Last Updated August 2005
Frege, Russell and Wittgenstein have had a unique and powerful influence on almost all aspects of twentieth century analytic philosophy. A study of these authors is thus an excellent introduction to a good range of the most important contemporary debates in philosophy.
Study in this area requires that you should know the work of at least two of these authors (somewhat artificially, Wittgenstein's early and late work are counted as separate bodies of work for this requirement). The best plan is to read carefully some of the main texts of all three, even if your natural interests leads to your putting more work into two of them.
The paper offers some chance to study related philosophers working at the same time as these three; some reading is attached concerning the Vienna Circle, with whom Wittgenstein had both contact and influence.
(*Items marked with an asterisk are specially suitable for students starting work on this topic.)
*The Foundations of Arithmetic: a Logico-mathematical Enquiry into the Concept of Number. Trans. by J. L. Austin. Oxford: Blackwell, 1953.
The Basic Laws of Arithmetic: Exposition of the System. Translated by M. Furth. Berkeley: University of California Press, 1964. Frege's Introduction, Sections 1-9.
Translations from the Philosophical Writings of Gottlob Frege. Edited by Peter Geach and Max Black. 3rd ed. Oxford: Basil Blackwell, 1980.
The Frege Reader. ed., M. Beaney. Oxford: Blackwell, 1997.
The first of these (the Grundlagen der Arithmetik, 1884) is Frege's brilliant informal exposition and defence of his views of the nature of cardinal numbers. It is worth starting here-the book is a delight to read, and contains many of Frege's key claims relevant both to his philosophy of mathematics and his philosophy of language. He is the father of mathematical logic and had published his 'Concept Script', the Begriffschrift in 1879 (a complete translation of which can be found in J. Van Heijenoort, ed., From Frege to Gödel), from this you should read the introduction. In his early work, Frege talks only of content (Inhalt), but from 1892 on, with 'On Sense and Reference (Bedeutung)', he introduced a distinction between the sense of a term and its Bedeutung (variously translated as reference, nominatum, semantic value or Meaning). In his Basic Laws (the Grundgesetze der Arithmetik, Vol. 1, 1893), Frege aimed to provide a fully rigorous account of his logicism about arithmetic; when the second volume was already in press, Frege was informed by letter of Russell's discovery of the paradoxes deriving from Frege's Basic Law V. Although Frege first attempted to provide a patch for this problem, he later came to think of his attempt to provide foundations for arithmetic a failure. Among the essays of his you should read are some from the time of 'On Sense and Reference', collected in Geach and Black and in Beaney:
Introduction to Begriffschrift.
*'Function and Concept'.
*'On Concept and Object'.
*'On Sense and Reference', in recent editions translated as 'On Sense and Meaning'.
'What is a Function?'.
And some late essays, particularly 'Thoughts' (1918-19), when Frege appears to have been intending to present his general views on logic
*'Thoughts'. In Logical Investigations, translated by P. T. Geach and R. H. Stoothoff (Oxford: Blackwell, 1977); Collected Papers On Mathematics Logic and Philosophy, edited by Brian McGuinness (Oxford: Basil Blackwell, 1984), or The Frege Reader; may also be found in N. Salmon & S. Soames, eds., Propositions & Attitudes; (Oxford: Oxford University Press, 1988) and, translated as 'The Thought', can be found in P. F. Strawson, ed., Philosophical Logic, (Oxford: Oxford University Press, 1967).
*Kenny, A. 1995. Frege. London: Penguin Books.
*Evans, G. 1982. Varieties of Reference. Edited by John McDowell. Oxford: Clarendon Press. Ch.1.
*Dummett, M. 1981. Frege: Philosophy of Language. 2nd ed. London: Duckworth.
*Dummett, M. 1991. Frege: Philosophy of Mathematics. London: Duckworth.
*Weiner, J. 1999. Frege. Oxford: Oxford University Press.
Beaney, M. 1996. Frege: Making Sense. London: Duckworth.
Dummett, M. 1981. The Interpretation of Frege's Philosophy. London: Duckworth.
Carl, W. 1994. Frege's Theory of Sense and Reference: Its Origins and Scope. Cambridge: Cambridge University Press.
*Furth, M. 1964. 'Editor's Introduction', to Gottlob Frege, The Basic Laws of Arithmetic: Exposition of the System, trans. by M. Furth. Berkeley: University of California Press.
Sluga, H. 1980. Gottlob Frege. London: Routledge & Kegan Paul.
Bell, D. 1979. Frege's Theory of Judgment. Oxford: Clarendon Press.
Currie, G. 1982. Frege: An Introduction to his Philosophy. Brighton: Harvester Press.
Wright, C. 1983. Frege's Conception of Numbers as Objects. Aberdeen: Aberdeen University Press.
Weiner, J. 1990. Frege in Perspective. Ithaca, N. Y.: Cornell University Press.
Resnik, M. D. 1980. Frege and the Philosophy of Mathematics. Ithaca: Cornell University Press.
Klemke, E. ed. 1968. Essays On Frege. Urbana: University of Illinois Press.
*Demopoulos, W. ed. 1995. Frege's Philosophy of Mathematics. Cambridge, Mass.: Harvard University Press.
Wright, C. ed. 1984. Frege: Tradition & Influence. Oxford: Blackwell.
Haaparanta, L., and J. Hintikka. eds. 1986. Frege Synthesized: Essays on the Philosophical and Foundational Work of Gottlob Frege. Dordrecht: Reidel.
Mind 101 (October), 1992, for the special issue on the centenary of the publication of 'On Sense and Reference'.
Russell's philosophy went through a number of phases, and he is well-known for changing his mind regularly on philosophical issues. His work in the first two decades of the twentieth century is among the major influences on the development of analytic philosophy, especially in logic, epistemology, metaphysics, philosophy of mathematics and philosophy of language.
Particularly significant from this period are the article 'On Denoting' (1905), which expounds his famous Theory of Descriptions, and Principia Mathematica (1910-1913), the monumental attempt to defend logicism, written jointly with A. N. Whitehead. The Introduction to Principia is essential reading, as is 'Mathematical Logic as based on the Theory of Types'; the 1919 Introduction to Mathematical Philosophy (London: Allen & Unwin, 1919; with a new introduction by John G. Slater, London: Routledge, 1993), contains a shorter, more informal presentation of his views on mathematics and logic. For Russell's epistemological twists and turns, start with the 'shilling shocker', Problems of Philosophy (London: Williams and Norgate, 1912; with a new introduction by John Skorupski, Oxford: Oxford Paperbacks, 1998); Russell devoted himself to an extended work of epistemology, The Theory of Knowledge, 1913, which he abandoned in despair after criticism by Wittgenstein, it has only recently come into print (Collected Papers of Bertrand Russell, Vol.7, London: Allen & Unwin, 1984; and Theory of Knowledge: the 1913 Manuscript, London: Routledge, 1992). Essential reading is also 'The Philosophy of Logical Atomism', 1918, a series of lectures, available in Logic & Knowledge: Essays 1901-1950, ed. R. C. Marsh (London: Allen & Unwin, 1956)—the most important collection of Russell's shorter pieces from this period in Russell's philosophy—and in Russell's Logical Atomism, ed. David Pears (London: Fontana, 1972). Russell himself gave an engaging and readable account of his ideas in My Philosophical Development (London: Allen and Unwin, 1959).
The Principles of Mathematics. Cambridge: Cambridge University Press, 1903.
Our Knowledge of the External World, as a Field for Scientific Method in Philosophy. Chicago: Open Court, 1914.
Introduction to Mathematical Philosophy. London: Allen & Unwin, 1919.
'On the Nature of Acquaintance'. In Logic & Knowledge, ed. R.C. Marsh. London: Allen & Unwin, 1956.
'On Knowledge by Acquaintance and Knowledge by Description'. In Mysticism & Logic. 2nd ed. London: Allen & Unwin, 1917.
*'On the Relation of Sense-data to Physics'. In Mysticism & Logic. 2nd ed. London: Allen & Unwin, 1917.
'Mathematical Logic as Based on the Theory of Types', 1908. In Logic and Knowledge: Essays 1901-1950, ed. R. C. Marsh. London: Allen & Unwin, 1956; also in Frege and Gödel: two Fundamental Texts in Mathematical Logic, edited by Jan van Heijenoort. Cambridge, Mass.: Harvard University Press, 1970.
*Sainsbury, R. M. 1979. Russell. London: Routledge and Kegan Paul.
*Grayling, A. C. 1996. Russell. Oxford: Oxford University Press.
Pears, D. F. 1972. Bertrand Russell and the British Tradition in Philosophy. London: Fontana.
Hylton, P. 1990. Russell, Idealism, and the Emergence of Analytic Philosophy. Oxford: Clarendon Press.
Klemke, E. ed. 1970. Essays on Bertrand Russell. Urbana: University of Illinois Press.
Savage, C. Wade, and C. Anthony Anderson. eds. 1989. Rereading Russell: Essays in Bertrand Russell's Metaphysics and Epistemology. Minneapolis: University of Minnesota Press.
Irvine, A. D., and G. A. Wedeking. eds. 1993. Russell & Analytic Philosophy. Toronto: University of Toronto Press.
Wittgenstein published in his lifetime only one book and one article and attempted to prepare one further book for publication. His philosophical writings are nevertheless prodigious. This work can be divided into three periods: an early period crystallised in the Tractatus; a middle period from which various manuscripts and notes on lectures survive; and a later period marked by the text we now know as the Philosophical Investigations.
The essential texts to read are
Tractatus Logico-Philosophicus, translation by D. F. Pears and B. F. McGuinness (London: Routledge and Kegan Paul, 1961).
Philosophical Investigations, translated by G. E. M. Anscombe (Oxford: Basil Blackwell, 1953; 3rd ed, 2001).
You should read both even if you intend just to focus on Wittgenstein's early period or his late period. Wittgenstein intended that both works should be published together as he took each to throw much light on the other.
The Tractatus is the only philosophical book that Wittgenstein sent to press, but he left behind a vast and complex collection of manuscripts and typescripts known as Wittgenstein's Nachlass. Wittgenstein's literary executors arranged some of this material for publication in book form (the Investigations fall to some extent in this category). Some of the most important volumes produced in this way include:
This contains first formulations of many of the ideas which appear in the Tractatus, together with many others which came to be rejected in the course of composition.
Philosophical Remarks, edited from his posthumous writings by Rush Rhees; translated by R. Hargreaves and R. White, (Oxford: Blackwell, 1975).
Philosophical Grammar, edited by Rush Rhees; translated by Anthony Kenny, (Oxford: Basil Blackwell, 1974).
These two collections of remarks constitute a transition between the early views expressed in the Tractatus, and the later ones of the Investigations.
The Blue & Brown Books (2nd ed. Oxford: Blackwell, 1969).
The Blue Book, so-called for the covers in which it circulated, was prepared by Wittgenstein for his students, and hence offers a more straightforward exposition of the tenets contained within it than the Investigations; the Brown Book with which it is published is an early draft, in typescript, of the first part of the Investigations.
On Certainty, edited by G. E. M. Anscombe and G. H. von Wright; translated by Denis Paul and G. E. M. Anscombe, (Oxford: Blackwell, 1969).
This is Wittgenstein's last work, and is of particular interest for his views on epistemology.
Remarks on the Foundation of Mathematics, edited by G. H. von Wright, R. Rhees, and G. E. M. Anscombe; translated by G. E. M. Anscombe, (3rd ed. Oxford: Blackwell, 1978).
Pts. I and VI of this volume are particularly important in the study of Wittgenstein's views about rule-following. Surveying this volume makes clear that Wittgenstein was inclined to think that his views on rule-following had radical implications for the philosophy of mathematics. Few of these conclusions are drawn in the Investigations, so it is unclear how far Wittgenstein held to them.
The whole Nachlass has been recently published electronically (see http://www.oup.co.uk/academic/humanities/philosophy/wittgenstein/), and is available from some college libraries.
Kenny, A. 1973. Wittgenstein. London: Penguin Books.
Hacker, P. M. S. 1972. Insight & Illusion. Oxford: Clarendon Press; rev. ed. Oxford: Clarendon Press, 1986. Note that there are two editions of this book; the second removes one chapter of the first edition, adds a new chapter and revises many of Hacker's earlier views. Both editions are worth looking at.
Pears, D. F. 1987-88. The False Prison: a Study of the Development of Wittgenstein's Philosophy. 2 Vols. Oxford: Clarendon Press. Part I of this book offers an excellent overview of Wittgenstein's work, emphasising the continuity in his thought over the discontinuities that it is more common to note. Part II deals with the early Wittgenstein, and Part III (vol. 2) with the late Wittgenstein.
Schulte, J. 1992. Wittgenstein. An Introduction. Albany, New York: State University of New York Press.
Stern, D. G. 1995. Wittgenstein on Mind and Language. New York and Oxford,
Oxford University Press.
Fogelin, R. 1976. Wittgenstein. London: Routledge and Kegan Paul.
Winch, P. ed. 1969. Studies in the Philosophy of Wittgenstein. London: Routledge & Kegan Paul.
Pitcher, G. ed. 1964. Wittgenstein. Englewood Cliffs, N. J.: Prentice-Hall.
Block, I. ed. 1981. Perspectives on the Philosophy of Wittgenstein. Oxford: Blackwell.
French, Peter A., Theodore E. Uehling, Jr., and Howard K. Wettstein. eds. 1992. The Wittgenstein Legacy. Midwest Studies in Philosophy 17. Notre Dame, In.: University of Notre Dame Press.
Sluga, H., and D. Stern. eds. 1996. The Cambridge Companion to Wittgenstein. Cambridge: Cambridge University Press.
Mounce, H. O. 1981. Wittgenstein's Tractatus: An Introduction. Oxford: Blackwell.
Anscombe, G. E. M. 1971. An Introduction to Wittgenstein's Tractatus. 4th ed. Philadelphia: University of Pennsylvania Press.
Stenius, E. 1960. Wittgenstein's Tractatus: a Critical Exposition of the Main Lines of Thought. Oxford: Blackwell.
Griffin, J. 1964. Wittgenstein's Logical Atomism. Oxford: Oxford University Press.
McGinn, M. 1997. Wittgenstein and the Philosophical Investigations. London: Routledge.
There is a series of scholarly works on Part One of the Investigations produced by Peter Hacker and Gordon Baker, and then by Peter Hacker alone, which contain essays full of contentious interpretation and detailed exegesis and analytical commentary, section by section through the Investigations. These are useful to browse.
Baker, G. P., and P. M. S. Hacker. 1983. Meaning and Understanding. Oxford: Blackwell. Together with An Analytical Commentary on Wittgenstein's Philosophical Investigations, originally published together as Wittgenstein-Understanding and Meaning. These two volumes cover §§1-184.
—. 1985. Rules, Grammar & Necessity. Oxford: Basil Blackwell. §§185-242.
Hacker, P. M. S. 1990. Wittgenstein: Meaning & Mind. Oxford: Basil Blackwell. §§243-427.
The Vienna Circle was a group of philosophers and scientists who met periodically for discussions in Vienna from 1922/3 to 1938. Building on the development of the logic of Frege, Russell and Wittgenstein and of the metamathematics of Hilbert, the conventionalisms of Poincaré and Duhem and Einstein's exemplar of the 'new' physics, the Circle proposed a controversial conception of scientific philosophy. By means of an empiricist criterion of meaning and use of the analytic-synthetic distinction they claimed to be able to discard metaphysics and put aside as 'pseudo-problems' most previous philosophy.
Initiated by the mathematician Hans Hahn and centred around the philosopher Moritz Schlick, the Vienna Circle included Rudolf Carnap, Herbert Feigl, Philipp Frank, Viktor Kraft, Otto Neurath and Friedrich Waismann and counted Kurt Gödel, Karl Menger and Edgar Zilsel among its associates. The Circle's activities were confined to private meetings until 1929, when they began publishing several series of monographs and collaborated with the Berlin "Society of Empirical Philosophy" (including Hans Reichenbach and C.G. Hempel) in organising international conferences and editing the journal Erkenntnis. The death and dispersion in exile of key members from 1934 onwards did not mean the extinction of Vienna Circle philosophy. Through the subsequent work of foreign visitors (A. J. Ayer, E. Nagel, W. V. O. Quine) and emigré members and collaborators in America, so-called 'logical positivism' or 'logical empiricism' strongly influenced the development of analytic philosophy, occasionally suffering distortions of its original conceptions. Current scholarship of the movement is concerned to retrieve the latter and combat the caricatures that obscure the continuities with present 'post-positivism'.
Carnap, R., H. Hahn, and O. Neurath. 1929. 'Scientific World-Conception: the Vienna Circle'. In O. Neurath, ed., Empiricism and Sociology. Dordrecht: Reidel, 1973. The original 1929 manifesto; popular.
Ayer, A. J. 1936. Language, Truth and Logic. London: Gollantz; 2nd ed., 1946. Potboiler by former visitor assimilating the Circle's thought too seamlessly to British empiricism.
Carnap, R. 1928. The Logical Structure of the World: Pseudo-problems in Philosophy. Translated by Rolf A. George. Routledge & Kegan Paul, 1967. (Originally published as 'Der logische Aufbau der Welt'. Benary, 1928.)
—. 1934. The Logical Syntax of Language. London: Kegan, Paul, Trench, Teubner & Cie., 1937. Studies of the foundations of the empirical and formal science by Circle's most influential theorist; difficult.
—. 1949. Meaning and Necessity: a Study in Semantics and Modal Logic. Chicago: University of Chicago Press; 2nd ed., 1956. Later work on intensional semantics, with important and accessible essays reprinted in supplement to 2nd ed.
Hahn, H. 1980. Empiricism. Logic. Mathematics: Philosophical Papers. Dordecht: Reidel. Collected philosophical papers (1928-34) by founding member, with bibliography.
Feigl, H. 1981. Inquiries and Provocations: Selected Writings 1929-1974. Dordrecht: Reidel. Essays by former student documenting the developments in 'received view' into the 70s.
Frank, P. 1949. Modern Science and Its Philosophy. Cambridge, Mass.: Harvard University Press. Philosophical papers (1907-1949) by founding member, with significant historical retrospective.
Hempel, C. G. 1965. Aspects of Scientific Explanation: and Other Essays in the Philosophy of Science. New York: Free Press. Essays by former student documenting the developments in 'received view' from 40s into the 60s.
Neurath, O. 1983. Philosophical Papers 1913-1946. Dordecht: Reidel. Representative selection of founding member, with bibliography.
—. 1973. Empiricism and Sociology. Dordrecht: Reidel. Selection of papers and monographs on social science and visual education, with memoirs.
Reichenbach, H. 1938. Experience and Prediction: an Analysis of the Foundations and the Structure of Knowledge. Chicago: The University of Chicago Press. General epistemology of important Berlin associate.
—. 1978. Selected Writings 1909-1953, 2 Vols. Dordecht: Reidel. Philosophical papers, reviews and monographs, with bibliography.
Schlick, M. 1918. General Theory of Knowledge. Lasalle, Ill.: Open Court, 1974 (orig. 1918; 2nd ed. 1925). Early epistemological work of later head of Circle, anticipating much that was to come.
—. 1979. Philosophical Papers, 2 Vols. Dordrecht: Reidel. Collected philosophical essays (1909-1936), incl. the important monograph on relativity (1917), with bibliography.
Kraft, V. 1953. The Vienna Circle: the Origin of Neo-positivism, a Chapter in the History of Recent Philosophy. New York: Greenwood Press, 1969. Influential but decontextualised and traditionalist account by participant.
Hanfling, O. 1981. Logical Positivism. Oxford: Blackwell. Traditionalist foundationalist account.
Skorupski, J. 1993. 'Modernism II: Vienna'. In English-Language Philosophy 1750-1945. Oxford: Oxford University Press. Pithy account of fate of original verificationism.
Schilpp, P. A. ed. 1963. The Philosophy of Rudolf Carnap. Lasalle, Ill.: Open Court, . Classic discussions of Carnap's work by collaborators, students and critics, with autobiographical essay and bibliography.
Achinstein, P., and S. F. Barker. eds. 1969. The Legacy of Logical Positivism: studies in the philosophy of science. Baltimore: Johns Hopkins Press. Critical assessments documenting the overthrow of the 'received view'.
Bell, D., and W. Vossenkuhl. eds. 1992. Science and Subjectivity. The Vienna Circle and 20th Century Philosophy. Berlin: Akademie Verlag.
Giere, R., and A. Richardson. eds. 1996. The Origins of Logical Empiricism. Minnesota Studies in the Philosophy of Science. Vol. 16. Minneapolis: University of Minnesota Press.
Rescher, N. ed. 1985. The Heritage of Logical Empiricism. University Press of America.
Sarkar, S. ed. 1993. Carnap Reconsidered. Synthèse.
Spohn, W. ed. 1991. Hans Reichenbach. Rudolf Carnap: A Centenary. Erkenntnis 35. Dordrecht: Kluwer.
Stadler, F. ed. 1993. Scientific Philosophy: Origins and Development. Vienna Circle Institute Yearbook I. Dordrecht: Kluwer.
Cartwright, N., J. Cat, L. Fleck, and T. E. Uebel. eds. 1996. Otto Neurath: Philosophy Between Science and Politics. Cambridge: University Press. Intellectual biography and legacy of Circle's enfant terrible.
Coffa, J. Alberto. 1991. The Semantic Tradition from Kant to Carnap: to the Vienna Station. Cambridge: Cambridge University Press. Defense of Carnap's logical reconstructivism with good account of interactions with Wittgenstein.
Oberdan, T. 1993. Protocols. Truth. Convention. Amsterdam: Rodopi. Examination of protocol sentence debate, with emphasis on Schlick's later philosophy.
Proust, J. 1989. Questions of Form: Logic and the Analytic Proposition from Kant to Carnap. Translated by Anastasios Albert Brenner. Minneapolis: University of Minnesota Press. Historical perspective on Carnap's efforts.
Richardson, A. 1998. Carnap's Construction of the World: the 'Aufbau' and the Emergence of Logical Empiricism. Cambridge: Cambridge University Press. Reconstruction of development of Carnap's early philosophy.
Uebel, T. E. 1992. Overcoming Logical Positivism From Within: the Emergence of Neurath's Naturalism in the Vienna Circle's Protocol Sentence Debate. Amsterdam: Rodopi. Analysis of variety of the epistemological positions adopted in the Viennese protocol sentence debate, with emphasis on Neurath's naturalism.
What is the nature of Frege's logicism? To what extent are his concerns philosophical, mathematical or a combination of the two?
Benacerraf, P. 1983. 'Frege: the Last Logicist', In Peter A. French, Theodore E. Uehling, and Howard K. Wettstein, eds., Contemporary Perspectives on the History of Philosophy, Midwest Studies in Philosophy 8, Minneapolis: University of Minnesota Press; reprinted in W. Demopoulos, ed., Frege's Philosophy of Mathematics, Cambridge, Mass.: Harvard University Press, 1995.
Wilson, M. 1992. 'Frege: The Royal Road from Geometry'. Noûs 26: 149-180; reprinted in W. Demopoulos, ed., Frege's Philosophy of Mathematics, Cambridge, Mass.: Harvard University Press, 1995.
Weiner, J. 1990. Frege in Perspective. Ithaca, N. Y.: Cornell University Press.
—. 1984. 'The Philosopher Behind the Last Logicist'. In C. Wright, ed., Frege: Tradition & Influence. Oxford: Blackwell.
Diamond, C. 1991. 'What does a Concept-Script Do?'. In The Realistic Spirit: Wittgenstein, Philosophy, and the Mind. Cambridge, Mass.: MIT Press.
Why Basic Law V; whence the contradiction; how does one escape?
Furth's Introduction to The Basic Laws of Arithmetic: Exposition of the System. Translated by M. Furth. Berkeley: University of California Press, 1964.
Dummett, M. 1991. Frege: Philosophy of Mathematics. London: Duckworth. Chs.16-18.
—. 1994. 'Chairman's Address: Basic Law V'. Proceedings of the Aristotelian Society 94: 243-251.
Resnik, M. 1980. Frege and the Philosophy of Mathematics. Ithaca: Cornell University Press. Final chapter.
Boolos, G. 1993. 'Basic Law V-Whence the Contradiction?'. Proceedings of the Aristotelian Society Supplementary Volume 67: 213-233.
—. 1987. 'The Consistency of Frege's Foundations of Arithmetic'. In J. J. Thomson, ed., On Being and Saying: Essays in Honour of Richard Cartwright, Cambridge, Mass.: MIT Press; reprinted in W. Demopoulos, ed., Frege's Philosophy of Mathematics, Cambridge, Mass.: Harvard University Press, 1995.
—. 1990. 'The Standard of Equality of Numbers'. Reprinted in W. Demopoulos, ed., Frege's Philosophy of Mathematics, Cambridge, Mass.: Harvard University Press, 1995.
How can the principle be justified; is it an analytic principle? What is 'the Julius Caesar Problem' that leads Frege to reject an implicit definition of cardinal number? What grounds Frege's commitment to treating numbers as objects?
Parsons, C. 1965. 'Frege's Theory of Number'. Reprinted in W. Demopoulos, ed., Frege's Philosophy of Mathematics, Cambridge, Mass.: Harvard University Press, 1995.
Wright, C. 1983. Frege's Conception of Numbers as Objects. Aberdeen: Aberdeen University Press. Chs.1-3.
Dummett, M. 1981. Frege: Philosophy of Language. 2nd ed. London: Duckworth. Ch.14.
—. 1991. Frege: Philosophy of Mathematics. London: Duckworth. Chs. 13-15.
Hale, B. 1987. Abstract Objects. Oxford: Basil Blackwell.
Brandom, R. 1996. 'The Significance of Complex Numbers for Frege's Philosophy of Mathematics'. Proceedings of the Aristotelian Society 96: 293-315.
Dialetica 55: 2 (June 2005). Contains recent articles on this subject.
Resnik, M. D. 1980. Frege and the Philosophy of Mathematics. Ithaca: Cornell University Press.
Dummett, M. 1991. Frege: Philosophy of Mathematics. London: Duckworth. Ch.8.
Kessler, G. 1980. 'Frege, Mill and the Foundations of Arithmetic'. Journal of Philosophy 77: 65-79.
Simons, P. 1982. 'Against the Aggregate Theory of Number'. Journal of Philosophy 79: 163-167.
Kitcher, P. 1983. The Nature of Mathematical Knowledge. Oxford: Oxford University Press.
Some topics here overlap with topics in the Logic and Metaphysics paper. However, preparing for the present paper will normally require additional work, to gain a deeper understanding and one better informed by details of Frege's texts.
What is the motivation for Frege's introduction of the distinction, and what argument can he provide for it?
Dummett, M. 1978. 'Frege's Distinction between Sense and Reference'. In Truth & Other Enigmas. London: Duckworth; reprinted in A. W. Moore, ed., Meaning & Reference. Oxford: Oxford University Press, 1993.
Salmon, N. 1986. Frege's Puzzle. Cambridge, Mass.: MIT Press.
Wiggins, D. 1976. 'Frege's Problem of the Morning Star and the Evening Star'. In M Schirn, ed., Studies on Frege. Stuttgart: Frommann-Holzboog.
McDowell, J. 1977. 'On the Sense and Reference of a Proper Name'. Mind 86: 159-185; reprinted in A. W. Moore, ed., Meaning & Reference. Oxford: Oxford University Press, 1993.
Evans, G. 1982. Varieties of Reference. Edited by John McDowell. Oxford: Clarendon Press. Ch.1.
Frege's term for the sense of a sentence is Gedank, thought. He seems to take such entities to be structured and composed out of the senses of the component words of a sentence; he takes the Bedeutung of true sentences to be an object, the True. He also thinks of thoughts as eternal, and as possessing absolute truth-values, how does reconcile this with the existence of tense and indexicality?
Dummett, M. 1981. Frege: Philosophy of Language. 2nd ed. London: Duckworth. Chs.6, 11, 12.
—. 1981. The Interpretation of Frege's Philosophy. London: Duckworth Ch.6.
—. 1989. 'More about Thoughts'. Reprinted in Frege & Other Philosophers. Oxford: Oxford University Press, 1991.
Burge, T. 1986. 'Frege on Truth'. In L. Haaparanta, and J. Hintikka, eds., Frege Synthesized: Essays on the Philosophical and Foundational Work of Gottlob Frege. Dordrecht: Reidel.
Ricketts, T. 1986. 'Objectivity & Objecthood: Frege's Metaphysics of Judgment'. In L. Haaparanta, and J. Hintikka, eds., Frege Synthesized: Essays on the Philosophical and Foundational Work of Gottlob Frege. Dordrecht: Reidel.
Evans, G. 1981. 'Understanding Demonstratives'. In H. Parret, and J. Bouveresse, eds., Meaning and Understanding. Berlin: W. de Gruyter. Reprinted in his Collected Papers. Oxford: Clarendon Press, 1985.
Perry, J. 1977. 'Frege on Demonstratives'. Philosophical Review 86: 474-497; reprinted in The Problem of the Essential Indexical & Other Essays. New York: Oxford University Press, 1993.
Harcourt, E. 1993. 'Are Hybrid Proper Names the Solution to the Completeness Problem? A Reply to Wolfgang Kunne'. Mind 102: 301-313.
Frege applies the sense/reference distinction to the task of explaining the significance of attitude ascriptions—he introduces the idea of both indirect reference and sense. This seems to threaten an infinite hierarchy of senses of senses.
Dummett, M. 1981. Frege: Philosophy of Language. 2nd ed. London: Duckworth. Ch.9.
Forbes, G. 1990. 'The Indispensability of Sinn'. Philosophical Review 99: 535-563.
Frege ascribes Bedeutung not only to names and descriptions, but also predicates. The referent of a name is an saturated entity, that of a predicate, an unsaturated entity, together they can be unified into a thought. Seemingly paradoxically, Frege must deny that the concept horse (which must be a saturated entity, since it is picked out by a description) is what the predicate 'horse' stands for.
Dummett, M. 1981. Frege: Philosophy of Language. 2nd ed. London: Duckworth. Ch.7.
Wiggins, D. 1984. 'The Sense and Reference of Predicates'. In C. Wright, ed., Frege: Tradition & Influence. Oxford: Blackwell.
Diamond, C. 1991. 'Frege and Nonsense', and 'What Nonsense Might Be', both in The Realistic Spirit: Wittgenstein, Philosophy, and the Mind. Cambridge, Mass.: MIT Press.
Burge, T. 1984. 'Frege on Extensions of Concepts, from 1884 to 1903'. Philosophical Review 93: 3-34.
Sullivan, P. M. 1992. 'The Functional Model of Sentential Complexity'. Journal of Philosophical Logic 21: 91-108.
Rumfitt, I. 1994. 'Frege's Theory of Predication: An Elaboration and Defense, with Some New Applications'. Philosophical Review 103: 599-637.
Russell's definition of number; the contrast with Frege; the no-class theory. Paradoxes: type theories, simple and ramified; semantic and logical paradox.
Copi, I. 1971. The Theory of Logical Types. London: Routledge and Kegan Paul.
Chihara, C. 1973. Ontology & the Vicious Circle Principle. Ithaca: Cornell University Press.
Gödel, K. 'Russell's Mathematical Logic'. Reprinted in P. Benacerraf, and H. Putnam, eds., Philosophy of Mathematics: Selected Readings. Cambridge University Press , 1983.
Goldfarb, W. D. 1989. 'Russell's Reasons for Ramification'. In C. Wade Savage, and C. Anthony Anderson, eds., Rereading Russell: Essays in Bertrand Russell's Metaphysics and Epistemology. Minneapolis: University of Minnesota Press.
Russell's theory of descriptions, names, identity, existence; his criticism of Frege's theory (the 'Gray's Elegy' argument); significance of descriptions for the philosophy of mathematics and for epistemology; belief, truth and the unity of the proposition.
Hylton, P. 1990. Russell, Idealism & the Emergence of Analytic Philosophy. Oxford: Clarendon Press. Ch.6 & 8.
Blackburn, S., and A. Code. 1978. 'The Power of Russell's Criticism of Frege: "On denoting"'. Analysis 38: 48-50.
Pakuluk, M. 1993. 'The Interpretation of Russell's Gray's Elegy Argument'. In Andrew Irvine, and Gary Wedekind, eds., Russell and Analytic Philosophy. Toronto: University of Toronto Press.
Hochberg, H. 1976. 'Russell's Attack on Frege's Theory of Meaning'. Philosophica 18: 9-34. Reprinted in his Logic, Ontology and Language: Essays on Truth and Reality. Munich and Vienna: Philosophia Verlag, 1984.
Griffin, N. 1985. 'Russell's Multiple Relation Theory of Judgement'. Philosophical Studies 47: 213-248.
—. 1986. 'Wittgenstein's Criticism of Russell's Theory of Judgement'. Russell 5: 132-145.
Perception: sense data, idealism. Knowledge by acquaintance and knowledge by description. Analysis, logical atomism, facts. Logical constructions: space, time, the external world.
Pears, D. F. ed. 1972. Russell's Logical Atomism. London: Fontana.
Why does Wittgenstein think that sentences can be analysed into simple signs and the world into simple objects? How are the linguistic and ontological aspects of his thinking about this topic interlinked?
2.0201, 3.2ff. especially 3.24-3.261 (the analysis of language).
1, 2, 2.02-2.0203 (the analysis of the world).
Fogelin, R. 1976. Wittgenstein. London: Routledge and Kegan Paul. Ch.I.
Anscombe, G. E. M. 1971. An Introduction to Wittgenstein's Tractatus. 4th ed. Philadelphia: University of Pennsylvania Press. Chs.1 & 2.
Stenius, E. 1960. Wittgenstein's Tractatus: a Critical Exposition of the Main Lines of Thought. Oxford: Blackwell. Chs.II-IV.
Pears, D.F. 1988. The False Prison: a Study of the Development of Wittgenstein's Philosophy. Vol.1. Oxford: Clarendon Press. Chs.4, 5.
What are pictures? What can picture what? How are pictures related to what they picture? In what sense are linguistic items pictures? What aspects of meaning might the picture theory serve to explain; is it intended to explain meaning at all?
2.1-2.1515, 3, 3.01, 3.1-3.1431, 4.01-4.0311, especially 4.012-4.0141.
Anscombe, G. E. M. 1971. An Introduction to Wittgenstein's Tractatus. 4th ed. Philadelphia: University of Pennsylvania Press. Chs.3-5
Stenius, E. 1960. Wittgenstein's Tractatus: a Critical Exposition of the Main Lines of Thought. Oxford: Blackwell. Chs.VI-VII.
Pears, D. F. 1988. The False Prison: a Study of the Development of Wittgenstein's Philosophy. Vol.1. Oxford: Clarendon Press. Ch.6.
What is Wittgenstein's conception of logical complexity? What is the status of the logical constants? What is Wittgenstein's notion of a formal concept? How is that related to his conception of generality, logical form and the general form of the proposition. What are operations and what is Wittgenstein's account of numbers? Why is logic a 'scaffolding' of the world, and why do tautologies say nothing?
3.3441-3.42, 4.023, 4.0312-4.0411, 4.12-4.5, 5-5.135, 5.14-5.151, 5.2-5.54, 6-6.3751.
Anscombe, G. E. M. 1971. An Introduction to Wittgenstein's Tractatus. 4th ed. Philadelphia: University of Pennsylvania Press. Chs.8-11.
Stenius, E. 1960. Wittgenstein's Tractatus: a Critical Exposition of the Main Lines of Thought. Oxford: Blackwell. Chs.VIII.
Why does Wittgenstein say that there is no such thing as the soul or 'the subject that thinks or entertains ideas'? What is the metaphysical subject and in what sense can philosophy talk about the self 'in a non-psychological way'? In what sense is what the solipsist means correct? Why is the world independent of my will?
5.54-5.5423, 5.6-5.641, 6.371-6.374, 6.41-6.4321.
Pears, D. F. 1988. The False Prison: a Study of the Development of Wittgenstein's Philosophy. Vol.1. Oxford: Clarendon Press. Ch.7.
Hacker, P. M. S. 1972. Insight & Illusion. Oxford: Clarendon Press (rev. ed. Oxford: Clarendon, 1986). Ch.3.
Anscombe, G. E. M. 1971. An Introduction to Wittgenstein's Tractatus. 4th ed. Philadelphia: University of Pennsylvania Press. Ch.13.
What is the distinction between saying and showing, and how does it bear on the most central lessons of the Tractatus?
6.432-7.
McGuinness, B. 1988. Wittgenstein A Life. London: Duckworth. Ch.9.
What are the consequences of the fact that the Tractatus declares its own propositions nonsensical?
Diamond, C. 1991. 'Throwing Away the Ladder: How to Read the Tractatus', reprinted in her The Realistic Spirit: Wittgenstein, Philosophy, and the Mind, Cambridge, Mass.: The MIT Press.
Conant, J. 1991. 'The Search for Logically Alien Thought: Descartes, Kant, Frege and the Tractatus', Philosophical Topics 20: 115-80.
Conant, J. 2000. 'Elucidation and Nonsense in Frege and Early Wittgenstein', in Crary, A. and Read, R. eds. The New Wittgenstein, London: Routledge.
Hacker, P.M.S. 2000. 'Was he Trying to Whistle it?', in Crary, A. and Read, R. eds. The New Wittgenstein, London: Routledge.
Kremer, M. 2001. 'The Purpose of Tractarian Nonsense', Noûs 35: 39-73.
Proops, Ian. 2001. 'The New Wittgenstein: A Critique', European Journal of Philosophy 9: 375-404.
Sullivan, Peter M. 2002. 'On Trying to be Resolute: A Response to Kremer
on the Tractatus', European Journal of Philosophy 10: 43-78.
What picture of language is Wittgenstein attacking? What role do language games play in this attack; and what is the force of the slogan, 'meaning is use'?
Investigations, §§1-65.
The Brown Book, pp.77-88.
Goldfarb, W. D. 1983. 'I Want You to Bring me a Slab: Remarks on the Opening Sections of the Philosophical Investigations'. Synthèse 56: 265-282.
Baker, G. P., and P. M. S. Hacker, 1983. Meaning and Understanding. Oxford: Blackwell. Ch.1.
What is wrong with thinking of understanding as a psychological process? How else should we conceive it?
Investigations, §§28-36; 66-87; 132-242; Pt.II, pp.175-6, 181-3, 216-9.
The Blue Book, pp.1-5.
Budd, M. J. 1989. Wittgenstein's Philosophy of Psychology. London: Routledge. Ch.II.
Baker, G. P., and P. M. S. Hacker, 1983. Meaning and Understanding. Oxford: Blackwell. Ch.XVI.
Goldfarb, W. D. 1992. 'Wittgenstein on Understanding'. In Peter A. French, Theodore E. Uehling, Jr., and Howard K. Wettstein, eds., The Wittgenstein Legacy. Midwest Studies in Philosophy 17. Notre Dame, In.: University of Notre Dame Press.
What is it for me to follow one rule rather than another? Is Wittgenstein a 'sceptic' about following a rule, or attacking a misconception of rule-following for which scepticism might be unavoidable?
Investigations, §§138-242.
Remarks on the Foundations of Mathematics, Pt.I, 1-3, 113-8; Pt.III, 8-9; Pt.V, 32-5, 45-6; Pt.VI, 15-49; Pt.VII, 47-60.
Brown Book, II, 5.
Kripke, S. 1982. Wittgenstein on Rules & Private Language: an Elementary Exposition. Oxford: Blackwell.
Miller, A. and C. Wright, eds. 2002. Rule-Following and Meaning. Chesham: Acumen. A useful recent collection, containing most of the central papers in this area.
Boghossian, P. 1989. 'The Rule-Following Considerations'. Mind 98: 507-549 (reprinted in Miller, A. and C. Wright, eds. 2002. Rule-Following and Meaning).
McDowell, J. 1983. 'Wittgenstein on Following a Rule'. Synthèse 58: 325-364 (reprinted in Miller, A. and C. Wright, eds. 2002. Rule-Following and Meaning).
Wright, C. 1980. Wittgenstein on the Foundation of Mathematics. London: Duckworth, Chapter XII.
—. 1984. 'Kripke's Account of the Argument against Private Language'. Journal of Philosophy 81: 759-777.
Diamond, C. 1991. 'Wittgenstein & Metaphysics'. In The Realistic Spirit: Wittgenstein, Philosophy, and the Mind. Cambridge, Mass.: MIT Press.
Is there only one private language argument? What is the disabling defect of a private language? How does Wittgenstein's arguments here bear on our conception of the 'inner'?
Investigations, §§243-315.
Blue Book.
Budd, M. J. 1989. Wittgenstein's Philosophy of Psychology. London: Routledge. Ch.III.
Hacker, P. M. S. 1972. Insight & Illusion. Rev. ed. Oxford: Clarendon, 1986. Rev. ed., Ch.8.
Kenny, A. 1995. Wittgenstein. London: Penguin Books. Ch.10.
Pears, D. F. 1988. The False Prison: a Study of the Development of Wittgenstein's Philosophy. Vol.2. Oxford: Clarendon Press. Chs.13-15 (look also at Chs.11 & 12).
McDowell, J. 1994. Mind & World. Cambridge, Mass.: Harvard University Press. Lec.2.
Is there a difference between seeing and seeing as? What is problematic about seeing aspects?
Investigations, Pt.II, sec. ix.
Remarks on the Philosophy of Psychology, (look in index for seeing and seeing as).
Budd, M. J. 1989. Wittgenstein's Philosophy of Psychology. London: Routledge. Ch.IV.
Mulhall, S. 1990. On Being in the World: Wittgenstein & Heidegger on Seeing Aspects. London: Routledge.
Strawson, P. F. 1974. 'Imagination and Perception'. In Freedom & Resentment: and Other Essays. London: Methuen.
Is there a sharp divide between necessary truths and what is simply beyond question? What are hinge propositions? What is Wittgenstein's attitude towards Moore's response to scepticism?
On Certainty.
Moore, G. E. 1959. 'Certainty'. In Philosophical Papers. London: George Allen and Unwin.
Kenny, A. 1995. Wittgenstein. London: Penguin Books. Ch.11.
Strawson, Peter F. 1983. Skepticism and Naturalism: Some Varieties. London: Methuen.
McGinn, M. 1989. Sense & Certainty: a Dissolution of Scepticism. Oxford: Blackwell.
Wright, C. 1985. 'Facts & Certainty'. Proceedings of the British Academy.