Important Works in which Propositional Functions Play a Key Role

• Church, Alonzo, forthcoming, Alonzo Church's Logic of Sense and Denotation, Cambridge: Cambridge University Press. (This has Church's papers in which he develops an intensional logic. In this logic the hierarchy of propositional functions plays an important role in dealing with paradoxes concerning propositional attitude reports—i.e., statements about what people believe, think, deny, etc.) (Scholar)
• Cresswell, M. J., 1973, Logics and Languages, London: Methuen. (This presents a simpler cousin of Montague semantics. The view is used as a semantics for propositional attitude reports in M. Cresswell, Structured Meanings, Cambridge, MA: MIT Press, 1985.) (Scholar)
• Frege, Gottlob, 1892, ‘On Concept and Object’, in Collected Papers, Oxford: Blackwell, 1991, 182–194. (This is the classic presentation of Frege's notion of a concept.) (Scholar)
• Goldblatt, Robert, 2011, Quantifers, Propositions and Identity, Cambridge: Cambridge University Press. (This presents a new semantics for modal predicate logic that uses propositions as well as worlds. Chapter 4 explores some formal reasons for also adding propositional functions to the semantics.) (Scholar)
• Montague, Richard, 1973, Formal Philosophy, New Haven: Yale University Press. (The latter half of the book is about Montague's intensional logic and his semantics for natural language.) (Scholar)
• Ramsey, Frank, 1925, ‘Foundations of Mathematics’, in Ramsey, Foundations: Essays in Philosophy, Logic, Mathematics and Economics, Atlantic Highlands, NJ: Humanities Press, 1978, 152–212. (This presents a theory of propositional functions as a key element of Ramsey's philosophy of mathematics.) (Scholar)
• Russell, Bertrand, 1903, The Principles of Mathematics, New York: Norton and Norton. (This is Russell's first sustained discussion of propositional functions.) (Scholar)
• Whitehead, Alfred North, and Bertrand Russell, 1910–1913 [1925], Principia Mathematica, Cambridge: Cambridge University Press. (This is a sustained, but extremely difficult, presentation of ramified type theory.) (Scholar)

Textbooks in which Propositional Functions Feature Prominently

• Dowty, David R., Robert E. Wall, and Stanley Peters, 1981, Introduction to Montague Semantics, Dordrecht: Reidel, 1981. (This is a very clear textbook on Montague semantics.) (Scholar)
• Gamut, L. T. F., 1991, Logic, Language, and Meaning, Chicago: University of Chicago Press. (A very good and clearly written textbook that covers modal logic, categorial grammar, and Montague semantics, among other topics.) (Scholar)
• Hylton, Peter, 1990, Russell, Idealism and the Emergence of Analytic Philosophy, Oxford: Oxford University Press, 1990. (Scholar)
• Hylton, Peter, 2005, Propositions, Functions, and Analysis: Selected Essays on Russell's Philosophy, Oxford: Oxford University Press. (This work and Hylton 1990 are important texts on the interpretation of Russell's logic. Hylton maintains that Russell's notion of a propositional function does not fit with the rest of his metaphysics.) (Scholar)
• Moortgat, Michael, 1988, Categorial Investigations: Logical and Linguistic Aspects of the Lambek Calculus, Dordrecht: Foris Publications. (This is a dated but excellent book on categorial grammar.) (Scholar)

Other Primary Sources:

• Boole, George, 1854, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, New York: Dover, 1958. (Scholar)
• Frege, Gottlob, 1891, Letter to Edmund Husserl, dated 24 May 1891, in Frege, Philosophical and Mathematical Correspondence, Chicago: University of Chicago Press, 1980, 61–64. (Scholar)
• Frege, Gottlob, 1919,‘Notes for Ludwig Darmstaedter’, in Frege, Posthumous Writings, Chicago: University of Chicago Press, 1979, 253–257. (Scholar)
• Frege, Gottlob, Collected Papers on Mathematics, Logic, and Philosophy, Oxford: Blackwell, 1991.
• Jevons, W. S., 1890, Pure Logic and other Minor Works, Whitefish, MT: Kessinger Publishing, 2009. (Scholar)
• Peano, Giuseppe, 1889, ‘The Principles of Arithmetic Presented by a New Method’, in J. van Heijenoort (ed.), From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879–1931, Cambridge, MA: Harvard University Press, 1981, 83–97. (Scholar)
• Peirce, C. S., 1883, ‘The Logic of Relatives’, in Collected Papers of Charles Sanders Peirce (Volume III: Exact Logic), Cambridge, MA: Harvard University Press, 1933, 195–209. (Scholar)
• Peirce, C. S., 1892, ‘The Critic of Arguments’, in Collected Papers of Charles Sanders Peirce (Volume III: Exact Logic), Cambridge, MA: Harvard University Press, 1933, 250–264. (Scholar)

Other Works Cited

• Church, Alonzo, 1976, ‘Comparison of Russell's Resolution of the Semantical Antinomies with that of Tarski’ The Journal of Symbolic Logic, 41: 747–760. (Scholar)
• Church, Alonzo, 1984, ‘Russell's Theory of Identity of Propositions’ Philosophia Naturalis, 21: 513–22. (Scholar)
• Gödel, Kurt, 1944, ‘Russell's Mathematical Logic’, in P. A. Schilpp (ed.), The Philosophy of Bertrand Russell, New York: Tudor Publishing Co., 123–144. (Scholar)
• Goldfarb, Warren, 1989, ‘Russell's Reasons for Ramification’, in C. W. Savage and C. A. Anderson (eds.), Rereading Russell: Essays on Bertrand Russell's Metaphysics and Epistemology, Minneapolis: University of Minnesota Press, 24–40. (Scholar)
• Hazen, A. P. and J. M. Davoren, 2000, ‘Russell's 1925 Logic’ Australasian Journal of Philosophy, 78: 534–556. (Scholar)
• Kneale, William and Martha Kneale, 1984, The Development of Logic, Oxford: Oxford University Press. (Scholar)
• Landini, Gregory, 1998, Russell's Hidden Substitutional Theory, Oxford: Oxford University Press. (Scholar)
• Lewis, C. I., 1918, A Survey of Symbolic Logic, Berkeley: University of California Press. (Scholar)
• Linsky, Bernard, 1999, Russell's Metaphysical Logic, Stanford: CSLI. (Scholar)
• Steadman, Mark, 1991, ‘Type Raising and Directionality in Combinatory Grammar’ University of Pennsylvania Department of Computer and Information Science Technical Report MS-CIS-91-11. (Scholar)
• Urquhart, Alasdair, 2003, ‘The Theory of Types’, in N. Griffin (ed.), Cambridge Companion to Russell, Cambridge Cambridge University Press, 286–309. (Scholar)