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)

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)

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.

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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)

Background Despite the growth of biomedical research in South Africa, there are few insights into the operation of Research Ethics Committees (RECs) in this setting. We investigated the composition, operations and training needs of health RECs in South Africa against the backdrop of national and international guidelines. Methods The 12 major health RECs in South Africa were surveyed using semi-structured questionnaires that investigated the composition and functions of each REC as well as the operational issues facing committees. Results Health RECs (...) in SA have an average of 16 members and REC members are predominantly male and white. Overall, there was a large discrepancy in findings between under-resourced RECs and well resourced RECs. The majority of members (56%) are scientists or clinicians who are typically affiliated to the same institution as the health REC. Community representatives account for only 8% of membership. Training needs for health REC members varied widely. Conclusion Most major health RECs in South Africa are well organized given the resource constraints that exist in relation to research ethics in developing countries. However, the gender, racial and occupational diversity of most of these RECs is suboptimal, and most RECs are not constituted in accordance with South African guidelines. Variability in the operations and training needs of RECs is a reflection of apartheid-entrenched influences in tertiary education in SA. While legislation now exists to enforce standardization of research ethics review systems, no provision has been made for resources or capacity development, especially to support historically-disadvantaged institutions. Perpetuation of this legacy of apartheid represents a violation of the principles of justice and equity. (shrink)

William Lane Craig's defence of the kalam cosmological argument rests heavily on two philosophical arguments against a past-eternal universe. In this article I take issue with one of these arguments, what I call the – namely, that the metaphysical absurdity of an actually infinite number of things existing precludes the possibility of a beginningless past. After explaining this argument, I proceed to raise some initial doubts. After setting those aside, I show that the argument is ineffective against proponents of presentism. (...) The remainder of the article considers and rejects possible replies on Craig's behalf. (shrink)

The semantic paradoxes are often associated with self-reference or referential circularity. Yablo (Analysis 53(4):251–252, 1993), however, has shown that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In this essay, we lay the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes and the semantic hypodoxes. We develop (...) a functionally complete infinitary propositional language endowed with a denotation assignment and extract the reference structural information in terms of graph-theoretic properties. We introduce the new concepts of dangerous and precarious reference graphs, which allows us to rigorously define the task: classify the dangerous and precarious directed graphs purely in terms of their graph-theoretic properties. Ungroundedness will be shown to fully characterize the precarious reference graphs and fully characterize the dangerous finite graphs. We prove that an undirected graph has a dangerous orientation if and only if it contains a cycle, providing some support for the traditional idea that cyclic structure is required for paradoxicality. This leaves the task of classifying danger for infinite acyclic reference graphs. We provide some compactness results, which give further necessary conditions on danger in infinite graphs, which in conjunction with a notion of self-containment allows us to prove that dangerous acyclic graphs must have infinitely many vertices with infinite out-degree. But a full characterization of danger remains an open question. In the appendices we relate our results to the results given in Cook (J Symb Log 69(3):767–774, 2004) and Yablo (2006) with respect to more restricted sentences systems, which we call $\mathcal{F}$ -systems. (shrink)

Prior to their announcement of the birth of gene-edited twins in China, Dr. He Jiankui and colleagues published a set of draft ethical principles for discussing the legal, social, and ethical aspects of heritable genome interventions. Within this document, He and colleagues made it clear that their goal with these principles was to “clarify for the public the clinical future of early-in-life genetic surgeries” or heritable genome editing. In light of He’s widely criticized gene editing experiments it is of interest (...) to place these draft principles in the larger ethical debate surrounding heritable genome editing. Here we examine the principles proposed by He and colleagues through the lens of Beauchamp and Childress’ Principles of Biomedical Ethics. We also analyze the stated goal that the “clinical future” of heritable genome editing was clarified by He and colleagues’ proposed principles. Finally, we highlight what might be done to help prevent individual actors from pushing forward ahead of broad societal consensus on heritable genome editing. (shrink)

Anti-vascular endothelial growth factor therapy has revolutionised the treatment of a variety of ophthalmic conditions and has become the first-line therapy for a range of retinal diseases. Bevacizumab, a VEGF inhibitor first approved for the treatment of colorectal cancer, has been shown to be nearly or virtually as effective and safe as other anti-VEGF therapies in the treatment of certain retinal diseases but is not approved or registered by the Food and Drug Administration or European Medicines Agency. While other anti-VEGF (...) options are approved and registered, they are generally more expensive and less accessible. Accordingly, despite its off-label status, bevacizumab is frequently used for a variety of disabling retinal diseases. Indeed, bevacizumab is included on the World Health Organization’s list of essential medicines. However, its use in some parts of the world remains restricted due to its off-label status. How, then, should healthcare authorities approach this situation? What are the ethical and societal implications of adhering to a standard and generally effective evaluation and approval system while restricting access to a potentially cost-saving therapy? In countries where its use is not restricted, how should providers approach off-label treatment with bevacizumab? By examining the evidence behind bevacizumab’s efficacy and safety and evaluating the individual and societal implications of off-label use and restriction, this paper illustrates the ethical factors providers and policy makers must consider in the off-label use of bevacizumab and ultimately argues for increased access to bevacizumab in the treatment of retinal disease. (shrink)

The notion that something can exist a se is central to Descartes’s overall metaphysics of causation. In the Meditations, divine aseity plays the role of explaining not only God’s existence but ultimately the existence of everything else apart from God. Yet in the Meditations proper, as well as in the early Replies, Descartes does little to clarify exactly what his view of divine aseity is and how it might differ from the sort of aseity commonly posited by the Scholastics. Despite (...) Descartes’s later attempts to assuage this worry and clarify his position, the positive aseity charge has not gone away. Here I shall argue that the charge is unjustified on all counts. Baldly stated, Descartes’s notion of aseity is no different than the negative sense of aseity endorsed by his Scholastic predecessors - especially Aquinas. Understanding this not only helps in clarifying the overall picture of Cartesian causality but also aids in seeing how commentaries on the Meditations, old and new, have obscured it. (shrink)

This paper will set out in plain language the basic ontology of “Deleuze’s Spinoza”; it will then critically examine whether such a Spinoza has, or indeed could have, ever truly existed. In this, it will be shown that Deleuze’s reading of Spinoza involves the imposition of three interlocking, formal principles. These are (1) Necessitarianism, (2) Immanence, and (3) Univocity. The uncovering of Deleuze’s use of these three principles, how they relate to one another, and what they jointly imply in terms (...) of ontology, will occupy Part 1 of this paper. The critique of these principles from a Spinozist perspective, i.e. that their use by Deleuze is incompatible with Spinoza’s own metaphysics, will occupy Part 2 of this paper. (shrink)

BackgroundThere is increasing need for peer reviewers as the scientific literature grows. Formal education in biostatistics and research methodology during residency training is lacking. In this pilot study, we addressed these issues by evaluating a novel method of teaching residents about biostatistics and research methodology using peer review of standardized manuscripts. We hypothesized that mentored peer review would improve resident knowledge and perception of these concepts more than non-mentored peer review, while improving review quality.MethodsA partially blinded, randomized, controlled multi-center study (...) was performed. Seventy-eight neurology residents from nine US neurology programs were randomized to receive mentoring from a local faculty member or not. Within a year, residents reviewed a baseline manuscript and four subsequent manuscripts, all with introduced errors designed to teach fundamental review concepts. In the mentored group, mentors discussed completed reviews with residents. Primary outcome measure was change in knowledge score between pre- and post-tests, measuring epidemiology and biostatistics knowledge. Secondary outcome measures included level of confidence in the use and interpretation of statistical concepts before and after intervention, and RQI score for baseline and final manuscripts.ResultsSixty-four residents (82%) completed initial review with gradual decline in completion on subsequent reviews. Change in primary outcome, the difference between pre- and post-test knowledge scores, did not differ between mentored (−8.5%) and non-mentored (−13.9%) residents (p = 0.48). Significant differences in secondary outcomes (using 5-point Likert scale, 5 = strongly agree) included mentored residents reporting enhanced understanding of research methodology (3.69 vs 2.61; p = 0.001), understanding of manuscripts (3.73 vs 2.87; p = 0.006), and application of study results to clinical practice (3.65 vs 2.78; p = 0.005) compared to non-mentored residents. There was no difference between groups in level of interest in peer review (3.00 vs 3.09; p = 0.72) or the quality of manuscript review assessed by the Review Quality Instrument (RQI) (3.25 vs 3.06; p = 0.50).ConclusionsWe used mentored peer review of standardized manuscripts to teach biostatistics and research methodology and introduce the peer review process to residents. Though knowledge level did not change, mentored residents had enhanced perception in their abilities to understand research methodology and manuscripts and apply study results to clinical practice. (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)

Don didn’t grasp what would eventually come to be one of the most successful ad campaigns ever because he didn’t recognise the person presenting the evidence as being appropriately trustworthy. He failed to know because Dr Guttman’s say-so was not enough to provide justification for a belief. But why would he think that? To get to the bottom of this, we need the help of an analytical approach known as standpoint theory.

Don didn’t grasp what would eventually come to be one of the most successful ad campaigns ever because he didn’t recognise the person presenting the evidence as being appropriately trustworthy. He failed to know because Dr Guttman’s say-so was not enough to provide justification for a belief. But why would he think that? To get to the bottom of this, we need the help of an analytical approach known as standpoint theory.

BackgroundCommentators believe that the ethical decision-making climate is instrumental in enhancing interprofessional collaboration in intensive care units. Our aim was twofold: to determine the perception of the ethical climate, levels of moral distress, and intention to leave one's job among nurses and physicians, and between the different ICU types and determine the association between the ethical climate, moral distress, and intention to leave.MethodsWe performed a cross-sectional questionnaire study between May 2021 and August 2021 involving 206 nurses and physicians in a (...) large urban academic hospital. We used the validated Ethical Decision-Making Climate Questionnaire and the Measure of Moral Distress for Healthcare Professionals tools and asked respondents their intention to leave their jobs. We also made comparisons between the different ICU types. We used Pearson's correlation coefficient to identify statistically significant associations between the Ethical Climate, Moral Distress, and Intention to Leave.ResultsNurses perceived the ethical climate for decision-making as less favorable than physicians. They also had significantly greater levels of moral distress and higher intention to leave their job rates than physicians. Regarding the ICU types, the Neonatal/pediatric unit had a significantly higher overall ethical climate score than the Medical and Surgical units and also demonstrated lower moral distress scores and lower “intention to leave” scores compared with both the Medical and Surgical units. The ethical climate and moral distress scores were negatively correlated ; moral distress and "intention to leave" was positively correlated ; and ethical climate and “intention to leave” were negatively correlated.ConclusionsSignificant differences exist in the perception of the ethical climate, levels of moral distress, and intention to leave between nurses and physicians and between the different ICU types. Inspecting the individual factors of the ethical climate and moral distress tools can help hospital leadership target organizational factors that improve interprofessional collaboration, lessening moral distress, decreasing turnover, and improved patient care. (shrink)

Though the interaction of philosophy with pop culture has so far mostly taken the form of books for nonphilosophers that use various shows and movies as sources of examples to illustrate “traditional” philosophical issues, this article contends that serious engagement with the informal philosophical discussions expressed in popular entertainments constitutes a kind of “ethnophilosophy” and should be considered an important part of the discipline. Our disciplinary responsibility for maintaining and considering the history of philosophy ought to include even the philosophical (...) conversations that occur outside the academy; however unlike “proper” philosophy this material may be, it nonetheless represents engagement—sometimes substantial engagement—with the same issues that concern those of us who are considered “professional” philosophers, and thus is legitimately of interest to us. (shrink)