Frege, Russell & Wittgenstein

Last Updated August 2005

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  1. The Paper
  2. Basic Reading
  3. Topics

1. The Paper

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.

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2. Basic Reading

(*Items marked with an asterisk are specially suitable for students starting work on this topic.)

Frege

Primary Texts

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:

And some late essays, particularly 'Thoughts' (1918-19), when Frege appears to have been intending to present his general views on logic

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Secondary Texts

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Collections of Articles

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Russell

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.

Main Texts

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).

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Additional Works

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Secondary Texts

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Wittgenstein

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.

Primary Texts

The essential texts to read are

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.

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 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.

This is Wittgenstein's last work, and is of particular interest for his views on epistemology.

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.

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Secondary Texts

Introductory Works on Wittgenstein's Philosophy as a Whole

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Useful Collections of Articles on Wittgenstein's Work as a Whole

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Books on the Tractatus

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Books on the Investigations

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.

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The Vienna Circle

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'.

Sources (general)

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Sources (individual authors)

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Secondary Literature (general)

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Secondary Literature (essays on individual authors & special topics)

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Secondary Literature (recent book-length treatments of individual authors/special topics)

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3. Topics

Frege

Philosophy of Mathematics

Logicism

What is the nature of Frege's logicism? To what extent are his concerns philosophical, mathematical or a combination of the two?

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Basic Law V

Why Basic Law V; whence the contradiction; how does one escape?

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Implicit Definition—'Hume's Principle'

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?

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Frege's Criticisms of Other Views

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Philosophy of Logic and Language

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.

Sense and Reference (Bedeutung)

What is the motivation for Frege's introduction of the distinction, and what argument can he provide for it?

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Thoughts

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?

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Indirect Sense

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.

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The Distinction between Concept and Object

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.

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Russell

Philosophy of Mathematics

Russell's definition of number; the contrast with Frege; the no-class theory. Paradoxes: type theories, simple and ramified; semantic and logical paradox.

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Philosophy of Logic and Language

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.

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Epistemology and Metaphysics

Perception: sense data, idealism. Knowledge by acquaintance and knowledge by description. Analysis, logical atomism, facts. Logical constructions: space, time, the external world.

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Wittgenstein

Tractatus

Analysis

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?

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The Picture Theory

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?

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Logic in the Tractatus

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?

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Self in the Tractatus

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?

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The Mystical

What is the distinction between saying and showing, and how does it bear on the most central lessons of the Tractatus?

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Nonsense

What are the consequences of the fact that the Tractatus declares its own propositions nonsensical?

Investigations

The 'Augustinian' Picture of Meaning

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'?

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Meaning and Understanding

What is wrong with thinking of understanding as a psychological process? How else should we conceive it?

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Rule Following

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?

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Private Languages

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'?

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Seeing As and Seeing Aspects

Is there a difference between seeing and seeing as? What is problematic about seeing aspects?

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Certainty

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?

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