Russell: Logic and Philosophy of Logic, Misc

According to what has long been the dominant school of thought in analytic meta-ontology––defended not only by W. V. O. Quine, but also by Bertrand Russell, Alvin Plantinga, Peter van Inwagen, and many others––the meaning of ‘there is’ is identical to the meaning of ‘there exists.’ The most (in)famous aberration from this view is advanced by Alexius Meinong, whose ontological picture has endured extensive criticism (and borderline abuse) from several subscribers to the majority view. Meinong denies the identity of being (...) and existence. That is, he denies that ‘there is’ and ‘there exists’ are semantically equivalent, and espouses a theory according to which there are things that do not exist. Here I defend a revised version of this view, which I call “Noncontradictory Neo-Meinongianism.” Focusing primarily on van Inwagen’s arguments in “Meta-Ontology” (1998), I argue that Noncontradictory Neo-Meinongianism is, on commonsensical grounds, preferable to the meta-ontological theories of van Inwagen and Meinong. (shrink)

Russell’s role in the controversy about the paradoxes of material implication is usually presented as a tale of how even the greatest minds can fall prey to basic conceptual confusions. Quine accused him of making a silly mistake in Principia Mathematica. He interpreted “if- then” as a version of “implies” and called it material implication. Quine’s accusation is that this decision involved a use-mention fallacy because the antecedent and consequent of “if-then” are used instead of being mentioned as the premise (...) and the conclusion of an implication relation. It was his opinion that the criticisms and alternatives to the material implication presented by C. I. Lewis and others would never be made in the first place if Russell simply called the Philonian construction “material conditional” instead of “material implication”. Quine’s interpretation of the topic became hugely influential if not universally accepted. This paper will present the following criticisms against this interpretation: (1) the notion of material implication does not involve a use-mention fallacy, since the components of “if-then” are mentioned and not used; (2) Quine’s belief that the components of “if-then” are used was motivated by a conditional-assertion view of conditionals that is widely controversial and faces numerous difficulties; (3) if anything, it was Quine who could be accused of fallacious reasoning: he ignored that in the assertion of a conditional is the whole proposition that is asserted and not its constituents; (4) the Philonian construction remains counter-intuitive even if it is called “material conditional”; (5) the Philonian construction is more plausible when it is interpreted as a material implication. (shrink)

I argue that, in the period 1910–15, Bertrand Russell’s theory of existence is inconsistent with his theory of acquaintance. This inconsistency not only highlights that Russell’s thinking about existence is bound up with his epistemology, but also shows that it is only in 1918–19 that he finally comes to his influential higher-order theory of existence. Finally, I briefly argue that Russell’s eventual rejection of the distinction between being and existence goes hand-in-hand with his acceptance of a theory of universals according (...) to which they are essentially predicative. (shrink)

In _Principia Mathematica,_ Russell thought that there are irreducibly general judgements with their own mode of truth. They are true in virtue of what the elementary judgements they collect together correspond to. In _The Philosophy of Logical Atomism_, Russell thought that they are true in virtue of general facts. In 1910, general facts are not even considered in order to reject them. In 1918, Russell announces that it cannot be doubted that there are general facts. This raises an intriguing question. (...) What was it that led Russell to drop his 1910 view and drove him to the conclusion that there are general facts? I propose an answer that relies on a core aspect of Russell’s views on which he stayed firm throughout this period and on a preoccupation of his that began well before 1910: theories of truth and the problem of how false judgements are possible. I argue that Russell’s 1910 view failed to account adequately for the falsity of general judgements, while the correspondence theory of truth pushed him to accepting general facts. To round things off I also consider three independent arguments for general facts. (shrink)

In Chapter III of Principia Mathematica and several later writings, Russell gave a proof to show that definite descriptions are “incomplete symbols” that have “no meaning in isolation”. Despite the importance Russell seems to attach to the proof, many commentators have regarded it as obviously fallacious. Perkins has offered an interpretation that aims to rehabilitate the proof, but does not, I suggest, vindicate the conclusion about meaning in isolation in a sufficiently robust sense. This paper aims to close that gap (...) by offering an alternative interpretation according to which the proof relies on Russellian ideas about propositional structure. It concludes by revisiting the frequently debated question of whether Russell could have accepted a generalized-quantifier treatment of definite descriptions on which they denote second-order properties. (shrink)

In this chapter I critically examine the hitherto neglected influence that Dorothy Wrinch had on her teacher, friend, and informal thesis adviser, Bertrand Russell, and the puzzling fact that Russell never cited Wrinch’s mathematical papers on Principia Mathematica. Wrinch never reshaped Russell’s general outlook; indeed, Wrinch adopted as her own many of Russell’s 1911–1919 views about logic, philosophy, science, and their relationships that are characteristic of logic-centered twentieth-century analytic philosophy. Still, the influence was not just in one direction, from teacher (...) to student, but also ran the other way. And while Wrinch’s own life and ideas have enjoyed far more attention in recent literature, most historians of philosophy have, for too long, largely overlooked how Wrinch influenced Russell. Here I critically discuss how Wrinch influenced Russell and tell a more well-rounded story of mutual influence and collaboration. (shrink)

Russell’s use of incomplete symbols constituted progress in philosophy. They allowed Russell to make true negative existential claims, like ‘the present King of France does not exist’, and to analyse away logical constructs like tables. Russell’s view rested on the availability of complete symbols, logically proper names, which single out objects which we know by acquaintance, which we are committed to, and to whose existence discourse about apparent complexes can be reduced. Susan Stebbing enthusiastically embraced incomplete symbols for use in (...) negative existentials and in her innovative theory of metaphysical analysis. Yet she also raised trenchant objections to Russell’s assumption that complete symbols are purely referring expressions, equivalent to mere demonstration or pointing. Stebbing thought it could not be assumed that analysis terminates in objects of acquaintance. In this chapter I lay out Stebbing’s arguments and argue that they bear a striking similarity to those made by Stebbing’s former college’s Mistress, Constance Jones, whose influence on Russell is now largely forgotten but worth recovering. Jones defended a sense-reference (signification-denotation) distinction before Frege. Russell’s objections to that distinction in ‘On Denoting’ appear to borrow from Jones’s presentation of it. In Russell and Jones’s 1911 exchange at the Aristotelian Society, Jones’s arguments that names have signification and are more than mere noises or shapes, and that unless both signification and denotation are taken into account, all identity statements reduce to the trivial ‘a=a’ form, foreshadow Stebbing’s later arguments against complete symbols. (shrink)

This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between objects and functions. (...) Russell understood propositional functions as what is obtained when constituents of propositions are replaced by variables, but eventually denied that they were entities in their own right. Both encountered contradictions when supposing there to exist as many objects as functions, and both adopted views about the meaningfulness of higher-order discourse that were difficult to state from within their own strictures. (shrink)

American philosophical realism developed in two forms: “new” and “critical” realism. While the new realists sought to ‘emancipate’ ontology from epistemology and defended a direct theory of perception, the critical realists promoted a representationalist account of perception and thus argued for an epistemological dualism. Bertrand Russell’s early philosophical writings figured prominently in both of these American realist camps. However, while the new realists quite enthusiastically embraced the Russellian analytic style of reasoning (and Russell himself appreciated the American new realists as (...) anti-idealist allies), the critical realists were significantly more reserved toward Russell’s point of view. In the present paper, I identify the reasons for this difference in reception. In particular, I will show that the critical realists’ reservations pertained primarily to a more traditionalist—‘continental’—account of philosophy, whereas the neo-realists proved instrumental in setting the stage for later full-blown analytic philosophy in the United States. (shrink)

The chapter offers a reconstruction of a possible conversation between Russell and Wittgenstein about truth-tables and the Sheffer Stroke on the basis of jottings in Russell’s and Wittgenstein’s handwriting on folio 1v of Russell’s paper ‘Matter – The Problem Stated’. A direct comparison with Wittgenstein’s Notes on Logic and preserved letters in the Bertrand Russell Archives suggests 23 April 1913 as the most likely date for such a conversation. In conclusion, it can be assumed that Wittgenstein developed and used truth-tables (...) at that time, but considered them to be of secondary importance for logic compared to the ab-functions and ab-diagrams developed at the same time. The chapter also presents a facsimile picture of folio 1v. (shrink)

Russell derived many of his logical symbols from the pioneering notation of Giuseppe Peano. Principia Mathematica (1910–13) made these “Peanese” symbols (and others) famous. Here I focus on one of the more peculiar notational derivatives from Peano, namely, Principia ’s dual use of a squared dot or dots for both conjunction and scope. As Dirk Schlimm has noted, Peano always had circular dots and only used them to symbolize scope distinctions. In contrast, Principia has squared dots and conventions such that (...) some dots mark scope distinctions while others symbolize conjunction. How did this come to pass? In this paper I trace a genealogy of Principia ’s square dots back to Russell’s appropriation of Peano’s use of circular dots. Russell never explicitly justifies appropriating Peano’s notations to symbolize two distinct notions, but below I explain why Russell deployed Peano’s dot notations in this manner. Further, I argue that it was Cambridge University Press who squared the circular dots. (shrink)

I consider, in the light of Horsten’s and Ito’s paper, how the theory of arbitrary objects might help to make sense of Russell’s views on the nature of variables.

This Tractatus’s engagement with the issue of the nature of truth and falsity emerged from engagement with Russell. This engagement reverberated through the Vienna Circle and in particular affected Gödel. The Tractatus’s “elementary sentences” must be seen against the backdrop of Russell’s “multiple relation theory of judgment”, his theory of truth in Principia Mathematica, which Wittgenstein discussed at length with Russell in 1912–1913 and Gödel studied in 1929–1932. Russell’s approach was directed against both Idealism and William James’s pragmatist view of (...) truth. It aimed at a direct treatment of the distinction between truth and falsity in terms of particular, logically simple beliefs (judgments lacking in truth-functional and quantification complexity). Schlick rejected Russell’s view in favor of his more holistic correspondence theory, one which, however, tipped easily into pragmatism, conventionalism and verificationism. The Tractatus begins, rather, with Russell’s bottom-up approach truth, and then draws in two further ideas: (1) The need for a medium of representation and (2) The importance of modality (possibility and necessity) to logic. This approach was developed further in his later work, i.e., Philosophical Investigations.Aware of the Tractatus and Russell’s engagement with Wittgenstein on truth, Gödel continued to engage with Russell’s multiple relation theory of truth and Principia philosophically up through 1944. The parallel yet distinct engagements of Gödel and Wittgenstein with Russell on truth (and Vienna positivism) show that each regarded Russell’s view as requiring amendment. However, their philosophical differences with one another are not merely to be understood in terms of the dichotomy between conventionalism (the usual view of Wittgenstein) and Platonism (the usual view of Gödel). They must rather be seen to emerge from the original approach to truth we find in Russell. (shrink)

This article has two purposes: first, to describe some archival discoveries about Nicod’s family background, academic development and political life; and second, to publish and comment on a newly discovered article by Nicod about Russell. This article acclaims not only Russell’s achievements in logic and philosophy—as one might expect from such a devoted protégé as Nicod—but also (albeit only in glimpses permitted by France’s wartime censorship) his anti-war politics and writings. As the reader will realize, the two objectives are connected: (...) what the archives reveal and what the article illustrates is a hitherto underappreciated level of political awareness and pacifist commitment in Nicod. (shrink)

In this article we compare Fine’s theory of arbitrary objects with the theory of variables that Russell formulated in his Principles of Mathematics. We argue that Russell’s early theory of variables can be seen as a prefiguration of Fine’s theory of arbitrary objects. The main difference between Russell’s theory and Fine’s account lies in their account of dependence relations between variables. Fine develops a stable view of dependence between arbitrary objects, whereas no such view is presented in Principles of Mathematics. (...) We then sketch how Russell developed the notion of dependence between arbitrary objects in some of his subsequent works. (shrink)

'Wolterstorff (2009) provides an important explanation to the question: What caused the surprising resurgence in philosophical theology that has occurred over the last 50 years—a resurgence that rivals its zenith in the Middle Ages? This article supplements that with a more fine-grained answer to the question. Recent discoveries in Arthur Norman Prior’s correspondence with J.J.C Smart and Mary Prior, between November 1953 and August 1954 on the possibility of necessary existence, demonstrates the importance of Prior’s discussion of the Barcan formulae (...) in Time and Modality (1957) for the resurgence of analytic theology. The correspondence establishes that Prior’s discovery of tense-logic, and his discussion of quantified tense-logic constituted the perfect opportunity for him to challenge key anti-metaphysical assumptions in analytic philosophy, from which four important consequences can be drawn for the resurgence of philosophical theology. First, Prior’s discussion of time and existence challenged the idea of Russell (1945) and Findlay (1948) on the logical status of a necessary existing being. Second, the discussion challenged the Analytic school’s view of analysis and gave Prior the opportunity to introduce a different perspective on the relationship between logic and metaphysics. Third, it gave Prior a good opportunity to demonstrate that the then-prevailing attitude towards medieval logic was wrong. Fourth, it made it possible for Prior to demonstrate that the highly surprising metaphysical conclusions of quantified tense-logic brings modern logicians into a discussion with the theologically minded medieval logicians. (shrink)

Wittgenstein gave a clearly erroneous refutation of Russell’s logicist project. The errors were ably pointed out by Mark Steiner. Nevertheless, I was motivated by Wittgenstein and Steiner to consider various ideas about the natural numbers. I ask which notations for natural numbers are ‘buck-stoppers’. For us it is the decimal notation and the corresponding verbal system. Based on the idea that a proper notation should be ‘structurally revelatory’, I draw various conclusions about our own concept of the natural numbers.

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)

Artificial formal languages played a pivotal role in early analytic philosophy. The branch of analytic philosophy which focused on new formal logic is often called “Ideal Language Philosophy”. The aim of the present paper is to shed light on how and why more exactly those influential philosophers gave such an enormously central place for formal languages in their whole philosophical thought. Different ways these thinkers viewed the role of formal languages and their relation to colloquial languages are tracked.

This paper consists in a comparative study of the notions of negative fact in the early works of Russell and Wittgenstein. How to account for our ability to think both that it is false that what is not the case is the case and incorrect to think that it is true that what is not the case is the case? Are the truth and the correctness of such thoughts and of their expressions meant to be insured by the existence of (...) negative facts? Or do we need to think of negative facts differently? In his early works, Russell argues not only that negative facts exist, but also that the philosophical problem they suffice to solve is real. While in the Tractatus, Wittgenstein dissolves the philosophical problem by letting the superfluity and misleadingness of the affirmation of the existence of negative facts be seen as such. (shrink)

Bertrand Russell was neither the first nor the last philosopher to engage in serious theorizing about propositions. But his work between 1903, when he published The Principles of Mathematics, and 1919, when his final lectures on logical atomism were published, remains among the most important on the subject. And its importance is not merely historical. Russell’s rapidly evolving treatment of propositions during this period was driven by his engagement with – and discovery of – puzzles that either continue to shape (...) contemporary theorizing about propositions, or ought to do so. Russell’s creative responses to these puzzles also laid the foundation for many later accounts (most obviously, contemporary ‘Russellian’ accounts of propositions). In this entry we provide an opinionated overview of Russell’s influential treatment of propositions, with a focus on the evolution of his views from 1903 to 1919. A growing secondary literature is dedicated to Russell’s changing views during this period, and their often complex or opaque motivations. We do not intervene overmuch in this ongoing scholarly discussion. Instead, our aim is to trace some of the central motivations for Russell’s evolving views, and highlight the extent to which these motivations remain relevant to contemporary theorizing about propositions. (shrink)

The purpose of this paper is to demonstrate how Bertrand Russell depicts the relation of mysticism to three other areas of human activity: philosophy, science, and religion, and thus: its special role. In his essay Mysticism and Logic (1914), Russell defines mystical thinking as beliefs in (1) the existence of special insight, (2) the unity of all things, (3) the unreality of time, and (4) the effacement of the boundaries between good and evil. Although he considers full mysticism – as (...) a belief about the ontic structure of the world – to be erroneous – as a life attitude he attributes to it an element of wisdom that is lacking in other areas of human intellectual activity. Mysticism proves wrong also at the epistemological level, i.e. as a certain test of truth. But in its spirit of inquiry, it contains something that science also benefits from, and from which, therefore, scientific philosophy should take its cue. What additionally gives mysticism its value is the claim of impartial contemplation which gives rise to an attitude of love towards the whole world. Significantly, it was the combination of the best features of mystical thinking with scientific thinking and method which gave rise to Russell’s advocacy of scientific philosophy. In light of this, I argue that according to Russell mysticism is not an exclusively religious phenomenon, which is demonstrated, among other things, by the fact that he attributes two aspects of mysticism to the field of mathematics. (shrink)

The paper traces the development of Russell’s thinking about relations in 1898. Central to the story is what Russell called “the contradiction of relativity” which he thought to be endemic in the mathematical sciences. Through most of the year he tried to deal with it within the constraints of the neo-Hegelian doctrine of internal relations until, towards the end of the year, he abandoned the doctrine and with it neo-Hegelianism. Most importantly, he came to see that the contradiction of relativity (...) showed that it was impossible to treat transitive, asymmetrical relations as internal. The paper also throws new light on Russell’s earliest debts to G. E. Moore. (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)

By means of a reductio argument, Wittgenstein’s Tractatus calls into question the very idea that we can represent logical form. My paper addresses three interrelated questions: first, what conception of logical form is at issue in this argument? Second, whose conception of logic is this argument intended to undermine? And third, what could count as an adequate response to it? I show that the argument construes logical form as the universal, underlying correlation of any representation and the reality it represents. (...) I further show that the argument seeks to undermine core commitments of Frege’s and Russell’s. But the reductio, as I read it, is not intended to establish the falsity of any of their specific assumptions. Rather, its aim is to make manifest the indeterminacies that underlie the language in which these assumptions are framed, and establish the need for a transformation of that language. So understood, Wittgenstein’s argument exemplifies his idea that philosophy is not a theory, but an activity of elucidation. The interpretation I propose bears on one of the central debates in the literature, namely how we should understand Wittgenstein’s contention that his elucidations succeed despite being nonsensical. (shrink)

We adjust the notion of typicality originated with Russell, which was introduced and studied in a previous paper for general first-order structures, to make it expressible in the language of set theory. The adopted definition of the class ${\rm NT}$ of nontypical sets comes out as a natural strengthening of Russell's initial definition, which employs properties of small (minority) extensions, when the latter are restricted to the various levels $V_\zeta$ of $V$. This strengthening leads to defining ${\rm NT}$ as the (...) class of sets that belong to some countable ordinal definable set. It follows that ${\rm OD}\subseteq {\rm NT}$ and hence ${\rm HOD}\subseteq {\rm HNT}$. It is proved that the class ${\rm HNT}$ of hereditarily nontypical sets is an inner model of ${\rm ZF}$. Moreover the (relative) consistency of $V\neq {\rm NT}$ is established, by showing that in many forcing extensions $M[G]$ the generic set $G$ is a typical element of $M[G]$, a fact which is fully in accord with the intuitive meaning of typicality. In particular it is consistent that there exist continuum many typical reals. In addition it follows from a result of Kanovei and Lyubetsky that ${\rm HOD}\neq {\rm HNT}$ is also relatively consistent. In particular it is consistent that ${\cal P}(\omega)\cap {\rm OD}\subsetneq{\cal P}(\omega)\cap {\rm NT}$. However many questions remain open, among them the consistency of ${\rm HOD}\neq {\rm HNT}\neq V$, ${\rm HOD}={\rm HNT}\neq V$ and ${\rm HOD}\neq {\rm HNT}= V$. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Scientific Method in PhilosophyAuthor's note: Thanks to Gregory Landini for helpful clarifications.Gregory Landini. Repairing Bertrand Russell's 1913 Theory of Knowledge. (History of Analytic Philosophy.) London: Palgrave Macmillan, 2022. Pp. x, 397. isbn: 978-3-030-66355-1, us$139 (hb); 978-3-030-66356-8, us$109 (ebook).The title of this book might suggest a rather narrow study of a problem with Russell's Theory of Knowledge and a proposed solution. But as with Landini's first book, Russell's Hidden Substitutional (...) Theory, the title does not capture the full scope of the work. That work did not just point out the lingering substitution theory in Principia, but gave a sweeping view of Russell's overall development from Principles to Principia and one of the most detailed accounts of the formal system in Principia in any work. This work gives a sweeping overview of Russell's philosophy up to 1918, including not just Russell's multiple-relation theory of judgment, but the whole project of what Russell called scientific method in philosophy, which was the subtitle to his 1914 Our Knowledge of the ExternalWorld. Landini thinks this is the height of Russell's philosophy and proposes a fix to the problems which led Russell to abandon the project.Landini does not just present Russell's views during this period, but vigorously defends them, and not just the multiple-relation theory of judgment mostly associated with Theory of Knowledge, but also the views that logic should be understood as synthetic a priori, Russell's doctrine of acquaintance, including the acquaintance with universals as the grounding of synthetic a priori knowledge, and Russell's view that logic is the essence of philosophy. The book contains a wide range of discussions, including issues in philosophy of mind, theories of representation, theories of universals, evolution in philosophy, and the metaphysics of time and space.The book opens with an overview of some main themes, including Landini's view of the three main phases of Russell's post-idealist philosophy and his discussion of what he calls the revolutions in logic and mathematics. The three phases Landini has in mind are the Principles phase, the Principia phase [End Page 81] (which includes The Problems of Philosophy and Theory of Knowledge) and the neutral monist phase, which Landini sees as a mistake Russell made when he didn't see how to repair his 1913 work. According to Landini, the Principles era ends with the failure of the substitution theory from the po /ao paradox, the Principia era ends by 1918 with the abandonment of the attempt to finish the project of the 1913 Theory of Knowledge, and the neutral monist era begins in 1919 and continues through 1948. Landini wants to concentrate on repairing the view in the Principia era. Any remarks of Russell's from later rejecting, for example, his view of the subject, of acquaintance, of neutral monism, and remarks concerning logic as consisting of tautologies are to be rejected. Landini firmly believes that after abandoning the 1913 project, Russell took a wrong turn. Landini's discussion of the multiple-relation theory of judgment is therefore quite different from the other discussion in the literature, in that most commentators have thought Russell was correct in abandoning the theory and most think there is something to Wittgenstein's criticism. Landini thinks Wittgenstein's criticism was based on his new vision of logic, and that Russell should have rejected it and proceeded with the project of Theory of Knowledge.Given the controversies involved in these claims, I think the best way forward is an explication of Landini's new emphasis on the revolutions in logic and mathematics and some of the key claims Landini makes concerning the Principia era. Then we can look at the details of Landini's repairing of the project.the two revolutionsWhat is striking about Landini's more recent work is his emphasis on these two revolutions. One is the revolution within logic, which originates with Frege; the other a revolution in mathematics which originates with Weierstrass, von Staudt, Pieri and Cantor. While most historians of this period are aware of the important shifts... (shrink)

Jean Nicod, born in 1893, died far too young in 1924. He is remembered today as one of the foreign disciples (among them Ludwig Wittgenstein and Norbert Wiener) attracted to Cambridge by Russell after the publication of the Principia. We publish here a translation of “Les tendances philosophiques de M. Bertrand Russell”, which appeared in the Revue de Métaphysique et de Morale in 1922. The article is testimony not only to Nicod’s philosophical talents, but also of how Russell’s philosophy could (...) be received in France at the beginning of the twentieth century. (shrink)

Jin Yuelin’s logical and philosophical thought was deeply influenced by the philosophy of Bertrand Russell. The same influence existed also in the case of his view on truth, which was considerably close to the views maintained by Russell in his phase of logical atomism. In their investigations, Russell and Jin not only focused on similar topics, but also occupied similar philosophical positions, such as realism in the domain of ontology, empiricism in epistemology, and the correspondence theory in the domain of (...) the theory of truth. Nevertheless, Jin Yuelin’s view on truth was not only a mere imitation or recapitulation or even plagiarized copy of Russell’s, but also contained innovations and characteristics of its own. Jin, for example, emphasized certain general characteristics of truth, including the notion of truth as a relational quality, that truth is not a matter of degree, and that it is relative neither to time and space nor to the different types of knowledge. By so doing, Jin underlined the objectiveness, reliability, and transcendence of true propositions. By arguing that the correspondence theory of truth possessed strong foundations in common sense, Jin set out to defend the role of common sense in philosophy and science, maintaining that the former cannot be completely eliminated and arguing against the notion that any modification of a part of common sense would ultimately be founded on yet another segment of common sense. Moreover, Jin delivered his own response against the theory of the gap between “subject and object/the internal and the external,” which had been used to question the correspondence theory of truth, proposing a variety of cognitivist theory, which defined facts as “the given” (datum) that has been received and arranged. Most importantly, facts are cognitive constructs created on the basis of “the given” and encapsulate both subjectiveness and objectiveness. Jin Yuelin was a modern Chinese philosopher who had achieved profound erudition in both Chinese and Western thought, and, above all, an independent an profoundly original thinker. (shrink)

Conceptual engineers have made hay over the differences of their metaphilosophy from those of conceptual analysts. In this article, I argue that the differences are not as great as conceptual engineers have, perhaps rhetorically, made them seem. That is, conceptual analysts asking ‘What is X?’ questions can do much the same work that conceptual engineers can do with ‘What is X for?’ questions, at least if conceptual analysts self-understand their activity as a revisionary enterprise. I show this with a study (...) of Russell's metaphilosophy, which was just such a revisionary conception of conceptual analysis. (shrink)

As Alasdair Urquhart has noted, Bertrand Russell asserted that developing the theory of definite descriptions from 1905 was the first step towards solving the paradoxes that were finally resolved after 1908 in Principia Mathematica with the theory of types. I extend Urquhart’s suggestion that Russell was referring to the use of the notion of incomplete symbol in his solution to the paradoxes in his doomed theory “substitutional theory” of “Russellian propositions” in 1906. The Introduction to PM states that expressions for (...) propositions are incomplete symbols. This paper assesses the status of propositions in PM and connects the theory of types with the theory of descriptions. (shrink)

Dans une recension des Principles de Russell datant de 1904, Edwin B. Wilson accorde une attention particulière aux travaux de Peano et de ses collaborateurs. Son but était de mieux les faire connaître aux USA, où leurs œuvres « étaient malheureusement peu diffusées et n’étaient en outre pas spécialement appréciées ». La reconnaissance dont Peano bénéficiait aux yeux de Russell est amplifiée par Wilson, ce dernier estimant que la logique de Peano est bien plus qu’un nouvel « outil logique», tout (...) en considérant le logicien italien comme un précurseur du logicisme. Wilson s’oppose ainsi au jugement dépréciatif dont Peano faisait l’objet de la part de Poincaré. Dans le domaine de la géométrie en particulier, Wilson revendique diverses avancées accomplies par l’école de Peano par rapport à Hilbert en ce qui concerne la philosophie de la méthode axiomatique. (shrink)

In Tractatus 5.132 Wittgenstein argues that inferential justification depends solely on the understanding of the premises and conclusion, and is not mediated by any further act. On this basis he argues that Frege’s and Russell’s rules of inference are “senseless” and “superfluous”. This line of argument is puzzling, since it is unclear that there could be any viable account of inference according to which no such mediation takes place. I show that Wittgenstein’s rejection of rules of inference can be motivated (...) by taking account of his holistic construal of the relation between inference and understanding. (shrink)

How can we think or say what is not? If we equate what-is-not with nothing, then a thought of nothing is no thought at all; if we don’t, we are condemned to admit that what-is-not is, seemingly incurring self-refutation. In this paper, I address this paradox through the lenses of Parmenides, Plato, Russell, and the early Wittgenstein.

Traditionally, logic was viewed as a purely European tradition, founded in Ancient Greece by Aristotle and then developed in Catholic and Byzantine scholasticism as well as in Islamic and Judaic Ar...

I investigate why Frege rejected the theory of types, as Russell presented it to him in their correspondence. Frege claims that it commits one to violations of the law of excluded middle, but this complaint seems to rest on a dogmatic refusal to take Russell’s proposal seriously on its own terms. What is at stake is not so much the truth of a law of logic, but the structure of the hierarchy of the logical categories, something Frege seems to neglect. (...) To come to a better understanding of Frege’s response, I proceed to investigate his conception of the nature of the logical categories, and how it differs from Russell’s. I argue that, for Frege, our grasp of the logical categories cannot be severed from our grasp of the Begriffsschrift notation itself. Russell, on the other hand, attaches no such importance to notation. From Frege’s point of view, Russell has not succeeded in presenting an alternative conception of the logical hierarchy, since such a conception must go in tandem with the development of a notation. Moreover, Frege has good reasons to think that Russell’s proposal does not admit of a suitable notation. (shrink)

In the years following Bertrand Russell's visit in China, fragments from his work on mathematical logic and the foundations of mathematics started to enter the Chinese intellectual world. While up...

This paper concerns Bertrand Russell’s changing views on negative judgement. ‘Negative judgement’ is considered in the context of three theories of judgement that Russell put forth at different times: a dual relation theory ; a multiple relation theory ; a psychological theory of judgement. Four issues are singled out for a more detailed discussion: quality dualism versus quality monism, that is, the question whether judgement comes in two kinds, acceptance and rejection, or whether there is only one judgement-quality ; the (...) structure of negative judging; the problem of truth-making for negative facts; the different roles of ‘fact’ in Russell’s theories of truth. What emerges from the discussion is a rough chronology of Russell’s views on negative judgement during the period from 1903 to 1948. (shrink)

Bis heute wird Russells Philosophie nicht selten der Vorwurf gemacht, es fehle ihr an Kohärenz und Zusammenhang. Russell wird als ein Autor charakterisiert, der alle paar Jahre eine neue alternative Philosophie vorgeschlagen habe. In der vorliegenden Arbeit soll dagegen argumentiert werden, daß diese These auf einer zu oberflächlichen Ein–schätzung von Russells Denken beruht. Seine Philosophie verfügte sehr wohl über eine Einheit, die durch ihre charakteristische einheitsstiftende Methode vermittelt wurde. Dies war die Methode der logischen Analyse, die sich als Invariante in (...) allen Phasen seines Denkens durchhielt. Die logische Analyse erlaubte es, die in gegebenen Sach–verhalten enthaltenen Möglichkeiten zu explizieren. Philosophie wurde damit für Russell zu einer “Möglichkeitswissenschaft”. (shrink)

This journal issue opens with Bruno Langlet’s French translation of the first section of Bertrand Russell’s article “Meinong’s theory of complexes and assumptions” (1904). Russell, a defender of logical realism, provides an analysis of Meinong’s thoughts at the turn of the century - thoughts which ultimately lead to Object Theory. Russell aknowledges the deep agreement between himself and Meinong, at this period in time, concerning several principles, arguments and theses. In this first section of his article, Russell discusses Meinong’s higher-order (...) objects theory. (shrink)

This journal issue opens with Bruno Langlet and Jean-François Rosecchi’s French translation of the second and third sections of Bertrand Russell’s article “Meinong’s theory of complexes and assumptions (1904).” Russell, a defender of logical realism, provides an analysis of Meinong’s thoughts at the turn of the century - thoughts that ultimately lead to Object Theory. Russell aknowledges the deep agreement between himself and Meinong, at this period in time, concerning several principles, arguments and theses. In these sections of his article, (...) Russell exposes and analyses Meinong’s theory of assumptions (1902), then proceeds to an analysis of the object of mental acts. (shrink)

The article presents a comparative analysis of neo-realist views of Russell and Whitehead on cosmology in the first decades of the 20th century. It is noted that despite the similarity of the basic theoretico-methodological principles of their philosophizing, these thinkers formulated philosophicocosmological conceptions that differed significantly from each other. The reason for this was that Russell, at the epistemological level, used the theory of degrees of certainty, and on the logical one he developed the theory of descriptions, but Whitehead, in (...) contrast, was a supporter of the theory of critical realism in epistemology and the method of extensive abstraction in logic. All this influenced the former to pay more attention to the questions of analysis and, accordingly, to use the basic concepts of facts, logical atoms, and propositions, and the latter to focus on the question of synthesis and to consider the structure of being through the prism of concepts of actual entities, eternal objects and prehension. Hence the world for Russell is a static formation, and we only need to define its laws, and for the Whitehead world is a dynamic formation, the laws of which still need to be understood. It is emphasized that as a result, Russell’s cosmology rejected the previous metaphysics, but Whitehead’s cosmology aimed at finding the origins of modern cosmology in the writings of early thinkers. Nevertheless, it is argued that the cosmological teachings of both had a significant influence on the development of analytic philosophy. (shrink)

Aristotle, who has come to the forefront with the significant contributions to the development of logic throughout the history, has been the source of different perspectives for his subsequent studies with his philosophical system and logic. Many thinkers and logicians, including Russell, have come face to face with Aristotle and his ideas, regardless of whether they are positive or negative. The aim of this study is to explain the meaning of Aristotle's syllogism theory from Russell's point of view. In accordance (...) with this aim, firstly the effects of the theory of syllogism on the development of logic and then Aristotle's own explanations are given. The study continues by examining the formal and contextual details of syllogism inferences from Russell's consideration. In the conclusion part, it is stated how studies in logic, which grew in size with the important contributions of Aristotle, reached a different point with the tradition in which Russell was involved. In the light of all these explanations, it will be seen that Aristotle and Russell look for ways to think correctly and consistently in their work, and they want to express the validity of inferences according to formal patterns. (shrink)