•  1348
    Frege’s Theorem: An Introduction
    The Harvard Review of Philosophy 7 (1): 56-73. 1999.
    A brief, non-technical introduction to technical and philosophical aspects of Frege's philosophy of arithmetic. The exposition focuses on Frege's Theorem, which states that the axioms of arithmetic are provable, in second-order logic, from a single non-logical axiom, "Hume's Principle", which itself is: The number of Fs is the same as the number of Gs if, and only if, the Fs and Gs are in one-one correspondence
  •  1237
    Semantic Accounts of Vagueness
    In J. C. Beall (ed.), Liars and Heaps, Oxford University Press Uk. pp. 106-27. 2004.
    Written as a comment on Crispin Wright's "Vagueness: A Fifth Column Approach", this paper defends a form of supervaluationism against Wright's criticisms. Along the way, however, it takes up the question what is really wrong with Epistemicism, how the appeal of the Sorities ought properly to be understood, and why Contextualist accounts of vagueness won't do.
  •  2079
    Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice.
  •  875
    Die Grundlagen der Arithmetik, 82-3
    with George Boolos
    In Matthias Schirn (ed.), The Philosophy of Mathematics Today, Clarendon Press. pp. 407-428. 1998.
    A close look at Frege's proof in "Foundations of Arithmetic" that every number has a successor. The examination reveals a surprising gap in the proof, one that Frege would later fill in "Basic Laws of Arithmetic".
  •  144
    Perhaps the most important argument against deflationism is the so-called Success Argument: The success of certain behavioral strategies depends upon the truth of a person's beliefs. If so, then the notion of truth appears to play an important role in psychological explanation, contradicting the central thesis of deflationism. I argue here that this type of argument poses a particularly difficult problem for disquotationalism, but that the important case concerns the role that the falsity of a p…Read more
  •  684
    Disquotation, Translation, and Context-Dependence
    In Ernest Lepore & David Sosa (eds.), Oxford Studies in Philosophy of Language, 3, Oxford University Press. pp. 99-128. 2023.
    It has been known for some time that context-dependence poses a problem for disquotationalism, but the problem has largely been regarded as one of detail: one that will be solved by the right sort of cleverness. I argue here that the problem is one of principle and that extant solutions, which are based upon the notion of translation, cannot succeed.
  •  1321
    What Bar-On and Simmons call 'Conceptual Deflationism' is the thesis that truth is a 'thin' concept in the sense that it is not suited to play any explanatory role in our scientific theorizing. One obvious place it might play such a role is in semantics, so disquotationalists have been widely concerned to argued that 'compositional principles', such as (C) A conjunction is true iff its conjuncts are true are ultimately quite trivial and, more generally, that semantic theorists have misconce…Read more
  •  3140
    How Not To Watch Feminist Pornography
    Feminist Philosophical Quarterly 7 (1). 2021.
    This paper has three goals. The first is to defend Tristan Taromino and Erika Lust (or some of their films) from criticisms that Rebecca Whisnant and Hans Maes make of them. Toward that end, I will be arguing against the narrow conceptions that Whisnant and Maes have of what `feminist' pornography must be like. More generally, I hope to show by example why it is important to take pornographic films seriously as films if we're to understand their potential to shape, or mis-shape, socio-sexual nor…Read more
  •  899
    Disquotationalism is the view that the only notion of truth we really need is one that can be wholly explained in terms of such trivialities as: “Snow is white” is true iff snow is white. The 'Classical Disquotational Strategy' attempts to establish this view case by case, by showing that each extant appeal to truth, in philosophical or scientific explanations, can be unmasked as an appeal only to disquotational truth. I argue here that the Classical Strategy fails in at least two cases: attribu…Read more
  •  226
    Reply to Hintikka and Sandu: Frege and Second-Order Logic
    Journal of Philosophy 90 (8): 416-424. 1993.
    Hintikka and Sandu had argued that 'Frege's failure to grasp the idea of the standard interpretation of higher-order logic turns his entire foundational project into a hopeless daydream' and that he is 'inextricably committed to a non-standard interpretation' of higher-order logic. We disagree.
  •  1590
    The Birth of Semantics
    Journal for the History of Analytical Philosophy 8 (6): 1-31. 2020.
    We attempt here to trace the evolution of Frege’s thought about truth. What most frames the way we approach the problem is a recognition that hardly any of Frege’s most familiar claims about truth appear in his earliest work. We argue that Frege’s mature views about truth emerge from a fundamental re-thinking of the nature of logic instigated, in large part, by a sustained engagement with the work of George Boole and his followers, after the publication of Begriffsschrift and the appearance of c…Read more
  •  1979
    Pornography and accommodation
    Inquiry: An Interdisciplinary Journal of Philosophy 64 (8): 830-860. 2021.
    ABSTRACT In ‘Scorekeeping in a Pornographic Language Game’, Rae Langton and Caroline West borrow ideas from David Lewis to attempt to explain how pornography might subordinate and silence women. Pornography is supposed to express certain misogynistic claims implicitly, through presupposition, and to convey them indirectly, through accommodation. I argue that the appeal to accommodation cannot do the sort of work Langton and West want it to do: Their case rests upon an overly simplified model of …Read more
  •  787
    The Logical Strength of Compositional Principles
    Notre Dame Journal of Formal Logic 59 (1): 1-33. 2018.
    This paper investigates a set of issues connected with the so-called conservativeness argument against deflationism. Although I do not defend that argument, I think the discussion of it has raised some interesting questions about whether what I call “compositional principles,” such as “a conjunction is true iff its conjuncts are true,” have substantial content or are in some sense logically trivial. The paper presents a series of results that purport to show that the compositional principles for…Read more
  •  2092
    Solving Frege's puzzle
    Journal of Philosophy 109 (1-2): 132-174. 2012.
    So-called 'Frege cases' pose a challenge for anyone who would hope to treat the contents of beliefs (and similar mental states) as Russellian propositions: It is then impossible to explain people's behavior in Frege cases without invoking non-intentional features of their mental states, and doing that seems to undermine the intentionality of psychological explanation. In the present paper, I develop this sort of objection in what seems to me to be its strongest form, but then offer a response to…Read more
  •  1150
    Formal Arithmetic Before Grundgesetze
    In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic, Oxford University Press. pp. 497-537. 2019.
    A speculative investigation of how Frege's logical views change between Begriffsschrift and Grundgesetze and how this might have affected the formal development of logicism.
  •  1010
    The Basic Laws of Cardinal Number
    In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic, Oxford University Press. pp. 1-30. 2019.
    An overview of what Frege accomplishes in Part II of Grundgesetze, which contains proofs of axioms for arithmetic and several additional results concerning the finite, the infinite, and the relationship between these notions. One might think of this paper as an extremely compressed form of Part II of my book Reading Frege's Grundgesetze.
  •  2156
    Logicism, Ontology, and the Epistemology of Second-Order Logic
    In Ivette Fred Rivera & Jessica Leech (eds.), Being Necessary: Themes of Ontology and Modality from the Work of Bob Hale., Oxford University Press. pp. 140-169. 2018.
    In two recent papers, Bob Hale has attempted to free second-order logic of the 'staggering existential assumptions' with which Quine famously attempted to saddle it. I argue, first, that the ontological issue is at best secondary: the crucial issue about second-order logic, at least for a neo-logicist, is epistemological. I then argue that neither Crispin Wright's attempt to characterize a `neutralist' conception of quantification that is wholly independent of existential commitment, nor Hale's …Read more
  •  359
    One of the earliest discussions of the so-called 'bad company' objection to Neo-Fregeanism, I show that the consistency of an arbitrary second-order 'contextual definition' (nowadays known as an 'abstraction principle' is recursively undecidable. I go on to suggest that an acceptable such principle should satisfy a condition nowadays known as 'stablity'.
  •  922
    Cognitive Hunger: Remarks on Imogen Dickie's Fixing Reference
    Philosophy and Phenomenological Research 95 (3): 738-744. 2017.
    The main focus of my comments is the role played in Dickie's view by the idea that "the mind has a need to represent things outside itself". But there are also some remarks about her (very interesting) suggestion that descriptive names can sometimes fail to refer to the object that satisfies the associated description.
  •  645
    The Frontloading Argument
    Philosophical Studies 175 (10): 2583-2608. 2018.
    Maybe the most important argument in David Chalmers’s monumental book Constructing the World is the one he calls the ‘Frontloading Argument’, which is used in Chapter 4 to argue for the book’s central thesis, A Priori Scrutability. And, at first blush, the Frontloading Argument looks very strong. I argue here, however, that it is incapable of securing the conclusion it is meant to establish.
  •  295
    Syntactic reductionism
    Philosophia Mathematica 8 (2): 124-149. 2000.
    Syntactic Reductionism, as understood here, is the view that the ‘logical forms’ of sentences in which reference to abstract objects appears to be made are misleading so that, on analysis, we can see that no expressions which even purport to refer to abstract objects are present in such sentences. After exploring the motivation for such a view, and arguing that no previous argument against it succeeds, sentences involving generalized quantifiers, such as ‘most’, are examined. It is then argued, …Read more
  •  1383
    The Function is Unsaturated
    with Robert May
    In Michael Beaney (ed.), The Oxford Handbook of The History of Analytic Philosophy, Oxford University Press. pp. 825-50. 2013.
    An investigation of what Frege means by his doctrine that functions (and so concepts) are 'unsaturated'. We argue that this doctrine is far less peculiar than it is usually taken to be. What makes it hard to understand, oddly enough, is the fact that it is so deeply embedded in our contemporary understanding of logic and language. To see this, we look at how it emerges out of Frege's confrontation with the Booleans and how it expresses a fundamental difference between Frege's approach to logic a…Read more
  •  2420
    Frege on Identity and Identity-Statements: A Reply to Thau and Caplan
    Canadian Journal of Philosophy 33 (1): 83-102. 2003.
    The paper argues, as against Thau and Caplan, that the traditional interpretation that Frege abandoned his earlier views about identity and identity--statements is correct
  •  3765
    Nonconceptual content and the "space of reasons"
    Philosophical Review 109 (4): 483-523. 2000.
    In Mind and World, John McDowell argues against the view that perceptual representation is non-conceptual. The central worry is that this view cannot offer any reasonable account of how perception bears rationally upon belief. I argue that this worry, though sensible, can be met, if we are clear that perceptual representation is, though non-conceptual, still in some sense 'assertoric': Perception, like belief, represents things as being thus and so.
  •  1603
    Predicative Frege Arithmetic and ‘Everyday’ Mathematics
    Philosophia Mathematica 22 (3): 279-307. 2014.
    The primary purpose of this note is to demonstrate that predicative Frege arithmetic naturally interprets certain weak but non-trivial arithmetical theories. It will take almost as long to explain what this means and why it matters as it will to prove the results
  •  186
    Frege's Theorem
    Clarendon Press. 2011.
    The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.
  •  967
    Use and Meaning
    In R. E. Auxier & L. E. Hahn (eds.), The Philosophy of Michael Dummett, Open Court. pp. 531--57. 2007.
    Many philosophers have been attracted to the idea that meaning is, in some way or other, determined by use—chief among them, perhaps, Michael Dummett. But John McDowell has argued that Dummett, and anyone else who would seek to draw serious philosophical conclusions from this claim, must face a dilemma: Either the use of a sentence is characterized in terms of what it can be used to say, in which case profound philosophical consequences can hardly follow, or it will be impossible to make out the…Read more
  •  430
    Julius Caesar and Basic Law V
    Dialectica 59 (2). 2005.
    This paper dates from about 1994: I rediscovered it on my hard drive in the spring of 2002. It represents an early attempt to explore the connections between the Julius Caesar problem and Frege's attitude towards Basic Law V. Most of the issues discussed here are ones treated rather differently in my more recent papers "The Julius Caesar Objection" and "Grundgesetze der Arithmetik I 10". But the treatment here is more accessible, in many ways, providing more context and a better sense of how thi…Read more
  •  1442
    Reason and Language
    In Cynthia Macdonald & Graham MacDonald (eds.), McDowell and His Critics, Wiley-blackwell. pp. 22--45. 2008.
    John McDowell has often emphasized the fact that the use of langauge is a rational enterprise. In this paper, I explore the sense in which this is so, arguing that our use of language depends upon our consciously knowing what our words mean. I call this a 'cognitive conception of semantic competence'. The paper also contains a close analysis of the phenomenon of implicature and some suggestions about how it should and should not be understood.
  •  2054
    The Composition of Thoughts
    with Robert May
    Noûs 45 (1): 126-166. 2010.
    Are Fregean thoughts compositionally complex and composed of senses? We argue that, in Begriffsschrift, Frege took 'conceptual contents' to be unstructured, but that he quickly moved away from this position, holding just two years later that conceptual contents divide of themselves into 'function' and 'argument'. This second position is shown to be unstable, however, by Frege's famous substitution puzzle. For Frege, the crucial question the puzzle raises is why "The Morning Star is a planet" and…Read more