• Editors’ Introduction
    In Landon D. C. Elkind & Alexander Mugar Klein (eds.), Bertrand Russell, Feminism, and Women Philosophers in his Circle, Palgrave Macmillan. pp. 1-9. 2024.
    This chapter contextualizes the book and summarizes its subsequent chapters.
  • 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-centur…Read more
  •  7
    Bertrand Russell, Feminism, and Women Philosophers in his Circle (edited book)
    with Alexander Mugar Klein
    Palgrave Macmillan. 2024.
  •  410
    The Genealogy of ‘∨’
    Review of Symbolic Logic 16 (3): 862-899. 2023.
    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 forma…Read more
  •  12
    Squaring the Circles: a Genealogy of Principia ’s Dot Notation
    Russell: The Journal of Bertrand Russell Studies 43 (1): 42-65. 2023.
    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 conventio…Read more
  •  13
    The Contact Argument: A Little Unduly Simple?
    American Philosophical Quarterly 59 (3): 247-261. 2022.
    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 the…Read more
  •  469
    Computer verification for historians of philosophy
    Synthese 200 (3): 1-28. 2022.
    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 …Read more
  •  293
    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…Read more
  •  22
    Frege's Curiously Two-Dimensional Concept-Script
    Journal for the History of Analytical Philosophy 9 (11). 2021.
    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 tha…Read more
  •  177
    An Argument for Completely General Facts
    Journal for the History of Analytical Philosophy 9 (7). 2021.
    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 fo…Read more
  •  67
    A Case Study in Formalizing Contingent a priori Claims
    Res Philosophica 97 (4): 571-591. 2020.
    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 formaliz…Read more
  •  254
    Śāntarakṣita and Kamalaśīla on the Jain Theory of Self
    with James Duerlinger and Siddarth Singh
    Indian International Journal of Buddhist Studies 16 63-89. 2015.
  •  249
    Fraser MacBride, On the Genealogy of Universals: The Metaphysical Origins of Analytic Philosophy
    Journal for the History of Analytical Philosophy 8 (8). 2020.
    Reviewed by Landon D. C. Elkind.
  •  34
    Why Russell Was Not an Epistemic Structural Realist
    Russell: The Journal of Bertrand Russell Studies 40 5-26. 2020.
    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 pr…Read more
  •  447
    On Russell's Logical Atomism
    In Landon D. C. Elkind & Gregory Landini (eds.), The Philosophy of Logical Atomism: A Centenary Reappraisal, Palgrave Macmillan. pp. 3-37. 2018.
    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 a…Read more
  •  487
    On Jain Anekantavada and Pluralism in Philosophy of Mathematics
    International School for Jain Studies-Transactions 2 (3): 13-20. 2019.
    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.
  •  364
    Word choice in mathematical practice: a case study in polyhedra
    with Lowell Abrams
    Synthese (4): 1-29. 2019.
    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 betwe…Read more
  •  26
    The search for logical forms: in defense of logical atomism
    Dissertation, University of Iowa. 2018.
    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 t…Read more
  •  35
    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 ninete…Read more
  •  87
    Book Review: Samuel Lebens (2017) "Bertrand Russell and the Nature of Propositions: a History and Defense of the Multiple Relation Theory of Judgement"
  •  9
    Bertrand Russell on Something
    Philosophy Now 120 21-22. 2017.
  •  42
    A New Metaphysics of Sense-Data
    Logos and Episteme 8 (3): 359-363. 2017.
    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.