Kevin C. Klement

Courses/Teaching

Research and Publications

Most of my work has focused on the philosophies of early analytic figures including Gottlob Frege, Bertrand Russell, and Ludwig Wittgenstein, especially their philosophical logics and their import for contemporary discussions in philosophy of language, intensional logic and the philosophy of mathematics. I am also interested in informal logic, ethics, and the history of logic and analytic philosophy generally.

Most of my publications are available below. If not, email me and I’ll send you a copy. Questions and comments welcome.

Works in progress and forthcoming

1. Russell’s Retreat from Pythagoras
   Forthcoming.
   Abstract
   This book argues that Russell’s mature mathematical logic and core logical atomist philosophy resulted from a systematic retreat from a position embracing a wide variety of abstract objects, and this retreat came mainly in response to the logical paradoxes plaguing his work on the foundations of mathematics. I argue that this retreat was nearly complete by 1912. This goes against the widespread position that Wittgenstein was responsible for Russell’s less realist position after the 19-teens. The work also aims to shed light on ways Russell’s views can continue to shed light on debates in the philosophy of language, metaphysics and philosophy of mathematics.
2. Never Going Back: Russellian Analysis as Progress
   Forthcoming in Festsschrift for Bernard Linsky (Synthese Library).
   Abstract
   In his 1918 Philosophy of Logical Atomism lectures, Russell claims that when doing philosophical analysis, “[y]ou do not want to go back to the vagueness of the child or monkey”. This and related remarks suggest that Russellian analysis should be thought of as progressive in a rather peculiar way. What one ends up with after analysis is somehow improved, more logically precise, and a better representation of reality. A question arises then with regard to its relation to the original “vaguer” understanding. Does analysis tell us what the vaguer understanding captured really “was” all along, its “real” or “true” nature? In this paper, I discuss what I take to be the development of Russell’s thought on this question, shifting from a more positive to a more negative answer. On this negative answer, one cannot really speak of the “correct” analysis of what one began with. Indeed, the attitude of “never going back” suggests that there is no reason post-analysis to even consider that question. I relate these issues to Russell’s views on meaning, acquaintance, vagueness and simplicity generally, and suggest it is important for evaluating the logical atomist project as a whole. The overall conclusion of the paper accords with Bernard Linsky’s suggestion (in “Russell’s Theory of Descriptions and Logical Constructions”) that the interpretation of Russellian analysis as aiming to provide an account of ordinary language stems from misunderstandings of later interpreters.
3. Bertrand Russell’s Life and Philosophical Works
   Forthcoming.
   Abstract
   This contribution provides an overview of Bertrand Russell's (1872–1970) long career as a philosopher. It gives details of the focus of his research at various points and how they relate to events in his life. It chronicles his important publications and their influence. It also provides a list of further resources for those interested in this topic.
4. Peano, Frege and Russell’s Logical Influences
   Forthcoming.
   Abstract PDF PhilPapers
   This chapter clarifies that it was the works Giuseppe Peano and his school that first led Russell to embrace symbolic logic as a tool for understanding the foundations of mathematics, not those of Frege, who undertook a similar project starting earlier on. It also discusses Russell’s reaction to Peano’s logic and its influence on his own. However, the chapter also seeks to clarify how and in what ways Frege was influential on Russell’s views regarding such topics as classes, functions, meaning and denotation, etc., and summarizes the correspondence between Frege and Russell and the light it sheds on the philosophical logic of both.
5. Morality, Schmorality
   Currently only a “published” presentation on this website; future plans undecided.
   Abstract Web Link
   This is not a research project so much as a kind of “personal manifesto” on meta-ethics, or my personal take on how to best think about and improve morality. Since my take on “morality” is not necessarily meant to be compatible with current or past understandings, I am amenable to calling it “schmorality” instead. I argue that (sch)morality can be taken to be teleological by definition, but that the objects of comparison for what produces the best results value-wise need not be taken as actions, but rather the holistic approaches to living and decision making themselves. The position therefore does not yield “consequentialism” in the usual sense. I further explain how this position is compatible with the emergence of something like deontological constraints from within a teleological approach to (sch)morality, and speculate about further likely consequences of this approach.

Published book

1. Frege and the Logic of Sense and Reference
   Routledge 2002.
   Abstract PDF PhilPapers
   This book aims to develop certain aspects of Gottlob Frege’s theory of meaning, especially those relevant to intensional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege. (The approach is contrasted with the less historically-minded Logic of Sense and Denotation of Alonzo Church.) Comparisons of Frege’s theory with those of Russell and others are given. It is in the end shown that developing Frege’s theory in these ways reveals serious problems hitherto largely unnoticed, including those possibly rendering a Fregean intensional logic inconsistent even if his naïve class theory is excluded.

Published journal articles and book chapters (selected)

1. Higher-Order Metaphysics in Frege and Russell
   In Higher-Order Metaphysics, edited by P. Fritz and N. K. Jones. (Oxford University Press 2024), pp. 355–377.
   Abstract PDF PhilPapers
   This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between objects and functions. Russell understood propositional functions as what is obtained when constituents of propositions are replaced by variables, but eventually denied that they were entities in their own right. Both encountered contradictions when supposing there to exist as many objects as functions, and both adopted views about the meaningfulness of higher-order discourse that were difficult to state from within their own strictures.
2. Logical Form and the Development of Russell’s Logicism
   In Origins and Varieties of Logicism, edited by F. Boccuni and A. Sereni. (Routledge 2022), pp. 147–166.
   Abstract PDF PhilPapers
   Logicism is the view that mathematical truths are logical truths. But a logical truth is commonly thought to be one with a universally valid form. The form of “7 > 5” would appear to be the same as “4 > 6”. Yet one is a mathematical truth, and the other not a truth at all. To preserve logicism, we must maintain that the two either are different subforms of the same generic form, or that their forms are not at all what they appear. The historical record shows that Russell pursued both these options, but that the struggle with the logical paradoxes pushed him away from the first kind of response and toward the second. An object cannot itself have a kind of inner logical complexity that makes a proposition have a different logical form merely in virtue of being about it, nor can their representatives in logical forms be single things different for different forms, at least not without postulating too many such objects and thereby creating Cantorian diagonal paradoxes. There are only apparent objects which are actually fragments of logical forms, different in different cases.
3. Grundgesetze and the Sense/Reference Distinction
   In Essays on Frege’s Basic Laws of Arithmetic, edited by P. Ebert and M. Rossberg. (Oxford University Press 2019), pp. 142–66.
   Abstract PDF PhilPapers
   Frege developed the theory of sense and reference while composing his Grundgesetze and considering its philosophical implications. The Grundgesetze is thus the most important test case for the application of this theory of meaning. I argue that evidence internal and external to the Grundgesetze suggests that he thought of senses as having a structure isomorphic to the Grundgesetze expressions that would be used to express them, which entails a theory about the identity conditions of senses that is relatively fine-grained, though still coarser than some other commentators have suggested. While this interpretation does not make Frege’s ontological commitment to the denizens of a “third realm” as profligate as some have alleged, it is sufficiently bloated to lead to Cantorian paradoxes and diagonal contradictions independent of his Basic Law V.
4. New Logic and the Seeds of Analytic Philosophy: Boole, Frege
   In A Companion to Nineteenth-Century Philosophy, edited by J. Shand. (Wiley Blackwell 2019), pp. 454–79.
   Abstract PDF PhilPapers
   This contribution surveys the revolution in logic that took place in the 19th Century and its influence on philosophy, with particular emphasis on the writings of George Boole and Gottlob Frege. Boole invented the algebraic treatment of logic, making a mathematical analysis of the Aristotelian syllogistic possible, and more. Frege invented modern quantificational logic and presented a fully axiomatized second-order function calculus. Frege’s logic was developed as part of his logicism, his aim to derive arithmetic from a logical basis, but unfortunately his precise method involved the use of an inconsistent theory of extensions of concepts. Frege’s very influential views on meaning and truth, including his distinction between sense and reference, and between objects and concepts of different levels, are also discussed. The influence of Frege, and the 19th Century revolution in logic generally, on later philosophy, especially analytic philosophy, is also outlined.
5. Russell’s Logicism
   In The Bloomsbury Companion to Bertrand Russell, edited by R. Wahl. (Bloomsbury Academic 2019), pp. 151–78.
   Abstract PDF PhilPapers
   Bertrand Russell was one of the best-known proponents of logicism: the theory that mathematics reduces to, or is an extension of, logic. Russell argued for this thesis in his 1903 The Principles of Mathematics and attempted to demonstrate it formally in Principia Mathematica (PM 1910–1913; with A. N. Whitehead). Russell later described his work as a further “regressive” step in understanding the foundations of mathematics made possible by the late 19th century “arithmetization” of mathematics and Frege’s logical definitions of arithmetical concepts. The logical system of PM sought to improve on earlier attempts by solving the contradictions found in, e.g., Frege’s system, by employing a theory of types. In this article, I also consider and critically evaluate the most common objections to Russell’s logicism, including the claim that it is undermined by Gödel’s incompleteness results, and Putnam's charge of “if-thenism”. I suggest that if we are willing to accept a slightly revisionist account of what counts as a mathematical truth, these criticisms do not obviously refute Russell’s claim to have established that mathematical truths generally are a species of logical truth.
6. G. E. Moore’s Unpublished Review of The Principles of Mathematics
   Russell n.s. 38 (2018–19): 131–64.
   Abstract PDF PhilPapers
   This file contains an introduction along with the text of Moore’s review.
   
   Several interesting themes emerge from G. E. Moore’s previously unpublished review of The Principles of Mathematics. These include a worry concerning whether mathematical notions are identical to purely logical ones, even if coextensive logical ones exist. Another involves a conception of infinity based on endless series neglected in the Principles but arguably involved in Zeno’s paradox of Achilles and the Tortoise. Moore also questions the scope of Russell’s notion of material implication, and other aspects of Russell’s claim that mathematics reduces to logic.
7. Russell on Ontological Fundamentality and Existence
   In The Philosophy of Logical Atomism: A Centenary Reappraisal, edited by L. Elkind and G. Landini. (Palgrave Macmillan 2018), pp. 155–79.
   Abstract PDF PhilPapers
   Russell is often taken as a forerunner of the Quinean position that “to be is to be the value of a bound variable”, whereupon the ontological commitment of a theory is given by what it quantifies over. Among other reasons, Russell was among the first to suggest that all existence statements should be analyzed by means of existential quantification. That there was more to Russell’s metaphysics than what existential quantifications come out as true is obvious in the earlier period where Russell still made a distinction between existence and being/subsistence. But even the later Russell, including that of the Logical Atomism lectures period, would not have understood ontological questions to be first and foremost questions of quantification. He would take fundamentality to be important too, which explains in part his assertions to the effect the the values of individual variables have a reality not attributable to values of higher-order variables, even ineliminable higher-order variables.
8. A Generic Russellian Elimination of Abstract Objects
   Philosophia Mathematica 25/1 (2017): 91–115.
   Abstract PDF PhilPapers
   In this paper I explore a position on which it is possible to eliminate the need for postulating abstract objects through abstraction principles by treating terms for abstracta as “incomplete symbols”, using Russell’s no-classes theory as a template from which to generalize. I defend views of this stripe against objections, most notably Heck’s charge that syntactic forms of nominalism cannot correctly deal with non-first-orderizable quantifcation over apparent abstracta. I further discuss how number theory may be developed in a system treating apparent terms for numbers using these definitions.
9. Three Unpublished Manuscripts from 1903
   Russell n.s. 36 (2016): 5–44.
   Abstract PDF PhilPapers
   I present and discuss three previously unpublished manuscripts written by Bertrand Russell in 1903, not included with similar manuscripts in Volume 4 of his Collected Papers. One is a one-page list of basic principles for his “functional theory” of May 1903, in which Russell partly anticipated the later Lambda Calculus. The next, catalogued under the title “Proof That No Function Takes All Values”, largely explores the status of Cantor's proof that there is no greatest cardinal number in the variation of the functional theory holding that only some but not all complexes can be analyzed into function and argument. The final manuscript, “Meaning and Denotation”, examines how his pre-1905 distinction between meaning and denotation is to be understood with respect to functions and their arguments. In them, Russell seems to endorse an extensional view of functions not endorsed in other works prior to the 1920s. All three manuscripts illustrate the close connection between his work on the logical paradoxes and his work on the theory of meaning.
10. The Constituents of the Propositions of Logic
    In Acquaintance, Knowledge, and Logic: New Essays on Bertrand Russell’s The Problems of Philosophy, edited by D. Wishon and B. Linsky. (CSLI Publications 2015), pp. 189–229.
    Abstract PDF PhilPapers
    In The Problems of Philosophy and other works of the same period, Russell claims that every proposition must contain at least one universal. Even fully general propositions of logic are claimed to contain “abstract logical universals”, and our knowledge of logical truths claimed to be a species of a priori knowledge of universals. However, these views are in considerable tension with Russell’s own philosophy of logic and mathematics as presented in Principia Mathematica. Universals generally are qualities and relations, but if, for example, PM’s disjunction (∨) is a relation, what is it a relation between? There is no obvious answer to this given Russell’s other philosophical commitments at this time, although hints are left in some of the pre-PM manuscripts. In this paper, I explore this tension in Russell's philosophy and relate it to developments both before and after Problems.
11. The Russell–Dummett Correspondence on Frege and his Nachlaß
    The Bertrand Russell Society Bulletin no. 150 (2014): 25–29.
    Abstract PDF PhilPapers
    Russell corresponded with Sir Michael Dummett (1925–2011) between 1953 and 1963 while the latter was working on a book on Frege, eventually published as Frege: Philosophy of Language (1973). In their letters they discuss Russell’s correspondence with Frege, translating it into English, as well as Frege’s attempted solution to Russell’s paradox in the appendix to vol. 2 of his Grundgesetze der Arithmetik. After Dummett visited the University of Münster to view Frege’s Nachlaß, he sent reports back to Russell concerning both the philosophical materials Frege left behind, as well as information from Frege’s journal revealing his anti-semitic political opinions. Their interaction contains interpretive conjectures and insights on Dummett’s side, and some dark humor on Russell’s.
12. The Paradoxes and Russell’s Theory of Incomplete Symbols
    Philosophical Studies 169/2 (2014): 183–207.
    Abstract PDF PhilPapers
    Russell claims in his Autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not be thought of as a single thing, neither can the meaning/intension of any expression capable of singling out one collection (class) of things as opposed to another. If this is right, it shows that Russell’s method of solving the logical paradoxes is wholly incompatible with anything like a Fregean dualism between sense and reference or meaning and denotation. I also discuss how this realization lead to modifications in his understanding of propositions and propositional functions, and suggest that Russell’s confrontation with these issues may be instructive for ongoing research.
13. Early Russell on Types and Plurals
    Journal for the History of Analytical Philosophy 2/6 (2014): 1–21.
    Abstract PDF PhilPapers
    In 1903, in The Principles of Mathematics (PoM), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was short-lived—rejected before PoM even appeared in print. However, aside from mentions of a few misgivings, there is little evidence about why he abandoned this view. In this paper, I attempt to clarify Russell’s early views about plurality, arguing that they did not involve countenancing special kinds of plural things distinct from individuals. I also clarify what his misgivings about these views were, making it clear that while the plural understanding of classes helped solve certain forms of Russell’s paradox, certain other Cantorian paradoxes remained. Finally, I aim to show that Russell’s abandonment of something like plural logic is understandable given his own conception of logic and philosophical aims when compared to the views and approaches taken by contemporary advocates of plural logic.
14. PM’s Circumflex, Syntax and Philosophy of Types
    In The Palgrave Centenary Companion to Principia Mathematica, edited by N. Griffin and B. Linsky. (Palgrave Macmillian 2013), pp. 218–46.
    Abstract PDF PhilPapers
    Along with offering an historically-oriented interpretive reconstruction of the syntax of Principia Mathematica (first ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circumflex on a variable. I argue that this notation is used in PM only when definitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) is not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary.
15. Neo-logicism and Russell’s Logicism
    Russell n.s. 32 (2012–13): 127–59.
    Abstract PDF PhilPapers
    Most advocates of the so-called “neologicist” movement in the philosophy of mathematics identify themselves as “Neo-Fregeans” (e.g., Hale and Wright), presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature, and when it is, often dismissed as not really logicism at all (in lights of its assumption of axioms of infinity, reducibiity and so on). In this paper I have three aims: firstly, to identify more clearly the primary metaontological and methodological differences between Russell’s logicism and the more recent forms; secondly, to argue that Russell’s form of logicism offers more elegant and satisfactory solutions to a variety of problems that continue to plague the neo-logicist movement (the bad company objection, the embarrassment of richness objection, worries about a bloated ontology, etc.); thirdly, to argue that Neo-Russellian forms of neologicism remain viable positions for current philosophers of mathematics.
16. Frege’s Changing Conception of Number
    Theoria 78 (2012): 146–67.
    Abstract PDF PhilPapers
    I trace changes to Frege’s understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning of Russell’s paradox, this position is natural position for him to have retreated to, when properly understood.
17. The Functions of Russell’s No Class Theory
    Review of Symbolic Logic 3/4 (2010): 633–64.
    Abstract PDF PhilPapers
    Certain commentators on Russell's “no class” theory, in which apparent reference to classes or sets is eliminated using higher-order quantification, including W. V. Quine and (recently) Scott Soames, have doubted its success, noting the obscurity of Russell’s understanding of so-called “propositional functions”. These critics allege that realist readings of propositional functions fail to avoid commitment to classes or sets (or something equally problematic), and that nominalist readings fail to meet the demands placed on classes by mathematics. I show that Russell did thoroughly explore these issues, and had good reasons for rejecting accounts of propositional functions as extra-linguistic entities. I argue in favor of a reading taking propositional functions to be nothing over and above open formulas which addresses many such worries, and in particular, does not interpret Russell as reducing classes to language.
18. The Senses of Functions in the Logic of Sense and Denotation
    Bulletin of Symbolic Logic 16/2 (2010): 153–88.
    Abstract PDF PhilPapers
    This paper discusses certain problems arising within the treatment of the senses of functions in Church’s Logic of Sense and Denotation. Church understands such senses themselves to be “sense-functions“, functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or “deviant” sense-functions. Certain absurdities result, e.g., an argument can be found for equating any two senses of the same type. An alternative treatment of the senses of functions is discussed, and is thought to do better justice to Frege’s original theory.
19. Gottlob Frege
    In The Routledge Companion to Nineteenth Century Philosophy, edited by Dean Moyar. (Routledge 2010), pp. 858–86.
    Abstract PDF PhilPapers
    A summary of the philosophical career and intellectual contributions of Gottlob Frege (1848–1925), including his invention of first- and second-order quantified logic, his logicist understanding of arithmetic and numbers, the theory of sense (Sinn) and reference (Bedeutung) of language, the third-realm metaphysics of “thoughts”, his arguments against rival views, and other topics.
20. Russell, His Paradoxes and Cantor’s Theorem [Parts I–II]
    Philosophy Compass 5/1 (2010): 16–28 and 29–41.
    Abstract PDF PhilPapers
    In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions and equivalence classes of coextensional properties. Part I focuses on Cantor’s theorem, its proof, how it can be used to manufacture paradoxes, and several broad categories of strategies for offering solutions to these paradoxes. Part II discusses the origins in and impact of these paradoxes on Bertrand Russell’s philosophy in particular, as well as his own favored brand of solution whereupon those purported entities that, if reified, lead to these contradictions, must not be genuine entities, but “logical fictions” or “logical constructions” instead.
21. A Cantorian Argument Against Frege’s and Early Russell’s Theories of Descriptions
    In Russell vs. Meinong: The Legacy of “On Denoting”, edited by N. Griffin and D. Jacquette. (Routledge 2008), pp. 65–77.
    Abstract PDF PhilPapers
    This paper discusses an argument, inspired by Russell, against certain theories of definite descriptions, like Frege’s and those of the pre-“On Denoting” Russell, that posit a sense or meaning for a descriptive phrase of the form “the φ” distinct from its denotation. If one is committed to (1) a liberal ontology of properties, (2) the existence of at least one descriptive sense for each property, (3) certain plausible principles regarding the identity conditions of senses, and (4) an account of descriptive senses whereupon they can themselves be presented by other senses of the same type, a violation of Cantor’s theorem results leading to a Russell-style antinomy. Let something have property H if and only if it is a descriptive sense that does not have its corresponding property. Consider the sense of “the [thing that is] H”. Does it have H? Various strategies for avoiding the problem are discussed and evaluated.
22. The Origins of the Propositional Functions Version of Russell’s Paradox
    Russell n.s. 24 (2004–05): 101–32.
    Abstract PDF PhilPapers
    Russell discovered the classes version of Russell’s paradox in spring 1901, and the predicates version near the same time. There is a problem, however, in dating the discovery of the propositional functions version. In 1906, Russell claimed he discovered it after May 1903, but this conflicts with the widespread belief that the functions version appears in The Principles of Mathematics, finished in late 1902. I argue that Russell’s dating was accurate, and that the functions version does not appear in the Principles. I distinguish the functions and predicates versions, give a novel reading of the Principles, section 85, as a paradox dealing with what Russell calls assertions, and show that Russell’s logical notation in 1902 had no way of even formulating the functions version. The propositional functions version had its origins in the summer of 1903, soon after Russell’s notation had changed in such a way as to make a formulation possible.
23. Does Frege Have Too Many Thoughts? A Cantorian Problem Revisited
    Analysis 65/1 (2005): 44–49.
    Abstract PDF PhilPapers
    This paper continues a thread in Analysis begun by Adam Rieger and Nicholas Denyer. Rieger argued that Frege’s theory of thoughts violates Cantor’s theorem by postulating as many thoughts as concepts. Denyer countered that Rieger’s construction could not show that the thoughts generated are always distinct for distinct concepts. By focusing on universally quantified thoughts, rather than thoughts that attribute a concept to an individual, I give a different construction that avoids Denyer’s problem. I also note that this problem for Frege’s philosophy was discovered by Bertrand Russell as early as 1902 and has been discussed intermittently since.
24. Putting Form Before Function: Logical Grammar in Frege, Russell and Wittgenstein
    Philosopher’s Imprint 4/2 (2004): 1–47.
    Abstract PDF PhilPapers
    The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the “judgment centered” aspects of the Tractatus to be inherited from Frege not Russell. Frege’s views on the priority of judgments are problematic, and unlike Wittgenstein’s. Russell’s views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and universals, are exposed. Wittgenstein’s and Russell’s views on logical grammar are shown to be very similar. Russell’s type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over “inexpressible truths” in the Tractatus. I lastly comment on the changes to Russell’s views brought about by Wittgenstein’s influence.
25. Russell’s 1903–05 Anticipation of the Lambda Calculus
    History and Philosophy of Logic 24 (2003): 15–37.
    Abstract PDF PhilPapers
    It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other functions as value. Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus.
26. The Number of Senses
    Erkenntnis 58 (2003): 302–23.
    Abstract PDF PhilPapers
    Many philosophers still countenance senses or meanings in the broadly Fregean vein. However, it is difficult to posit the existence of senses without positing quite a lot of them, including at least one presenting every entity in existence. I discuss a number of Cantorian paradoxes that seem to result from an overly large metaphysics of senses, and various possible solutions. Certain more deflationary and nontraditional understanding of senses, and to what extent they fare better in solving the problems, are also discussed. In the end, it is concluded that one must divide senses into various ramified-orders in order to avoid antinomy, but that the philosophical justification of such orders is, as yet, still somewhat problematic.
27. Russell on ‘Disambiguating With the Grain’
    Russell n.s. 21 (2001–02): 101–27.
    Abstract PDF PhilPapers
    Fregeans face the difficulty finding a notation for distinguishing statements about the sense or meaning of an expression as opposed to its reference or denotation. Famously, in “On Denoting”, Russell rejected methods that begin with an expression designating its denotation, and then alter it with a “the meaning of” operator to designate the meaning. Such methods attempt an impossible “backward road” from denotation to meaning. Contemporary neo-Fregeans (especially Pavel Tichý), however, have suggested that we can disambiguate with, rather than against, the grain, by using a notation that begins with expressions designating senses or meanings, and then alters them with a “the denotation of” operator to designate the denotation. I show that in his manuscripts of 1903–05 Russell both considered and rejected a similar notation along with the metaphysical suppositions underlying it. This discussion sheds light on the evolution of Russell’s thought, and may yet be instructive for ongoing debates.
28. When is Genetic Reasoning not Fallacious?
    Argumentation 16 (2002): 383–400.
    Abstract PDF PhilPapers
    Attempts to evaluate a belief or argument on the basis of its cause or origin are usually condemned as committing the genetic fallacy. However, I sketch a number of cases in which causal or historical factors are logically relevant to evaluating a belief, including an interesting abductive form that reasons from the best explanation for the existence of a belief to its likely truth. Such arguments are also susceptible to refutation by genetic reasoning that may come very close to the standard examples given of supposedly fallacious genetic reasoning.
29. Russell’s Paradox in Appendix B of the Principles of Mathematics: Was Frege’s Response Adequate?
    History and Philosophy of Logic 22 (2001): 13–28.
    Abstract PDF PhilPapers
    In their correspondence in 1902 and 1903, after discussing Russell’s paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naïve class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein.
30. Agency, Character and the Real Failure of Consequentialism
    Auslegung 23/1 (2000): 1–34.
    Abstract PDF PhilPapers
    Certain consequentialists have responded to deontological worries regarding personal projects or options and agent-centered restrictions or constraints by pointing out that it is consistent with consequentialist principles that people develop within themselves, dispositions to act with such things in mind, even if doing so does not lead to the best consequences on every occasion. This paper argues that making this response requires shifting the focus of moral evaluation off of evaluation of individual actions and towards evaluation of whole character traits and patterns of behavior. However, this weds consequentialism to a sort of psychological determinism, with which it is incompatible, because it makes any sort of assessment in terms of right or wrong incoherent. The paper concludes by sketching an ethical theory that abandons right and wrong as its organizing concepts, but nevertheless preserves much of the spirit of consequentialism. Relationships between whole patterns of behavior and the production of good and bad consequences can be studied and analyzed, and this information can be used to improve society and ourselves, without it being required that any individual acts or dispositions to behave be evaluated as right or wrong.
31. Is Pacifism Irrational?
    Peace Review 11/1 (1999): 65–70.
    Abstract PDF PhilPapers
    In this paper, I counter arguments to the effect that pacifism must be irrational which cite hypothetical situations in which violence is necessary to prevent a far greater evil. I argue that for persons similar to myself, for whom such scenarios are extremely unlikely, promoting in oneself the disposition to avoid violence in any circumstances is more likely to lead to better results than not cultivating such a disposition just for the sake of such unlikely eventualities.

Reviews and review essays

1. Review of On the Genealogy of Universals: The Metaphysical Origins of Analytic Philosophy, by Fraser MacBride (Oxford 2018)
   Notre Dame Philosophical Reviews 2018.
   Web Link PhilPapers
2. Review of Basic Laws of Arithmetic, ed. and trans. by P. Ebert and M. Rossberg (Oxford 2013)
   Studia Logica 104 (2016): 175–80.
   PDF PhilPapers
3. Review of Russell’s Philosophy of Logical Atomism 1897–1905, by Jolen Galaugher (Palgrave Macmillan 2013)
   Journal for the History of Analytical Philosophy 3/2 (2015): 1–7.
   PDF PhilPapers
4. Review of The Oxford Handbook of the History of Analytic Philosophy, ed. by Michael Beaney (Oxford 2013)
   Notre Dame Philosophical Reviews 2014.
   Web Link
5. Review of Logic as Universal Science: Russell’s Early Logicism and Its Philosophical Context, by Anssi Korhonen (Palgrave Macmillan 2013)
   Russell n.s. 34/1 (2014): 79–84.
   PDF PhilPapers
6. Review of Russell’s Unknown Logicism, by Sébastien Gandon (Palgrave Macmillan 2012)
   Notre Dame Philosophical Reviews 2012.
   Web Link PhilPapers
7. Review of Russell, by Gregory Landini (Routledge 2011)
   Journal for the History of Analytical Philosophy 1/2 (2012): 21–28.
   PDF PhilPapers
8. A New Century in the Life of a Paradox, Review of One Hundred Years of Russell’s Paradox, ed. by Godehard Link (de Gruyter 2004)
   Review of Modern Logic 11/1‒2 (2007–2008): 7–29.
   PDF PhilPapers
9. Review of “On Denoting” 1905–2005, ed. by G. Imaguire and B. Linsky (Philosophia 2005)
   Notre Dame Philosophical Reviews 2006.
   Web Link PhilPapers
10. Review of The Cambridge Companion to Bertrand Russell, ed. by Nicholas Griffin (Cambridge 2003)
    Review of Modern Logic 10/1–2 (2005): 161–70.
    PDF PhilPapers
11. Review of The Philosophy of Gottlob Frege, by Richard Mendelsohn (Cambridge 2005)
    Notre Dame Philosophical Reviews 2005.
    Web Link PhilPapers
12. A Faithful Companion, Review of The Cambridge Companion to Bertrand Russell, ed. by Nicholas Griffin (Cambridge 2003)
    The Bertrand Russell Society Quarterly no. 121 (2004): 25–41.
    Web Link PhilPapers
13. Review of Logicism and the Philosophy of Language: Selections from Frege and Russell, ed. by A. Sullivan (Broadview 2003)
    The Bertrand Russell Society Quarterly no. 120 (2003): 39–43.
    Web Link PhilPapers
14. Review of From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy, ed. by Erich Reck (Oxford 2002)
    The Review of Metaphysics 57 (2003): 177–178.
    PDF PhilPapers

Encyclopedia articles

1. Russell’s Logical Atomism (The Stanford Encyclopedia of Philosophy)
   Abstract Web Link PhilPapers
   A summary of Russell’s logical atomism, understood to include both a metaphysical view and a certain methodology for doing philosophy. The metaphysical view amounts to the claim that the world consists of a plurality of independently existing things exhibiting qualities and standing in relations. The methodological view recommends a process of analysis, whereby one attempts to define or reconstruct more complex notions or vocabularies in terms of simpler ones. The origins of this theory, and its influence and reception are also discussed.
2. Frege, Gottlob (The Internet Encyclopedia of Philosophy)
   Web Link PhilPapers
3. Propositional Logic (The Internet Encyclopedia of Philosophy)
   Web Link PhilPapers
4. Paradox, Russell’s (The Internet Encyclopedia of Philosophy)
   Web Link PhilPapers
5. Paradox, Russell-Myhill (The Internet Encyclopedia of Philosophy)
   Web Link PhilPapers
6. Validity and Soundness (The Internet Encyclopedia of Philosophy)
   Web Link
7. Square of Opposition (The Internet Encyclopedia of Philosophy)
   Web Link

Online Editions

I think it is a good idea for academics to produce high-quality open access editions of important public-domain works, which are often available only in much lower quality than books not in the public domain. This is the only way to preserve the integrity of these texts in the centuries to come.

So far I have worked on three such projects, and hope to do more in the future.

• Bertrand Russell: The Principles of Mathematics
  Free online edition. First published in 1903.
• Bertrand Russell: Introduction to Mathematical Philosophy
  Online corrected edition. First published in 1919.
• Ludwig Wittgenstein: Tractatus Logico-Philosophicus
  Side-by-side-by-side edition. First published 1922. This version contains the German alongside both major English translations.

E-Projects

Logic Penguin

Logic Penguin aims to be a flexible, extensible, self-hostable, framework for creating introductory logic exercises, which interfaces with LMS systems like Moodle or Canvas through the LTI protocol. It aims to be compatible with multiple logical systems and notations. It includes a proof-checker, a translation and equivalence checker, truth-tables, and more.

Here is a sample of what it looks like in action:

While I am already employing an early version in my own courses, it still needs a lot of development. You can track my progress on its GitHub repository.

Open Guide Typesetting Framework / Open Guide Editor

The Open Guide Typesetting Framework is a simple but powerful open source framework for open access academic publishing. It can be used to produce and typeset high-quality journal articles, anthology chapters or similar, with multiple output formats (HTML, ePub, LaTeX-generated PDF, or others).

The framework makes use of the pandoc document converter by default, and its academic flavor of markdown, although it can be configured to use other tools instead or additionally. It also provides mechanisms for editors to distribute page proofs to authors and for them to submit comments and corrections.

It includes its own web based markdown and LaTeX editor, the Open Guide Editor, built on codemirror, which provides a live-updating-as-you-type preview of PDF or html output. This editor can be installed and used independently of the framework.

Here is a demonstration of what the editor looks like and how it is used.

Both are recent projects which still may need some testing and bug fixing, They replace previous projects of mine. I created a less powerful web-based framework for academic typesetting (originally for The Journal for the History of Analytical Philosophy), "Journal Tools", which also was made freely available and open source. You can find its git repository on Bitbucket. It uses an earlier editor built on an earlier version of codemirror also providing a live-updating web-based markdown and LaTeX editor, K(ev)E(dit). Their code is still available for archival purposes.

The Amazing Fregeifier

The Fregeifier provides tools for leveraging LaTeX-packages for creating complex or unusual mathematical and logical formulas, and including them in other kinds of documents, including html, epub, docx, odt, etc.

The name comes from one obvious use case: Gottlob Frege’s unique logical notation, for which LaTeX tools exist, but is difficult to do inside other file formats.

Currently, there are two tools in the Fregeifier.

1. A pandoc filter for selecting certain mathematical contexts, usually in a source markdown file, and processing them with a full LaTeX engine, and converting the result to an image that can be used in other formats such as html, epub, docx, odt. This allows the usage of Frege’s notation, or any other mathematical symbolism LaTeX can handle, in a markdown document, regardless of the format it is converted to.
   
2. A web interface which anyone can use to generate images to include in whatever documents they like. A live, hopefully working, instance of the web interface can be found here:
   https://russellguide.org/fregeifier

The Fregeifier has other uses, such as leveraging Landon Elkind’s principia package for using Russell and Whitehead’s historical notation in other documents.

You can find more information, download the pandoc filter, and view the code for both it and the web interface, in the project’s git repo on GitHub.

KNAP: Kevin's Neovim Auto-Previewer

KNAP is a configurable lua plugin for neovim that allows for custom-defined routines for launching self-updating previews of documents such as LaTeX, markdown, etc., in the PDF viewer or Web Browser of your choice. Visit its git repo on GitHub for installation and usage instructions.

At some point in the past, I wrote similar plugins for the micro editor, and for regular vim, which may still be floating out there on the internet, though I shudder to think of them now …

Philosophical rock

I maintain the website for The 21st Century Monads; the rockingest of all philosophical rock bands.

Other/Stuff I Like

Open source/free software

The internet was built on the back on free software, but is increasingly being taken over by commercial interests.

When you give yourself over to Apple, Microsoft, Google, et al., you are making a vote for a more corporation-controlled digital world. Take back the web!

The free-license, open source alternatives may take awhile to learn, but they more than make up for it in power, efficiency, adaptability and freedom.

GNU/Linux

Your choices for operating systems for your computer are these:

1. MacOS: An operating system best known for being defective by design in that (i) it is only licensed to be run on expensive Apple hardware, (ii) it only interoperates well with other Apple devices, and (iii) it is so inefficient that if you haven’t purchased new Apple hardware in the past two years, it is completely unusable. The reason for its popularity in academia remains a mystery, but prevailing theories postulate it is because people are drawn to things in shiny white cases.
2. MS Windows: An operating system best known for using 60% of its cpu cycles to gather information about you and send it to Microsoft, 30% of its cpu cycles running virus and malware scans to make up for its own security deficiencies, and at most 5% for doing the things the user actually intended to do. No one knows what the other 5% does. But your parents probably already know how to use it, which is a big plus.
3. ChromeOS: An operating system for Chromebooks designed mainly to get children hooked on Google products in much the same way drug dealers give out their first doses of crack to get returning customers. It also makes you feel special by taking note of everything you do and relaying it to Google.
4. GNU/Linux: A family of operating systems known for their superior stability, reliability, efficiency, security, flexibility, open source codebase, large repositories of free software, respect for privacy, and lack of cost. They power 70% of web servers and all 500 top supercomputers in the world. Distributions of linux are available to meet almost any use case, from beginner friendly systems designed for education to those more suited for the advanced user. Linux is unpopular among academics mainly because smart people who teach for a living rarely like to learn new things, especially when they’ve already gone through the trouble of learning something else.
5. Others: FreeBSD, OpenBSD, Haiku, RedoxOS, TempleOS, ReactOS, etc. Sure, why not? Have fun.

Useful GNU/Linux links:

• Find a distribution (version) of GNU/Linux that is right for you with distrochooser.
• Try a beginner’s distro like Ubuntu, Fedora, PopOS, or Linux Mint.
• Graduate to a grown up distro like Arch Linux, Void or what the heck, Gentoo.
• Read Riki Heck on how they started using linux and why you should too.
• UNIX/Linux StackExchange.

Other stuff I like

• Society for the Study of the History of Analytical Philosophy
• The Bertrand Russell Society
• Amnesty International
• University of Massachusetts Amherst
• Pandoc document converter and markdown processor
• My kids