This paper examines Russell's substitutional theory of classes and relations, and its influence on the development of the theory of logical types between the years 1906 and the publication of Principia Mathematica (volume I) in 1910. The substitutional theory proves to have been much more influential on Russell's writings than has been hitherto thought. After a brief introduction, the paper traces Russell's published works on type-theory up to Principia. Each is interpreted as presenting a (...) version or modification of the substitutional theory. New motivations for Russell's 1908 axiom of infinity and axiom of reducibility are revealed. (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)

Economic models are founded in the idea of taking individuals' preferences as both known and given. This article explores the evolution of personal preferences, within a context of both entrepreneurial discovery and Objectivist philosophy. It begins by formalizing Ayn Rand's theory of Objectivism applied to human values, and continues by modeling preference changes similar to Schumpeter's theory of creative destruction—a process of self-discovery. Next the role of societal factors is examined in forming shared preference sets. Finally, the article (...) describes how the strength of human preferences is used to narrow choice sets in the presence of greater consumption options. (shrink)

This volume of Bertrand Russell's Collected Papers finds Russell focused on writing Principia Mathematica during 1905–08. Eight previously unpublished papers shed light on his different versions of a substitutional theory of logic, with its elimination of classes and relations, during 1905-06. A recurring issue for him was whether a type hierarchy had to be part of a substitutional theory. In mid-1907 he began writing up the final version of Principia , now using a ramified theory (...) of types, and eleven unpublished drafts from 1907-08 deal with this. Numerous letters show his thoughts on the process. The volume's 80-page introduction covers the evolution of his logic from 1896 until 1909, when volume I of Principia went to the printer. (shrink)

This book explores an important central thread that unifies Russell's thoughts on logic in two works previously considered at odds with each other, the Principles of Mathematics and the later Principia Mathematica. This thread is Russell's doctrine that logic is an absolutely general science and that any calculus for it must embrace wholly unrestricted variables. The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory. On Landini's showing, the substitutional theory reveals (...) the unity of Russell's philosophy of logic and offers new avenues for a genuine solution of the paradoxes plaguing Logicism. (shrink)

According to deontic justice theory, individuals often feel principled moral obligations to uphold norms of justice. That is, standards of justice can be valued for their own sake, even apart from serving self-interested goals. While a growing body of evidence in business ethics supports the notion of deontic justice, skepticism remains. This hesitation results, at least in part, from the absence of a coherent framework for explaining how individuals produce and experience deontic justice. To address this need, we argue (...) that a compelling, yet still missing, step is to gain further understanding into the underlying neural and psychological mechanisms of deontic justice. Here, we advance a theoretical model that disentangles three key processes of deontic justice: The use of justice rules to assess events, cognitive empathy, and affective empathy. Together with reviewing neural systems supporting these processes, broader implications of our model for business ethics scholarship are discussed. (shrink)

In his 1903 Principles of Mathematics, Russell holds that “it is a characteristic of the terms of a proposition”—that is, its “logical subjects”—“that any one of them may be replaced by any other entity without our ceasing to have a proposition”. Hence, in PoM, Russell holds that from the proposition ‘Socrates is human’, we can obtain the propositions ‘Humanity is human’ and ‘The class of humans is human’, replacing Socrates by the property of humanity and the class of humans, respectively. (...) Hence also, in PoM, Russell accepts the doctrine of the unrestricted variable: if we replace a logical subject of a proposition by a variable to yield a propositional function, the range of that variable includes absolutely every entity. For absolutely any entity can be taken as a value of that variable to yield a proposition, true or false. The doctrine of the unrestricted variable is thus incompatible with any type-theoretic metaphysics, according to which only entities of a certain restricted type can replace a logical subject of a given proposition so as to yield another proposition. (shrink)

In his 1903 Principles of Mathematics, Russell holds that “it is a characteristic of the terms of a proposition”—that is, its “logical subjects”—“that any one of them may be replaced by any other entity without our ceasing to have a proposition”. Hence, in PoM, Russell holds that from the proposition ‘Socrates is human’, we can obtain the propositions ‘Humanity is human’ and ‘The class of humans is human’, replacing Socrates by the property of humanity and the class of humans, respectively. (...) Hence also, in PoM, Russell accepts the doctrine of the unrestricted variable: if we replace a logical subject of a proposition by a variable to yield a propositional function, the range of that variable includes absolutely every entity. For absolutely any entity can be taken as a value of that variable to yield a proposition, true or false. The doctrine of the unrestricted variable is thus incompatible with any type-theoretic metaphysics, according to which only entities of a certain restricted type can replace a logical subject of a given proposition so as to yield another proposition. (shrink)

From 1905–1908 onward, Russell thought that his new ‘substitutional theory’ provided him with the right framework to resolve the set-theoretic paradoxes. Even if he did not finally retain this resolution, the substitutional strategy was instrumental in the development of his thought. The aim of this paper is not historical, however. It is to show that Russell's substitutional insight can shed new light on current issues in philosophy of mathematics. After having briefly expounded Russell's key notion of (...) a ‘structured variable’, I connect it to two ongoing discussions: the Caesar problem, and absolute generality. (shrink)

The paper argues that philosophers commonly misidentify the substitutivity principle involved in Russell’s puzzle about substitutivity in “On Denoting”. This matters because when that principle is properly identified the puzzle becomes considerably sharper and more interesting than it is often taken to be. This article describes both the puzzle itself and Russell's solution to it, which involves resources beyond the theory of descriptions. It then explores the epistemological and metaphysical consequences of that solution. One such consequence, it argues, (...) is that Russell must abandon his commitment to propositions. (shrink)

Bertrand Russell was one of the greatest logicians since Aristotle, and one of the most important philosophers of the past two hundred years. As we approach the 125th anniversary of the Nobel laureate's birth, his works continue to spark debate, resounding with unmatched timeliness and power. The Problems of Philosophy, one of the most popular works in Russell's prolific collection of writings, has become core reading in philosophy. Clear and accessible, this little book is an intelligible and stimulating guide to (...) those problems of philosophy which often mistakenly lead to its status as too lofty and abstruse for the lay mind. Focusing on problems he believes will provoke positive and constructive discussion, Russell concentrates on knowledge rather than metaphysics, steering the reader through his famous 1910 distinction between "knowledge by acquaintance and knowledge by description," and introducing important theories of Descartes, Kant, Hegel, Hume, Locke, Plato, and others to lay the foundation for philosophical inquiry by general readers and scholars alike.With a new introduction by John Perry, this valuable work is a perfect introduction to the field and will continue to stimulate philosophical discussion as it has done for nearly forty years. (shrink)

This note presents a transcription of Russell's letter to Hawtrey of 22 January 1907 accompanied by some proposed emendations. In that letter Russell describes the paradox that he says "pilled" the "substitutional theory" developed just before he turned to the theory of types. A close paraphrase of the derivation of the paradox in a contemporary Lemmon-style natural deduction system shows which axioms the theory must assume to govern its characteristic notion of substituting individuals and propositions for (...) each other in other propositions. Other discussions of this paradox in the literature are mentioned. I conclude with remarks about the significance of the paradox for Russell. (shrink)

This note presents a transcription of Russell's letter to Hawtrey of 22 January 1907 accompanied by some proposed emendations. In that letter Russell describes the paradox that he says "pilled" the "substitutional theory" developed just before he turned to the theory of types. A close paraphrase of the derivation of the paradox in a contemporary Lemmon-style natural deduction system shows which axioms the theory must assume to govern its characteristic notion of substituting individuals and propositions for (...) each other in other propositions. Other discussions of this paradox in the literature are mentioned. I conclude with remarks about the significance of the paradox for Russell. (shrink)

This paper argues that human psychological resilience is a central virtue in sport and in human life generally. Despite its importance, it is an overlooked virtue in philosophy of sport and classical and contemporary virtue theory. The phenomenon of human resilience has received a great deal of attention recently in other quarters, however. There is a large and instructive empirical psychological literature on resilience, but connections to virtue theory are rarely drawn and there is no agreement about what (...) the concept refers to. This paper attempts to clarify the concept of resilience and explain how it fits into and supports a traditional Aristotelian conception of virtue. It shows how resilience figures centrally in sport and can extend and enrich our understanding of virtue and success in sport and of sport's internal values. The investigations into the nature of resilience in sport can also help us to understand better sport's contributions to human culture and well-being. (shrink)

This paper argues that human psychological resilience is a central virtue in sport and in human life generally. Despite its importance, it is an overlooked virtue in philosophy of sport and classical and contemporary virtue theory. The phenomenon of human resilience has received a great deal of attention recently in other quarters, however. There is a large and instructive empirical psychological literature on resilience, but connections to virtue theory are rarely drawn and there is no agreement about what (...) the concept refers to. This paper attempts to clarify the concept of resilience and explain how it fits into and supports a traditional Aristotelian conception of virtue. It shows how resilience figures centrally in sport and can extend and enrich our understanding of virtue and success in sport and of sport's internal values. The investigations into the nature of resilience in sport can also help us to understand better sport's contributions to human culture and well-being. (shrink)

In this article I try to show the philosophical continuity of Russell's ideas from his paradox of classes to Principia mathematica. With this purpose, I display the main results (descriptions, substitutions and types) as moments of the same development, whose principal goal was (as in his The principles) to look for a set of primitive ideas and propositions giving an account of all mathematics in logical terms, but now avoiding paradoxes. The sole way to reconstruct this central period in Russell (...) is to resort to unpublished manuscripts, which show the publications of these years to be the extremities of one same iceberg. Thus the logical problems (doubts about propositions, matrices and functions) are parallel to the ontological (the searching for genuine logical subjects) and methodological ones (the status of eliminative reduction). Paradoxes were the cause that the kind of (constructive) definition already applied by Russell, as an inheritance of Moorean analysis, obtained a new trait: ontological elimination, which, beginning with a ?no classes theory? and the theory of descriptions, led to a new theory of judgment (already present in manuscripts from 1906), ?incomplete symbols, and logical constructions. (shrink)

Intimacy and Alienation puts forward the author's unique paradigm for psychotherapy and counselling based on the assumption that each patient has suffered a disruption of the `self', and that the goal of the therapist is to identify and work with that disruption. Using many clinical illustrations, and drawing on self psychology, attachment therapy and theories of trauma, Russell Meares looks at the nature of self and how it develops, before going on to explore the form and feeling of experience when (...) self is disrupted in a traumatic way, and focusing on ways towards the restoration of the self. Written in an accessible style from the author's singular perspective, Intimacy and Alienation will appeal to professionals in the fields of psychotherapy, counseling, social work and psychiatry, as well as to students and the lay reader. (shrink)

Ten brilliant essays on logic appear in this collection, the work of one of the world’s best-known authorities on logic. In these thought-provoking arguments and meditations, Nobel Prize winner Bertrand Russell challenges the romantic mysticism of the 19th century, positing instead his theory of logical atomism. These essays are categorized by Russell as "entirely popular" and "somewhat more technical." The former include the well-known title essay plus "A Free Man’s Worship" and "The Place of Science in a Liberal Education"; (...) the latter comprise "On the Notion of Cause" and "Knowledge by Acquaintance and Knowledge by Description," along with other essays written in the cogent and witty style for which their author is justly renowned. (shrink)

This third volume of Boston Studies in the Philosophy of Science contains papers which are based upon Colloquia from 1964 to 1966. In most cases, they have been substantially modified subsequent to presentation and discussion. Once again we publish work which goes beyond technical analysis of scientific theories and explanations in order to include philo sophical reflections upon the history of science and also upon the still problematic interactions between metaphysics and science. The philo sophical history of scientific ideas has (...) increasingly been recognized as part of the philosophy of science, and likewise the cultural context of the genesis of such ideas. There is no school or attitude to be taken as de fining the scope or criteria of our Colloquium, and so we seek to under stand both analytic and historical aspects of science. This volume, as the previous two, constitutes a substantial part of our final report to the U. S. National Science Foundation, which has continued its support of the Boston Colloquium for the Philosophy of Science by a grant to Boston University. That report will be concluded by a subse quent volume of these Studies. It is a pleasure to record our thanks to the Foundation for its confidence and funds. We dedicate this book to the memory of Norwood Russell Hanson. During this academic year of 1966-67, this beloved and distinguished American philosopher participated in our Colloquium, and he did so before. (shrink)

The present study was designed to explore the relationship between self-reported dissociative experiences and performance in tasks eliciting right-hemisphere processing load. Thirty-four participants performed a vigilance task in two conditions: with task-irrelevant negative-arousing pictures and task-irrelevant neutral pictures. Dissociation was assessed with the Dissociative Experience Scale. Consistent with theories positing right-hemisphere deregulation in high non-clinical dissociators, dissociative experiences correlated with greater vigilance decrement only in the negative picture condition. As both the vigilance task and negative picture processing are right lateralized, (...) this result provides support for a right-hemisphere dysfunction in high dissociators, at least in negative conditions. (shrink)

Norman Kretzmann's recent analysis of the natural lawslogan ``lex iniusta non est lex'' (an unjust law is nota law) demonstrates the coherence of the slogan andmakes a case for its practical value, but I shallargue that it also ends up showing that the sloganfails to mark any interesting conceptual or practicaldivision between natural law and legal positivistviews about the nature of law. I argue that this is ahappy result. The non-est-lex slogan has been used toexaggerate the extent of disagreement about (...) the natureof law and has diverted critics of natural law theoryfrom recognizing that the main disagreement betweennatural lawyers and legal positivists centres ontheories of practical reason and how they affect ourunderstanding of the relationship between law andmorality. This extends the debate about the nature oflaw somewhat beyond the traditional boundaries ofphilosophy of law, but these boundaries are due inpart to the diversion created by debate over thenon-est-lex slogan. Recognizing that the non-est-lexslogan fails on its own to mark any interestingpractical or conceptual division between natural lawtheories and legal positivism should therefore focusand encourage debate on matters of genuine substancebetween these outlooks. The disagreement, however, mayturn out to be primarily metaphysical and explanatoryand not normative in nature. (shrink)

In the third and final part of his A Theory of Determinism (TD) Ted Honderich addresses the fundamental question concerning “the consequences of determinism.” The critical question he aims to answer is what follows if determinism is true? This question is, of course, intimately bound up with the problem of free will and, in particular, with the question of whether or not the truth of determinism is compatible or incompatible with the sort of freedom required for moral responsibility. It (...) is Honderich’s aim to provide a solution to “the problem of the consequences of determinism” and a key element of this is his articulation and defence of an alternative response to the implications of determinism that collapses the familiar Compatibilist/Incompatibilist dichotomy. Honderich offers us a third way – the response of “Affirmation” (HFY 125-6). Although his account of Affirmation has application and relevance to issues and features beyond freedom and responsibility, my primary concern in this essay will be to examine Honderich’s theory of “Affirmation” as it concerns the free will problem. (shrink)

People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable (...) Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

‘Free action’ is subject to the causal theory of reference and thus that The essential nature of free actions can be discovered only by empirical investigation, not by conceptual analysis. Heller ’s proposal, if true, would have significant philosophical implications. Consider the enduring issue we will call the Compatibility Issue : whether the thesis of determinism is logically compatible with the claim that.

In order to explain that sentences containing empty definite descriptions are nevertheless true or false, Russell famously analyzes sentences of the form ‘The F is G’ as ‘There is exactly one F and it is G’. Against this it has been objected that Russell’s analysis provides the wrong truth-conditions when it comes to non-doxastic attitude ascriptions. For example, according to Heim, Kripke, and Elbourne (HKE), there are circumstances in which (1) is true and (2) is false. Hans wants the (...) ghost in his attic to be quiet tonight.Hans wants there to be exactly one ghost in his attic and for it to be quiet tonight. After all, the argument goes, unlike (2), (1) can be true without Hans wanting there to be exactly one ghost in his attic. Kaplan and Neale famously reply that the HKE objection presupposes that non-doxastic attitudes are closed under entailment, which they are not. For Rostworowski, on the other hand, the problematic principle used by the HKE objection is a substitutivity principle for non-doxastic attitude ascriptions. This is further supported by the fact that, as Elbourne points out, Russell’s analysis already leads to a problem similar to the HKE objection together with substitutivity alone. By questioning substitutivity for non-doxastic attitude ascriptions, Rostworowski tries to block both the HKE objection and Elbourne’s variant of the HKE objection. In this paper, I will argue that Russell’s analysis of definite descriptions leads to a variant of the HKE objection even in the context of doxastic attitude ascriptions. Since, as we will see, doxastic attitude ascriptions do not seem to suffer from the substitutivity problems discussed by Rostworowski in the context of non-doxastic attitude ascriptions, this will further exacerbate the problem for Russell’s analysis. I will then discuss the possibility to reject substitutivity for doxastic attitude ascriptions using a contextualist analysis of attitude ascriptions. However, we will see that, independent of whether we accept substitutivity for doxastic attitude ascriptions, a complete solution of the doxastic problem has to reject Russell’s analysis of the truth-conditions of sentences of the form ‘The F is G’. Concluding, I will show that, unlike Russell’s analysis, the Frege–Strawson analysis of definite descriptions, according to which a sentence of the form ‘The F is G’ presupposes that there is exactly one F, rather than asserting it, provides an explanation of the HKE objection, Elbourne’s variant of the HKE objection, and the doxastic problem presented in this paper. This will speak not only in favor of a Fregean analysis of definite descriptions, but also of a Fregean conception of propositions. (shrink)

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.

Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response.

Norman Kretzmann''s recent analysis of the natural lawslogan ``lex iniusta non est lex'''' (an unjust law is nota law) demonstrates the coherence of the slogan andmakes a case for its practical value, but I shallargue that it also ends up showing that the sloganfails to mark any interesting conceptual or practicaldivision between natural law and legal positivistviews about the nature of law. I argue that this is ahappy result. The non-est-lex slogan has been used toexaggerate the extent of disagreement about (...) the natureof law and has diverted critics of natural law theoryfrom recognizing that the main disagreement betweennatural lawyers and legal positivists centres ontheories of practical reason and how they affect ourunderstanding of the relationship between law andmorality. This extends the debate about the nature oflaw somewhat beyond the traditional boundaries ofphilosophy of law, but these boundaries are due inpart to the diversion created by debate over thenon-est-lex slogan. Recognizing that the non-est-lexslogan fails on its own to mark any interestingpractical or conceptual division between natural lawtheories and legal positivism should therefore focusand encourage debate on matters of genuine substancebetween these outlooks. The disagreement, however, mayturn out to be primarily metaphysical and explanatoryand not normative in nature. (shrink)

Hume's place in history -- Moral psychology -- Strategic analysis -- Convention -- Political theory -- Justice as order -- Utilitarianism -- Value theory -- Retrospective.

Fried and Kollár constructed a fully faithful functor from the category of graphs to the category of fields. We give a new construction of such a functor and use it to resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure${\cal S}$, there exists a countable field${\cal F}$of arbitrary characteristic with the same essential computable-model-theoretic properties as${\cal S}$. Along the way, we develop a new “computable category theory”, and prove that our (...) functor and its partially defined inverse are computable functors. (shrink)