strawson and his influential paper "Freedom and Resentment". (shrink)

Recasting Hume and Early Modern Philosophy is a collection of essays that are all concerned with major figures and topics in the early modern philosophy. Most of the essays are concerned, more specifically, with the philosophy of David Hume (1711-1776). The sixteen essays included in this collection are divided into five parts. These parts are arranged under the headings of: (1) Metaphysics and Epistemology; (2) Free Will and Moral Luck; (3) Ethics, Virtue and Optimism; (4) Skepticism, Religion and Atheism; and (...) (5) Irreligion and the Unity of Hume’s Thought. A particularly important theme running through many of these essays is the subject of Hume’s irreligious aims and intentions. The fifth and final part of the collection is devoted to an articulation and defence of this specific understanding of Hume’s philosophical thought. (shrink)

In his The Problems of Philosophy Bertrand Russell presents us with his famous argument for representative realism. After a clear and accessible analysis of sensations, qualities and the multiplicity of perceptions of the qualities of physical objects, Russell concludes with a bold statement: -/- "The real table, if there is one, is not immediately known to us at all, but must be an inference from what is immediately known". -/- My argument and analysis strongly suggests that the conclusion that Russell (...) reaches in his argument is counterintuitive and incoherent. The philosophical statement that he presents on the table, in the opening pages of his famous Problems argument is fundamentally misconstrued, and as it stands, it is logically unacceptable. (shrink)

Russell’s second philosophy of time (1899–1913), which will be the subject of this paper, is of special interest for two reasons. (1) It was basic to his New Philosophy, later called the “philosophy of logical atomism”. In fact, this philosophy didn’t initially emerge in the period of 1914– 1919, as many interpreters (e.g. A. J. Ayer) suggest, but with the introduction of Russell’s second philosophy of time (and space). The importance of Russell’s second philosophy of time for his early and (...) middle philosophy can be seen from the fact that it survived the dramatic changes in his philosophy of August–December 1900, and of July 1905. There is of course no surprise about this point: it served as their fundament. (2) Russell’s second philosophy of time is a locus classicus of all so called B-theories of time which define it in terms of the relations of before, after and simultaneous between events or moments. 20th century philosophy; absolute theory of time; theory of time; order; relation; relationist theory of time; B-series. (shrink)

[First published in Italian as: “L’irreligione e lo spettatore imparziale nel sistema morale di Adam Smith”, in Rivista di Filosofia 3 (3):375-403 (2005). -/- Translated by E. Lecaldano.] -/- A number of commentators on Smith’s philosophy have observed that the relationship between his moral theory and his theological beliefs is “exceedingly difficult to unravel.” The available evidence, as generally presented, suggests that although Smith was not entirely orthodox by contemporary standards, he has no obvious or significant irreligious commitments or orientation. (...) Contrary to this view of things, this essay argues that behind the veneer of orthodoxy that covers Smith’s discussion in The Theory of the Moral Sentiments there are significant irreligious themes present in his work. -/- . (shrink)

Hume’s Letter from a Gentleman is an important document for Hume scholarship because, among other things, it serves as a useful tool for the interpretation and analysis of Hume’s philosophical intentions in the Treatise. The Letter itself, however, raises several difficult problems of interpretation. One of the most important of these concerns the identity of Hume’s “accuser“-the author of A Specimen of the Principles concerning Religion and Morality &c., to which Hume is responding in the Letter. Clearly the interpretation of (...) the Letter, and its relevance to the Treatise, will vary depending on who is identified as the source of the accusations against Hume, and what is made of this person’s motivation and philosophical commitments. The immediate difficulty is that the Specimen is presented anonymously, and thus conjectures must be made about the author on the basis of available evidence. (shrink)

This is a contribution to a Book symposium on The Limits of Free Will: Selected Essays by Paul Russell. Russell provides replies to three critics of The Limits of Free Will. The first reply is to Robert Wallace and focuses on the question of whether there is a conflict between the core compatibilist and pessimist components of the "critical compatibilist" position that Russell has advanced. The second reply is to Angela Smith's discussion of the "narrow" interpretation of moral responsibility responsibility (...) (as defended by R. Jay Wallace) and how best to respond to it. The third and last reply is concerned with Christopher Bennett's criticism of Russell's views concerning "motivational scepticism" and the possibility of pure practical reasons. (shrink)

There are few who would deny that P. F. Strawson’s “Freedom and Resentment” (1962) ranks among the most significant contributions to modern moral philosophy. Although any number of essays have been devoted to it, Pamela Hieronymi’s 'Freedom, Resentment, and the Metaphysics of Morals' is the first book-length study. The aim of Hieronymi’s study is to show that Strawson’s “central argument” has been “underestimated and misunderstood.” Hieronymi interprets this argument in terms of what she describes as Strawson’s “social naturalism”. Understood this (...) way, Hieronymi maintains, “the argument is powerful”. In what follows I argue that while Hieronymi’s discussion is stimulating and provides valuable insights into “Freedom and Resentment,” neither the interpretation advanced nor the social naturalist position that it describes is convincing. (shrink)

This introduction provides a brief overview of the issues and arguments that arise in Hume's _Dialogues concerning Natural Religion_ (1779). It also provides a few brief comments relating to the historical context in which this text should be interpreted , as well as an account of the place of the _Dialogues_ in relation to Hume's other philosophical works.

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)

“Responsibility After ‘Morality’: Strawson’s Naturalism and Williams’ Genealogy” -/- Although P.F. Strawson and Bernard Williams have both made highly significant and influential contributions on the subject of moral responsibility they never directly engaged with the views of each other. On one natural reading their views are directly opposed. Strawson seeks to discredit scepticism about moral responsibility by means of naturalistic observations and arguments. Williams, by contrast, employs genealogical methods to support sceptical conclusions about moral responsibility (and blame). This way of (...) reading their views depends, however, on the assumption that the concept of responsibility that Strawson aims to defend is the same as Williams aims to discredit. The conception of responsibility that Williams aims to discredit is one that is based around the assumptions and aspirations of “the morality system”. This paper argues that while there is a plausible way of interpreting Strawson’s naturalism that uncouples it from the assumptions of “the morality system”, there remain significant differences between Strawson and Williams. More specifically, even if Strawson’s understanding of moral responsibility abandons the (narrow) assumptions of “morality”, Strawson is still committed to “conservative” and “optimistic” conclusions about moral responsibility that cannot be sustained. [March 2022] -/- . (shrink)

In "Pascal's Mugging" (Bostrom 2009), Pascal gives away his wallet for an extremely tiny chance of an extremely large reward. In this continuation of Bostrom's story, Pascal's friend counsels him to take into account the possibility of making mistakes about his true expected utilities, and they consider to what extent this will help Pascal make plans to avoid future muggings.

The argument and discussion in this paper begins from the premise that Hume was an atheist who denied the religious or theist hypothesis. However, even if it is agreed that that Hume was an atheist this does not tell us where he stood on the question concerning the value of religion. Some atheists, such as Spinoza, have argued that society needs to maintain and preserve a form of “true religion”, which is required for the support of our ethical life. Others, (...) such as D’Holbach have argued that religion is not only false it is pernicious and it should be eradicated. This paper argues that Hume rejected both these proposals, on the ground that they rest, in different ways, on excessively optimistic assumptions. The sensible, practical form of atheism that Hume defends has a more modest and realistic aim, which is simply to restrict and limit the most pernicious forms of religion. Understood this way, Hume’s practical atheism is very different from the forms of “old” atheism associated with Spinoza and D’Holbach, as well as from the “new atheism” of thinkers such as Dawkins and Dennett. -/- Reprinted in Paul Russell, "Recasting Hume and Early Modern Philosophy: Selected Essays" (New York: Oxford University Press, 2021): 340-383. (shrink)

Should we make significant sacrifices to ever-so-slightly lower the chance of extremely bad outcomes, or to ever-so-slightly raise the chance of extremely good outcomes? *Fanaticism* says yes: for every bad outcome, there is a tiny chance of extreme disaster that is even worse, and for every good outcome, there is a tiny chance of an enormous good that is even better. I consider two related recent arguments for Fanaticism: Beckstead and Thomas's argument from *strange dependence on space and time*, and (...) Wilkinson's *Indology* argument. While both arguments are instructive, neither is persuasive. In fact, the general principles that underwrite the arguments (a *separability* principle in the first case, and a *reflection* principle in the second) are *inconsistent* with Fanaticism. In both cases, though, it is possible to rehabilitate arguments for Fanaticism based on restricted versions of those principles. The situation is unstable: plausible general principles tell *against* Fanaticism, but restrictions of those same principles (with strengthened auxiliary assumptions) *support* Fanaticism. All of the consistent views that emerge are very strange. (shrink)

The present essay argues that Bergson’s account of the comic can only be fully appreciated when read in conjunction with his later metaphysical exposition of the élan vital in Creative Evolution and then by the account of fabulation that Bergson only elaborates fully three decades later in The Two Sources of Morality and Religion. The more substantive account of the élan vital ultimately shows that, in Laughter, Bergson misses his own point: laughter does not simply serve as a means for (...) correcting human behavior but is rather the élan vital’s vital summons, the demand of life itself, that human beings challenge their obligations, question their societal forms, and thereby create new and, for Bergson, more ideal forms of life and community. (shrink)

David Hume was clearly a critic of religion. It is still debated, however, whether or not he was an atheist who denied the existence of God. According to some interpretations he was a theist of some kind and others claim he was an agnostic who simply suspends any belief on this issue. This essay argues that Hume’s theory of belief tells against any theistic interpretation – including the weaker, “attenuated” accounts. It then turns to the case for the view that (...) Hume’s criticisms of theism were limited to the “soft” skeptical (agnostic) aim of discrediting theist arguments, and shows that he is committed to a “harder” skeptical view that denies the theist hypothesis (in all its forms). Hume’s atheistic commitments are, the paper concludes, entirely consistent with his mitigated skeptical principles. (shrink)

In his Treatise of Human Nature Hume makes clear that it is his aim to make moral philosophy more scientific and properly grounded on experience and observation. The “experimental” approach to philosophy, Hume warns his readers, is “abstruse,” “abstract” and “speculative” in nature. It depends on careful and exact reasoning that foregoes the path of an “easy” philosophy, which relies on a more direct appeal to our passions and sentiments . Hume justifies this approach by way of an analogy concerning (...) the relevance of anatomy to painting. “The anatomist,” he says, “ought never to emulate the painter.” At the same time, the painter cannot afford to ignore the anatomist: An anatomist [...] is admirably fitted to give advice to a painter ... We must have an exact knowledge of the parts, their situation and connexion, before we can design with any elegance or correctness. And thus the most abstruse speculations concerning human nature, however cold and uninteresting, become subservient to practical morality; and may render this latter science more correct in its precepts, and more persuasive in its exhortations. As these remarks suggest, Hume’s anatomy of virtue is not without its own practical aims and objectives. It is advanced with a view to identifying and carefully delineating the true foundations of morality in human nature and correcting our practices in light of this. With this improvement in our understanding of the nature and basis of virtue, we can better appreciate the way in which virtue secures happiness for ourselves and others and may also avoid the distortions and corruptions of morality by religious superstition. (shrink)

Mechanistic explanations are often said to explain because they reveal the causal structure of the world. Conversely, dynamical models supposedly lack explanatory power because they do not describe causal structure. The only way for dynamical models to produce causal explanations is via the 3M criterion: the model must be mapped onto a mechanism. This framing of the situation has become the received view around the viability of dynamical explanation. In this paper, I argue against this position and show that dynamical (...) models can themselves reveal causal structure and consequently produce nonmechanistic, dynamical explanations. Taking the example of cell fates from systems biology, I show how dynamical models, and specifically the attractor landscapes they describe, identify the causes of cell differentiation and explain why cells select particular fates. These dynamical features of the system better fit Woodward’s (2010, 2018) criteria of specificity and proportionality and make them the best candidate causes of cell fates than mechanisms. I also show how these causes are irreducible and inaccessible to mechanistic models, making 3M unworkable and counterproductive in this case. Dynamical models can reveal dynamical causes and thereby provide causal explanations. (shrink)

The conventional wisdom has it that between 1905 and 1919 Russell was critical to pragmatism. In particular, in two essays written in 1908–9, he sharply attacked the pragmatist theory of truth, emphasizing that truth is not relative to human practice. In fact, however, Russell was much more indebted to the pragmatists, in particular to William James, as usually believed. For example, he borrowed from James two key concepts of his new epistemology: sense-data, and the distinction between knowledge by acquaintance and (...) knowledge by description. Reasonable explanation of this is that, historically, Russell’s logical realism and James’s pragmatism have the same roots—the German philosopher Rudolph Hermann Lotze (1817–1881). In this paper we are going to explore the fact that in 1905, under Lotze’s influence, Russell married propositions with beliefs. A few years later this step also made Russell prone to embrace the theory of truth-making that has its roots in James. In contrast to the concept of sense-data and to the distinction between knowledge by acquaintance and knowledge by description, however, the understanding that we believe propositions—and not, for example, simply grasp them—was in tension with Russell’s Principle of Extensionality, according to which propositions can be logically connected with other propositions only as truth-functions. The point is that when we judge a mind-relation (for example, a relation of belief) to a proposition, the latter cannot be determined as true or false. The two most talented pupils of Russell, Wittgenstein and Ramsey, severely criticized the central place propositional attitudes play in Russell’s logic. Wittgenstein analyzed “A believes that p” to “ ‘p’ says p” (5.542). Ramsey criticized Russell’s beliefs in propositions the other way round: He stressed that belief is an ambiguous term that can be interpreted for the better in the sense of pragmatism. Prima facie surprisingly, he maintained that his “pragmatism is derived from Mr Russell.” (1927: 51). (shrink)

Hume's Treatise of Human Nature was published in the form of three separate books. The first two, "Of the Understanding" and "Of the Pas- sions," were published in London in January 1739 by John Noon. The third, "Of Morals," was published independently in London by Thomas Longman in November 1740.2 The title and subtitles on all three books are the same: A Treatise of Human Nature: Being An Attempt to introduce the experimental Method of Reasoning into Moral Subjects. On the (...) title page of the first two books Hume employs an epigram from Tacitus: Rara temporumfelicitas, ubi sentire, quae velis; & quae sentias, dicere licet. ["Seldom are men blessed with times in which they may think what they like and say what they think."] On the title page of the third book this epigram is replaced by an epigram taken from the ninth book of Lucan's Pharsalia: Durae semper virtutis amator, Quaere quid est virtus, et posce exemplar honesti. ["Thou that to virtue ever wer't inclined, learn what it is, how certainly defin'd, and leave some perfect Rule to guide Mankind."] Given the context and the prominence of these epigrams, it is a curious fact that they have attracted little or no attention or comment from Hume scholars. -/- In this paper I argue that Hume's use of the epigram from Lucan is directly relevant to his use of the epigram from Tacitus. The epigrams flag very clearly the anti-Christian nature of Hume's intentions in the Treatise and his affiliations with and allegiance to an anti-Christian tradition of thought that stretches from Hobbes and Spinoza in the late seventeenth century to a circle of anti-Newtonian radical freethinkers that appeared in Britain in the first part of the eighteenth century. In more general terms these epigrams are a notable and illuminating example of esoteric communication in this context, and they indicate that the Treatise has an important place in the literature of the radical enlightenment. (shrink)

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy (...) due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein. (shrink)

This paper considers the question of “atheism” as it arises in Hume’s _Dialogues_. It argues that the concept of “atheism” involves several signficiant ambiguities that are indicative of philosophical and interpretive disagreements of a more substantial nature. It defends the view that Philo’s general sceptical orientation accurately represents Hume’s own “irreligious” and “atheistic” commitments, both in the _Dialogues_ and in his other (“earlier”) writings. While Hume was plainly a “speculative atheist”, his “practical atheism” was targeted more narrowly against “superstition” - (...) as opposed to deism or religion of a more “philosophical” kind. (shrink)

The central thesis of this paper is that the scope and structure of Hume's Treatise of Human Nature is modelled, or planned, after that of Hobbes's The Elements of Law and that in this respect there exists an important and unique relationship between these works. This relationship is of some importance for at least two reasons. First, it is indicative of the fundamental similarity between Hobbes's and Hume's project of the study of man. Second, and what is more important, by (...) recognizing this relationship between Hume's and Hobbes's works we can come to appreciate the unity of the project of the Treatise itself. My discussion will proceed in three stages. In section I present the evidence for my central thesis. In the second section I shall consider why Hume does not, as one might expect, acknowledge this important debt to Hobbes in the Introduction to the Treatise or in the Abstract. Finally, in the third section I shall note a few points of some importance to the understanding of Hume's philosophy which this relationship between Hobbes's and Hume's work touches upon. (shrink)