Philosophy of Language: The Key Thinkers

Barry Lee, Barry Lee

• Publisher: Bloomsbury Academic
• Year: 2019
• ISBN:
  9781350084063
• Edition: 2
• Topic: Philosophie
• Subtopic: Sprache in der Philosophie

Playing a key role in our lives, as a vehicle for our thoughts and a powerful medium of communication, language is at the centre of philosophical investigation. The fifteen specially commissioned essays in this book introduce and explore the ideas of major philosophers who have shaped philosophical thinking about language, providing insights into crucial developments in this fascinating field over the last 140 years. Chapters examine the work of Frege, Russell, Wittgenstein, Carnap, Austin, Quine, Chomsky, Grice, Davidson, Dummett, Kripke and Derrida. This second edition broadens coverage of the area with new chapters on Susan Stebbing and on recent developments in feminist philosophy of language. Featuring contributions from Arif Ahmed, Kent Bach, Thomas Baldwin, Michael Beaney, Siobhan Chapman, Kirk Ludwig and other leading experts in the field, Philosophy of Language: The Key Thinkers provides a thorough introduction to the puzzles, debates and ideas that animate contemporary philosophy of language. It is an ideal resource for undergraduate students in philosophy, linguistics and related disciplines.

CHAPTER ONE

FREGE

Michael Beaney

Gottlob Frege (1848–1925) was primarily a mathematician, logician and philosopher of mathematics rather than a philosopher of language as that might be understood today. However, in inventing modern logic and pursuing his main goal – the demonstration that arithmetic can be reduced to logic – he was led to reflect on how language works, and the ideas he introduced in doing so laid the foundations for the development of philosophy of language, especially within the analytic tradition, in the twentieth century.

1. Life and works

Frege was born in Wismar, on the Baltic coast in northern Germany, in 1848, and he studied mathematics, physics, chemistry and philosophy at the Universities of Jena and Göttingen from 1869 to 1873. In 1874 he was appointed to teach mathematics at Jena, where he remained for the rest of his academic career. He retired in 1918 and moved back to the Baltic coast, where he died in 1925.¹

Frege published three books in his lifetime: Begriffsschrift (Conceptual Notation) in 1879, Die Grundlagen der Arithmetik (The Foundations of Arithmetic) in 1884 and Grundgesetze der Arithmetik (Basic Laws of Arithmetic) in 1893 (Volume I) and 1903 (Volume II). Frege’s main aim in these books was to demonstrate the logicist thesis that arithmetic is reducible to logic. To do so, Frege realized that he needed to develop a better logical theory than was then available: he gave his first exposition of this in Begriffsschrift, ‘Begriffsschrift’ (literally, ‘concept-script’ or ‘conceptual notation’) being the name he gave to his logical system. (In what follows, I shall use ‘Begriffsschrift’ in italics to refer to the book and without italics to refer to Frege’s logical system.) In Grundlagen he criticized other views about arithmetic, such as those of Kant and Mill, and offered an informal account of his logicist project. In Grundgesetze he refined his logical system and attempted to provide a formal demonstration of his logicist thesis. In 1902, however, as the second volume was in press, he received a letter from Russell informing him of a contradiction in his system – the contradiction we know now as Russell’s paradox. Although Frege hastily wrote an appendix attempting to respond to this, he soon realized that the response failed and was led to abandon his logicism. He continued to develop and defend his philosophical ideas, however, writing papers and corresponding with other mathematicians and philosophers. It is these philosophical writings, and his four most important papers, in particular, which have established his status as one of the founders of modern philosophy of language. These papers are ‘Function and Concept’ (1891), ‘On Sense and Reference’ (1892a), ‘On Concept and Object’ (1892b) and ‘Thought’ (1918). The main ideas in these four papers form the subject of the present chapter. We start with the idea that lay at the heart of his new logical system.

2. Frege’s use of function–argument analysis

The key to understanding Frege’s work is his use of function–argument analysis, which he extended from mathematics to logic. Indeed, it is no exaggeration to say that all Frege’s main doctrines follow from his thinking through the implications of this use.² We can begin with a simple example from mathematics. In analytic geometry, the equation for a line is y = ax + b: this exhibits y as a function of x, with a and b here being constants (a being the gradient of the line and b the point where the line cuts the y-axis on a graph). Let a = 2 and b = 3. If x = 4, then y = 11: we say that 11 is the value of the function 2x + 3 for argument 4. We call x and y the variables here: as x varies, so too does y, in the systematic way reflected in the function. By taking different numerical values for x, we get different numerical values for y, enabling us to draw the relevant line on a graph. Frege thought of sentences – and what those sentences express or represent – in the same way: they can be analysed in function–argument terms. Sentences, too, have a ‘value’ which can be seen as the result of an appropriate function for an appropriate argument or arguments. If we think of this value as in some sense its ‘meaning’, then we can regard this meaning, too, as a function of the ‘meanings’ of what we might loosely call its ‘parts’, that is, of what function–argument analysis yields as the constituent elements of the sentence. What are these ‘meanings’ and ‘parts’? This is the question that Frege attempted to answer in his philosophical work, and it is the main aim of the present chapter to explain his answer.

Let us see how Frege applied function–argument analysis in the case of sentences, starting with simple sentences such as ‘Gottlob is human’. In traditional (Aristotelian) logic, such sentences were regarded as having subject–predicate form, represented by ‘S is P’, with ‘S’ symbolizing the subject (‘Gottlob’) and ‘P’ the predicate (‘human’), joined together by the copula (‘is’). According to Frege, however, they should be seen as having function–argument form, represented by ‘Fa’, with ‘a’ symbolizing the argument (‘Gottlob’) and ‘Fx’ the function (‘x is human’), the variable x here indicating where the argument term goes to complete the sentence. The sentence ‘Gottlob is human’ is thus viewed as the value of the functional expression ‘x is human’ for the argument term ‘Gottlob’. Besides the terminological change, though, there might seem little to choose between the two analyses, the only difference being the absorption of the copula (‘is’) into the functional expression (‘x is human’).³

The advantages of function–argument analysis begin to emerge when we consider relational sentences, which are analysed as functions of two or more arguments. In ‘Gottlob is shorter than Bertrand’, for example, ‘Gottlob’ and ‘Bertrand’ are taken as the argument terms and ‘x is shorter than y’ as the relational expression, formalized as ‘Rxy’ or ‘xRy’. This allows a unified treatment of a wide range of sentences which traditional logic had had difficulties in dealing with in a single theory.

The superior power of function–argument analysis only fully comes out, though, when we turn to sentences involving quantifier terms such as ‘all’ and ‘some’. Take the sentence ‘All logicians are human’. In traditional logic, this was also seen as having subject–predicate form, ‘All logicians’ in this case being the subject, with ‘human’ once again the predicate, joined together by the plural copula ‘are’. According to Frege, however, such a sentence has a quite different and more complex (quantificational) form: in modern notation, symbolized as ‘(∀x)(Lx → Hx)’,⁴ read as ‘For all x, if x is a logician, then x is human’. Here there is nothing corresponding to the subject; instead, what we have are two functional expressions (‘x is a logician’ and ‘x is human’) linked together by means of the propositional connective ‘if … then …’ and bound by a quantifier (‘for all x’). In developing his Begriffsschrift, Frege’s most significant innovation was the introduction of a notation for quantification, allowing him to formalize – and hence represent the logical relations between – sentences not just with one quantifier term but with multiple quantifier terms.

Traditional logic had had great difficulty in formalizing sentences with more than one quantifier term. Such sentences are prevalent in mathematics, so it was important for Frege to be able to deal with them. Consider, for example, the sentence ‘Every natural number has a successor’. This can be formalized as follows, ‘Nx’ symbolizing ‘x is a natural numbe...