Richard Heck Romeo Elton Professor of Natural Theology

Richard Heck attended Duke University as an undergraduate, graduating summa cum laude , with distinction, with a B.S. in Mathematics. A Marshall Scholar, he then studied at Oxford University for two years, receiving a B.Phil. in philosophy. His received a doctorate from the Massachusetts Institute of Technology in 1991 and taught at Harvard University from 1991-2005.

Brown Affiliations

Research Areas

scholarly work

‘The Basic Laws of Cardinal Number’ and ‘Formal Arithmetic Before Grundgesetze’, in P. Ebert and M. Rossberg, A Companion to Frege’s Grundgesetze

‘Consistency and the Theory of Truth’, in Review of Symbolic Logic

‘Is Frege’s Definition of the Ancestral Correct?’, in Philosophia Mathematica

Truth in Frege" (with Robert May), forthcoming in M. Glanzberg, ed., The Oxford Handbook of Truth

"Introduction", in Crispin Wright, The Riddle of Vagueness, forthcoming from Oxford University Press

‘Frege Arithmetic and “Everyday Mathematics”’, Philosophia Mathematica 22 (2014), pp. 279–307

‘In Defense of Formal Relationism’, Thought 3 (2014), pp. 243–50

‘Intuition and the Substitution Argument’, Analytic Philosophy 55 (2014), pp. 1–30

"Semantics and Context-Dependence: Towards a Strawsonian Account",  in A. Burgess and B. Sherman, eds., Metasemantics: New Essays on the Foundations of Meaning (Oxford: Oxford University Press, 2014), pp. 327–64

"The Function is Unsaturated" (with Robert May), in M. Beaney, ed., The Oxford Handbook of the History of Analytic Philosophy (Oxford: Oxford University Press, 2013), pp. 825–50

"Is Compositionality a Trivial Principle?", Frontiers of Philosophy in China 8 (2013), pp. 140–55

"Solving Frege's Puzzle", Journal of Philosophy 109 (2012), pp. 132-74

Reading Frege's Grundgesetze (Oxford: Oxford University Press)

"A Liar Paradox", Thought 1 (2012), pp. 36-40

"A Logic for Frege's Theorem," in Frege's Theorem, pp. 267-96

"Ramified Frege Arithmetic", Journal of Philosophical Logic 40 (2011), pp. 715-35

"The Composition of Thoughts" (with Robert May), Noûs 45 (2011), pp. 126-66

"The Existence (and Non-existence) of Abstract Objects", in Frege's Theorem, pp. 200-26

Frege's Theorem (Oxford: Oxford University Press)

"Frege's Theorem: An Overview", in Frege's Theorem, pp. 1-39

"Frege and Semantics," Grazer Philosophische Studien 75 (2007), pp. 27-63; also in The Cambridge Companion to Frege, ed. by T. Ricketts and M. Potter (Cambridge: Cambridge University Press, 2010), pp. 342-78

"Are There Different Kinds of Content?," in J. Cohen and B. McLaughlin, eds., Contemporary Debates in the Philosophy of Mind (Oxford: Blackwells, 2007), pp. 117-38

"Self-reference and the Languages of Arithmetic", Philosophia Mathematica 15 (2007), pp. 1-29

"Meaning and Truth-conditions", in Truth and Speech Acts: Studies in the Philosophy of Language, edited by D. Greimann and G. Siegwart (New York: Routledge, 2007), pp. 349-76

"Use and Meaning", in The Philosophy of Michael Dummett, edited by R.E. Auxier and L.E. Hahn (Chicago: Open Court, 2007), pp. 531-57

"Reason and Language", in C. Macdonald and G. Macdonald, eds., McDowell and His Critics (Oxford: Blackwell Publishing, 2006), pp. 22-45

"Idiolects," in J. J. Thomson and A. Byrne, eds., Content and Modality: Themes from the Philosophy of Robert Stalnaker (Oxford: Oxford University Press, 2006), pp. 61-92

"Frege's Contribution to Philosophy of Language" (with Robert May), E. Lepore and B. Smith, eds., The Oxford Handbook of Philosophy of Language (Oxford: Oxford University Press, 2006), pp. 3-39

"Julius Caesar and Basic Law V", Dialectica 59 (2005), pp. 161-78; reprinted in Frege's Theorem, pp. 111-26

"Truth and Disquotation", Synthese 142 (2004), pp. 317-52

"Frege on Identity and Identity-Statements: A Reply to Thau and Caplan," Canadian Journal of Philosophy 33 (2003), pp. 83-102

"Semantic Accounts of Vagueness", in J.C. Beall, ed., Liars and Heaps (Oxford: Oxford University Press, 2003), pp. 106-27

"Do Demonstratives Have Senses?" Philosophers' Imprint 2 (2002),

"Non-conceptual Content and the 'Space of Reasons,'" Philosophical Review 109 (2000), pp. 483-523

"Cardinality, Counting, and Equinumerosity," Notre Dame Journal of Formal Logic 41 (2000), pp. 187-209; reprinted in Frege's Theorem, pp. 156-79

"Syntactic Reductionism", Philosophia Mathematica 8 (2000), pp. 124-49; reprinted in Frege's Theorem, pp. 180-99

"Grundgesetze der Arithmetik I §10," Philosophia Mathematica 7 (1999), pp. 258-92

"Grundgesetze der Arithmetik I §§29-32," Notre Dame Journal of Formal Logic 38 (1998), pp. 437-74

"Die Grundlagen der Arithmetik §§82-3" (with George Boolos), in M. Schirn, ed., The Philosophy of Mathematics Today, pp. 407-28; reprinted in George Boolos, Logic, Logic, and Logic (Cambridge MA: Harvard University Press, 1998), pp. 315-38; also reprinted, with a Postscript, in Frege's Theorem, pp. 69-89

"The Finite and the Infinite in Frege's Grundgesetze der Arithmetik", in M. Schirn, ed., The Philosophy of Mathematics Today (Oxford: Clarendon Press, 1998), pp. 429-66

"That There Might Be Vague Objects (So Far as Concerns Logic)", The Monist 81 (1998), pp. 277-99

"The Julius Caesar Objection," in R. Heck, ed., Language, Thought, and Logic: Essays in Honour of Michael Dummett (Oxford: Oxford University Press, 1997), pp. 273-308; reprinted in Frege's Theorem, pp. 127-55

"Tarski, Truth, and Semantics," Philosophical Review 106 (1997), pp. 533-54

"Finitude and Hume's Principle," Journal of Philosophical Logic 26 (1997), pp. 589-617; ; reprinted in R. T. Cook, ed., The Arché Papers on the Mathematics of Abstraction (Dordrecht: Springer, 2007), pp. 62-84; also reprinted, with a Postscript, in Frege's Theorem, pp. 237-66.

"The Consistency of Predicative Fragments of Frege's Grundgesetze der Artithmetik", History and Philosophy of Logic 17 (1996), pp. 209-20

"The Sense of Communication," Mind 104 (1995), pp. 79-106

"Definition by Induction in Frege's Grundgesetze der Arithmetik", in W. Demopoulos, ed., Frege's Philosophy of Mathematics (Cambridge MA: Harvard University Press, 1995), pp. 295-333; reprinted in M. Schirn, ed., Frege: Importance and Legacy (New York: de Gruyter, 1996), pp. 200-33

"Frege's Principle", in J.Hintikka, ed., From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics (Dordrecht: Kluwer, 1995), pp. 119-42; reprinted, with a Postscript, in Frege's Theorem, pp. 90-110.

"The Development of Arithmetic in Frege's Grundgesetze der Arithmetik", Journal of Symbolic Logic 58 (1993), pp. 579-601; reprinted, with a postscript, in Demopoulos, ed., Frege's Philosophy of Mathematics, pp. 257-94; also in Frege's Theorem, pp. 40-68

"A Note on the Logic of Higher-order Vagueness", Analysis 53 (1993), pp. 201-8; reprinted in D. Graff and T. Williamson, eds., Vagueness (Dartmouth: Ashgate, 2002), pp. 315-22.

"On the Consistency of Second-order Contextual Definitions", Noûs 26 (1992), pp. 491-4; reprinted, with a Postscript, in Frege's Theorem, pp. 227-36.

research overview

Richard Heck is best known for his work on Frege's philosophy of mathematics. A collection of papers, Frege's Theorem, was published in 2011, by Oxford, and a second book, Reading Frege's Grundgesetze, appeared in 2012.

Professor Heck also works on philosophy of language. He has published on sense and reference and has written several pieces on general questions about the nature of linguistic competence.

Heck has recently been working on Frege's philosophical development and on truth.

research statement

Professor Heck works on various aspects of Frege's philosophy. His first project concerned the question what, precisely, Frege proves in the little-read formal sections of Grundgesetze der Arithmetik . He has also written extensively on Frege's philosophy of logic, in particular on the question how we should understand Part I of Grundgesetze , in which, as Heck and others have noted, Frege develops a semantic theory for his formal language and attempts to prove that theory's adequacy. His book Reading Frege's Grundgesetze covers these topics.

More recently, Heck has been working on how Frege's characteristic semantic doctrines develop. He has written four papers on this subject with Robert May, of the University of California at Davis.

Professor Heck has also worked on technical problems connected to so-called neo-Fregean foundations for arithmetic. In 1996, Heck published a proof of the consistency of the predicative fragment of Frege's formal theory. That paper inspired a good deal of additional research by several people, which has recently been summarized in John Burgess's Fixing Frege . In addition, Heck has also recently closed one of the few outstanding mathematical questions by proving that Frege's proofs of the axioms of arithmetic go through, with some changes, in ramified second-order logic plus a single axiom known as HP, induction being the sole exception. His book Frege's Theorem collects many of his papers on these topics.

Professor Heck's work in philosophy of language proceeds along two lines. His earliest papers in the area were concerned with defending Frege's claim that proper names and other referring expressions have "sense" as well as "reference." More recently, he has been arguing that we cannot properly understand human linguistic behavior, even from a "philosophical" point of view, without attributing semantic knowledge to speakers. Heck regards that project as nearly complete and is working on a book based on several papers that recently have been or shortly will be published.

In philosophy of logic, Heck has worked primarily on truth. He has a lengthy technical study of axiomatic truth-theories formulated over weak base theories in progress.

Finally, Professor Heck dabbles in philosophy of mind. He has published two papers on the question whether perceptual content is 'non-conceptual' and has worked on the question whether the contents of beliefs are intensional.

funded research

Visiting Scholar, Arché, the AHRC Research Center for the Philosophy of Logic, Language, Mathematics and Mind, 2005
British Academy Visiting Professor, University of St Andrews, 2004