Online Papers

(In J. Cohen and B. McLaughlin, eds, Contemporary Debates in the Philosophy of Mind (Oxford: Blackwells), pp. 117--38)
In an earlier paper, "Non-conceptual Content and the 'Space of Reasons'", I distinguished two forms of the view that perceptual content is non-conceptual, which I called the 'state view' and the 'content view'. On the latter, but not the former, perceptual states have a different kind of content than do cognitive states. Many have found it puzzling why anyone would want to make this claim and, indeed, what it might mean. This paper attempts to address these questions.

(W. Demopoulos, ed., Frege's Philosophy of Mathematics (Cambridge MA: Harvard University Press, 1995), pp. 295-333)
This paper discusses Frege's account of definition by induction in Grundgesetze and the two key theorems Frege proves using it.

(Grazer Philosophische Studien 75 (2007), pp. 27-63)
This paper discusses the question to what extent Frege made serious use of semantical notions such as reference and truth. It focuses on his apparent uses of these notions in his apparently semantical discussions of his formal system in Grundgesetze der Arithmetik and defends the view that they are to be taken at face value. This paper is in some ways a companion to "Grundgesetze der Arithmetik I §§29-32", in which there is an extended, but mostly technical, discussion of Frege's attempt to prove that every well-formed expression in his formal language denotes: "Frege and Semantics" contains more in the way of a discussion of the wider, interpretive significance of the technical interpretation given there.

(The Harvard Review of Philosophy 7 (1999), pp. 56-73)
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.

Primarily a response to Paul Horwich's "Composition of Meanings", the paper attempts to refute his claim that compositionality—roughly, the idea that the meaning of a sentence is determined by the meanings of its parts and how they are there combined—imposes no substantial constraints on semantic theory or on our conception of the meanings of words or sentences.

(Dialectica 59 (2005), pp. 161-78)
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 this issue relates to broader issues in Frege's philosophy.

(forthcoming in the Journal of Philosophical Logic)
Oystein Linnebo has shown that the existence of successors cannot be proven in predicative Frege arithmetic, that is, predicative second-order logic plus "Hume's Principle" and Frege's definitions of zero, predecessor, and natural number. It is shown in the present paper that the existence of successors can be proven if the logic is strengthened to ramified predicative second-order logic. It then follows from work by John Burgess and Allen Hazen that Robinson arithmetic, Q, can be interpreted in ramified Frege arithmetic.

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 it. I grant that psychological explanation must invoke non-intentional features of mental states, but it is of crucial importance which such features must be referenced. It emerges from a careful reading of Frege's own view that we need only invoke what I call 'formal' relations between mental states. I then claim that referencing such 'formal' relations within psychological explanation does not undermine its intentionality in the way that invoking, say, neurological features would. The central worry about this view is that either (a) 'formal' relations bring narrow content in through back door or (b) 'formal' relations end up doing all the explanatory work. Various forms of each worry are discussed. The crucial point, ultimately, is that the present strategy for responding to Frege cases is not available either to the 'psycho-Fregean', who would identify the content of a belief with its truth-value, nor even to someone who would identify the content of a belief with a set of possible worlds. It requires the sort of rich semantic structure that is distinctive of Russellian propositions. There is therefore no reason to suppose that the invocation of 'formal' relations threatens to deprive content of any work to do.

(forthcoming in Status Belli, ed. by P. Ebert and M. Rossberg)
This paper is concerned with neo-Fregean accounts of reference to abstract objects. It develops an objection to the most familiar such accounts, due to Bob Hale and Crispin Wright, based upon what I call the 'proliferation problem': Hale and Wright's account makes reference to abstract objects seem too easy, as is shown by the fact that any equivalence relation seems as good as any other. The paper then develops a response to this objection, and offers an account of what it is for abstracta to exist that is Fregean in spirit but more robust than familiar views.

(in R. Heck, ed., Language, Thought, and Logic: Essays in Honour of Michael Dummett (Oxford: Oxford University Press, 1997), pp. 273-308)
This paper argues that that Caesar problem had a technical aspect, namely, that it threatened to make it impossible to prove, in the way Frege wanted, that there are infinitely many numbers. It then offers a solution to the problem, one that shows Frege did not really need the claim that "numbers are objects", not if that claim is intended in a form that forces the Caesar problem upon us.

(Synthese 142 (2004), pp. 317-52)
Hartry Field has suggested that we should adopt at least a methodological deflationism: "[W]e should assume full-fledged deflationism as a working hypothesis. That way, if full-fledged deflationism should turn out to be inadequate, we will at least have a clearer sense than we now have of just where it is that inflationist assumptions...are needed." I argue here that we do not need to be methodological deflationists. More precisely, I argue that we have no need for a disquotational truth-predicate; that the word "true", in ordinary language, is not a disquotational truth-predicate; and that it is not at all clear that it is even possible to introduce a disquotational truth-predicate into ordinary language. If so, then we have no clear sense how it is even possible to be a methodological deflationist. My goal here is not to convince a committed deflationist to abandon his or her position. My goal, rather, is to argue, contrary to what many seem to think, that reflection on the apparently trivial character of T-sentences should not incline us to deflationism.

(manuscript)
This paper discusses the question whether it is possible to explain the notion of a singular term without invoking the notion of an object or other ontological notions. The framework here is that of Michael Dummett's discussion in Frege: Philosophy of Language. I offer an emended version of Dummett's conditions, accepting but modifying some suggestions made by Bob Hale, and defend the emended conditions against some objections due to Crispin Wright.
This paper dates from about 1989. It originally formed part of a very early draft of what became my Ph.D. dissertation. I rediscovered it and began scanning it, when I had nothing better to do, in Fall 2001, making some minor editing changes along the way. Suffice it to say that it no longer represents my current views. I hope, however, that it remains of some small interest.