The use of the symbol ∨for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and (...) Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of ∨ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed. (shrink)

In his 1918 logical atomism lectures, Russell argued that there are no molecular facts. But he posed a problem for anyone wanting to avoid molecular facts: we need truth-makers for generalizations of molecular formulas, but such truth-makers seem to be both unavoidable and to have an abominably molecular character. Call this the problem of generalized molecular formulas. I clarify the problem here by distinguishing two kinds of generalized molecular formula: incompletely generalized molecular formulas and completely generalized molecular formulas. I next (...) argue that, if empty worlds are logically possible, then the model-theoretic and truth-functional considerations that are usually given address the problem posed by the first kind of formula, but not the problem posed by the second kind. I then show that Russell’s commitments in 1918 provide an answer to the problem of completely generalized molecular formulas: some truth-makers will be non-atomic facts that have no constituents. This shows that the neo-logical atomist goal of defending the principle of atomicity—the principle that only atomic facts are truth-makers—is not realizable. (shrink)

Interactive theorem provers might seem particularly impractical in the history of philosophy. Journal articles in this discipline are generally not formalized. Interactive theorem provers involve a learning curve for which the payoffs might seem minimal. In this article I argue that interactive theorem provers have already demonstrated their potential as a useful tool for historians of philosophy; I do this by highlighting examples of work where this has already been done. Further, I argue that interactive theorem provers can continue to (...) be useful tools for historians of philosophy in the future; this claim is defended through a more conceptual analysis of what historians of philosophy do that identifies argument reconstruction as a core activity of such practitioners. It is then shown that interactive theorem provers can assist in this core practice by a description of what interactive theorem provers are and can do. If this is right, then computer verification for historians of philosophy is in the offing. (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)

This chapter contextualizes the book and summarizes its subsequent chapters.

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)

Bertrand Russell’s work in philosophy of science has been identified as a progenitor of structuralism in contemporary philosophy. It is often unclear, however, how the philosophical problems facing contemporary structuralist programmes relate to the problems of philosophy as Russell saw them. We contend that Russell has been mistakenly identified as an epistemic structural realist. The goal of this essay is to clarify the relationship between Russell’s programme and contemporary structuralist projects. In doing so, we hope to display the motivation for (...) a broad, truly Russellian structuralist project in the philosophy of science. (shrink)

Some philosophers, like Kripke, Williamson, Hawthorne, and Turri, have offered examples of claims that are allegedly contingent and a priori justifiable. If any of these examples is genuine, this would upend the traditional epistemological classification on which (a) all and only a priori justifiable claims are necessary and (b) all and only a posteriori ones are contingent. I argue here that these examples are not genuine. This conclusion is not new, but the strategy pursued here is to formalize these muchdiscussed (...) examples in symbolic logics. Once formalized, a perspicuous representation of their logical form will bring into sharp relief that these examples are not both contingent and a priori. Two takeaways are (1) that the traditional epistemological classification remains plausible and (2) that one’s proposed examples of contingent a priori claims should be supported by a formalization in one’s preferred background symbolic logic. (shrink)

This book examines Bertrand Russell’s complicated relationships to the women around him, and to feminism more generally. The essays in this volume offer scholarly reassessments of these relationships and their import for the history of feminism and of analytic philosophy. Russell is a founder of analytic philosophy. He has also been called a feminist due to his public, decades-long advocacy for women’s rights and equality of the sexes. But his private behavior towards wives and sexual partners, and his apparently dismissive (...) (occasionally public) responses to some women philosophers, raises the question of what sort of feminist (or chauvinist) Russell actually was. Focusing on women in Russell’s circle of acquaintance, including feminist activists and his philosophical interlocutors, this book casts new light on a timeless thinker’s feminism and the women who played critical roles in the making of analytic philosophy. (shrink)

This book offers a comprehensive critical survey of issues of historical interpretation and evaluation in Bertrand Russell's 1918 logical atomism lectures and logical atomism itself. These lectures record the culmination of Russell's thought in response to discussions with Wittgenstein on the nature of judgement and philosophy of logic and with Moore and other philosophical realists about epistemology and ontological atomism, and to Whitehead and Russell’s novel extension of revolutionary nineteenth-century work in mathematics and logic. Russell's logical atomism lectures have had (...) a lasting impact on analytic philosophy and on Russell's contemporaries including Carnap, Ramsey, Stebbing, and Wittgenstein. Comprised of 14 original essays, this book will demonstrate how the direct and indirect influence of these lectures thus runs deep and wide. (shrink)

The contact argument is widely cited as making a strong case against a gunk-free metaphysics with point-sized simples. It is shown here that the contact argument's reasoning is faulty even if all its background assumptions and desiderata for contact are accepted. Further, the simples theorist can offer both metric and topological accounts of contact that satisfy all the contact argument's desiderata. This indicates that the contact argument's persuasiveness stems from a tacit reliance on the thesis that objects in contact are (...) inseparable: the simples theorist must allow that separated objects might be in contact. The concluding section critically considers this contact-separability thesis and argues that rejecting it is not so terrible. The upshot of all this is that the contact argument is simply unconvincing. (shrink)

In this paper I argue that the two-dimensional character of Frege’s Begriffsschrift plays an epistemological role in his argument for the analyticity of arithmetic. First, I motivate the claim that its two-dimensional character needs a historical explanation. Then, to set the stage, I discuss Frege’s notion of a Begriffsschrift and Kant’s epistemology of mathematics as synthetic a priori and partly grounded in intuition, canvassing Frege’s sharp disagreement on these points. Finally, I argue that the two-dimensional character of Frege’s notations play (...) the epistemological role of facilitating our grasp of logical truths independently of intuition. The rest of this paper critically evaluates Frege’s view and discusses Macbeth’s account. (shrink)

I characterize and argue against the standard interpretation of logical atomism. The argument against this reading is historical: the standard interpretation of logical atomism (1) fails to explain how the view is inspired by nineteenth-century developments in mathematics, (2) fails to explain how logic is central to logical atomism, and (3) fails to explain how logical atomism is a revolutionary and new "scientific philosophy." In short, the standard interpretation is a bad history of logical atomism. A novel interpretation of the (...) view that repairs these difficulties is sketched in the concluding section. (shrink)

I claim that a relatively new position in philosophy of mathematics, pluralism, overlaps in striking ways with the much older Jain doctrine of anekantavada and the associated doctrines of nyayavada and syadvada. I first outline the pluralist position, following this with a sketch of the Jain doctrine of anekantavada. I then note the srrong points of overlaps and the morals of this comparison of pluralism and anekantavada.

Book Review: Samuel Lebens (2017) "Bertrand Russell and the Nature of Propositions: a History and Defense of the Multiple Relation Theory of Judgement".

I critically discuss a new proposal for a metaphysics of sense-data. This proposal is due to Peter Forrest. Forrest argues that, if we accept Platonism about universals, sense-data are best understood as structured universals–in particular, as structured universals with temporal and spatial properties as components. Against this proposal, I argue sense-data as structured universals are not universals at all.

I here defend logical atomism. This defense rests on reinterpreting logical atomism as a search for logical forms. This reinterpretation has two parts comprising six chapters. In the first part, I do some historically-driven recovery. In the introduction, I review the literature on Russell's logical atomism. In Chapter 1, I argue that the dominant interpretation of logical atomism is wrong on historical grounds: it accounts for neither the history of logical atomism nor for crucial elements of the logical atomist texts. (...) In Chapter 2, I then use Russell's writings to recover what I argue is the core of logical atomism. I explicate the critical notions and essential ingredients of logical atomism using "Principia Mathematica" as the archetype of logical atomism. I argue that logical atomsts are term busters. The essential ingredient of a logical atomist's term busting practice is a higher-order logic with the power of impredicative comprehension. In Chapter 3, I discuss the widespread view that Wittgenstein held a version of logical atomism. Focusing on his pre-"Tractatus" writings and changes in his earlier views, I argue that Wittgenstein embraced a philosophy of logic incompatible with emulating impredicative comprehension in April 1914. As such, Wittgenstein was a logical atomist, if ever, in October 1913, possibly through April 1914. In the second part, having clarified what logical atomism is, I present a modern logical atomism. In Chapter 4, I develop a philosophy of logic for logical atomism based on the notion of a pure logic. I critically discuss normativity in logic, the epistemology of pure logic, and logical pluralism. In Chapter 5, I propose a formal logic for logical atomism. I argue for the logic of logical atomism being an infinitely-descending and infinitely-ascending simple type theory with impredicative comprehension compatible with a domain empty of particulars. In Chapter 6, I critically discuss what the ontology of logical atomism should be, that is, what the ontology of the logical atomist's logic must be. This includes an ontology of logical concepts and of logical forms as completely-general, necessarily-existing logical facts with no constituents. I conclude by indicating avenues for new work on logical atomism. (shrink)

We examine the influence of word choices on mathematical practice, i.e. in developing definitions, theorems, and proofs. As a case study, we consider Euclid’s and Euler’s word choices in their influential developments of geometry and, in particular, their use of the term ‘polyhedron’. Then, jumping to the twentieth century, we look at word choices surrounding the use of the term ‘polyhedron’ in the work of Coxeter and of Grünbaum. We also consider a recent and explicit conflict of approach between Grünbaum (...) and Shephard on the one hand and that of Hilton and Pedersen on the other, elucidating that the conflict was engendered by disagreement over the proper conceptualization, and so also the appropriate word choices, in the study of polyhedra. (shrink)

As interest in Owen Barfield grows, we aim to meet the need for a scholarly introduction to his thought. Our primary purpose is to present an overview, analysis, and synthesis of Barfield's most salient ideas in a manner that will be of interest to neophytes and initiates alike. Barfield's work can, at time, be difficult to understand; C. S. Lewis put it well when he described Barfield's style of argument as 'dark, labyrinthine,' and 'pertinacious.' But Lewis ardently promoted Barfield's work (...) because he knew that people who willingly walk in those dim and winding corridors are, in time, richly rewarded by the bright light at their end. We offer the present work in service to those who wish to undertake this adventure. While the present book will help those readers who wish to engage Barfield for the sake of achieving a greater understanding of and appreciation for other writers who have been associated with or influenced by him, we aim first and foremost to present Barfield as a profound and original thinker in his own right. (shrink)

The Defining Issues Test 2 (DIT-2) and Engineering Ethical Reasoning Instrument (EERI) are designed to measure ethical reasoning of general (DIT-2) and engineering-student (EERI) populations. These tools—and the DIT-2 especially—have gained wide usage for assessing the ethical reasoning of undergraduate students. This paper reports on a research study in which the ethical reasoning of first-year undergraduate engineering students at multiple universities was assessed with both of these tools. In addition to these two instruments, students were also asked to create personal (...) concept maps of the phrase “ethical decision-making.” It was hypothesized that students whose instrument scores reflected more postconventional levels of moral development and more sophisticated ethical reasoning skills would likewise have richer, more detailed concept maps of ethical decision-making, reflecting their deeper levels of understanding of this topic and the complex of related concepts. In fact, there was no significant correlation between the instrument scores and concept map scoring, suggesting that the way first-year students _conceptualize_ ethical decision making does not predict the way they behave when _performing_ scenario-based ethical reasoning (perhaps more situated). This disparity indicates a need to more precisely quantify engineering ethical reasoning and decision making, if we wish to inform assessment outcomes using the results of such quantitative analyses. (shrink)

C. A. J. Coady offers to clear up confusion about what terrorism is. His "tactical definition" focuses on terrorist acts as violent attacks upon non-combatants. He discusses what it means to be a non-combatant, considers various philosophical attempts to defend terrorism, and examines the idea of a connection between religion and terrorism.

Gravitational decoherence (GD) refers to the effects of gravity in actuating the classical appearance of a quantum system. Because the underlying processes involve issues in general relativity (GR), quantum field theory (QFT), and quantum information, GD has fundamental theoretical significance. There is a great variety of GD models, many of them involving physics that diverge from GR and/or QFT. This overview has two specific goals along with one central theme:(i) present theories of GD based on GR and QFT and explore (...) their experimental predictions;(ii) place other theories of GD under the scrutiny of GR and QFT, and point out their theoretical differences. We also describe how GD experiments in space in the coming decades can provide evidence at two levels:(a) discriminate alternative quantum theories and non-GR theories;(b) discern whether gravity is a fundamental or an effective theory. (shrink)

This review article provides a new perspective on the ethics of green nudging. We advance a new model for assessing the ethical permissibility of green nudges (GNs). On this model, which provides normative guidance for policymakers, a GN is ethically permissible when the intervention is (1) efficacious, (2) cost-effective, and (3) the advantages of the GN (i.e. reducing the environmental harm) are not outweighed by countervailing costs/harms (i.e. for nudgees). While traditional ethical objections to nudges (paternalism, etc.) remain potential normative (...) costs associated with GNs, any such costs must be weighed against the injunction to reduce environmental harm to third parties. (shrink)

Proposed quantum experiments in deep space will be able to explore quantum information issues in regimes where relativistic effects are important. In this essay, we argue that a proper extension of quantum information theory into the relativistic domain requires the expression of all informational notions in terms of quantum field theoretic (QFT) concepts. This task requires a working and practicable theory of QFT measurements. We present the foundational problems in constructing such a theory, especially in relation to longstanding causality and (...) locality issues in the foundations of QFT. Finally, we present the ongoing Quantum Temporal Probabilities program for constructing a measurement theory that (i) works, in principle, for any QFT, (ii) allows for a first- principles investigation of all relevant issues of causality and locality, and (iii) it can be directly applied to experiments of current interest. (shrink)

In this interview, C. P. Goodman invites British Polanyi scholar Richard T. Allen to reflect on his interest in Polanyi’s philosophical ideas and share what he believes is valuable in his thought.

In this talk presented at the 2022 conference of the Catholic Bar Association, C’Zar Bernstein unpacks the meaning of the word person in the Fourteenth Amendment and, through his exegesis, identifies philosophical arguments that may be instrumental in affording legal protection to the most vulnerable members of society.

We give a short, critical review of the issue of decoherence. We estab- lish the most general framework in which decoherence can be discussed, how it can be quantified and how it can be measured. We focus on environment induced decoher- ence and its degree of usefulness for the interpretation of quantum theory. We finally discuss the emergence of a classical world. An overall emphasis is given in pointing at common fallacies and misconceptions.

Ivancovsky et al. propose a novelty-seeking model linking curiosity to creativity. This commentary suggests integrating their work with a stage-based creativity model for additional insights. It also encourages readers to address knowledge gaps identified by the authors, including factors that trigger the pursuit of creative solutions. We aim to refine theory and direct future research to clarify the complex curiosity–creativity relationship.

Interdisciplinarity has seemingly become a paradigm for modern and meaningful research. Clearly, the interdisciplinary modus of deliberation enables to unfold relevant but quite different disciplinary perspectives to the reflection of broader scientific questions or societal problems. However, whether the comprehensive results of interdisciplinary reflection prove to be valid or to be acceptable in trans-disciplinary terms depends upon certain preconditions, which have to be fulfilled for securing scientific quality and social trust in advisory contexts. The present book is written by experts (...) and practitioners of interdisciplinary research and policy advice. It analyses topical and methodological approaches towards interdisciplinarity, starting with the current role of scientific research in society. The volume continues with contributions to the issues of knowledge and acting and to trans-disciplinary deliberation. The final conclusions address the scientific system as substantial actor itself as well as the relevant research and education politics. (shrink)

Moral pragmatism has been largely ignored in Business Ethics, despite its natural attraction and the fact that it is prominent in philosophy and socio-economic theories. The main premise of the book is that the complexity of today's business world does not permit a grand ethical theory, notwithstanding the different attempts made by scientists. Moral pragmatism is the 'go-to' approach where the ethical decision-making of managers varies dependent on different circumstances but it always integrates moral considerations. Ethical decision-making is no longer (...) based simply on known rules, but entails the constant dynamic interaction of circumstances, the development of new rules, managers' past experiences, their knowledge concerning ethics, and skills of moral reasoning. This book interweaves the postmodern approach to management studies and, based on its innovative research, reintroduces moral pragmatism in Business Ethics. The combination of decision-making theories, philosophy and postmodernism paves the way for future novel research in Business Ethics, making it an excellent resource for researchers, academics, and advanced students in the field of Business Ethics. Practitioners, on the other hand, will benefit by improving their skills in ethical decision-making and leadership. (shrink)

In his recent work, David DeGrazia (2020) explores the possibility of insect sentience, focusing on bees as a case study. He advances a novel evolutionary approach, arguing that, from an evolutionary perspective, it’s more likely that bees are sentient than insentient., insofar as bees (allegedly) would have a selective advantage if they are motivated—in the form of feeling—to achieve their aims. His argument assumes two questionable claims: (1) if X is a selective advantage for an organism, then the organism likely (...) has X, and (2) conscious creatures would have a selective advantage if they are sentient. I challenge both claims, and consequently call into question DeGrazia’s claim that we have an evolutionary-based reason to attribute sentience to bees (and other insects). (shrink)

The probability ‘measure’ for measurements at two consecutive mo- ments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We demonstrate that there are only two ways to resolve this problem. The first solution places emphasis on the precise use of the concept of conditional probability for successive mea- surements. The physically correct conditional probabilities define additive probabilities for two-time measurements. These probabilities (...) depend ex- plicitly on the resolution of the physical device and do not, therefore, correspond to a function of the associated projection operators. It follows that quantum theory distinguishes between physical events and proposi- tions about events, the latter are not represented by projection operators and that the outcomes of two-time experiments cannot be described by quantum logic. The alternative explanation is rather radical: it is conceivable that the relative frequencies for two-time measurements do not converge, unless a particular consistency condition is satisfied. If this is true, a strong revision of the quantum mechanical formalism may prove necessary. We stress that it is possible to perform experiments that will distinguish the two alternatives. (shrink)