David Dolby

Inspired by Bertrand Russell's theory of descriptions, Wittgenstein held that the surface grammar of a proposition may be highly misleading as to the underlying structure of a proposition. Wittgenstein explains how elementary propositions can have sense by drawing an analogy with a picture or model, such as the model of the scene of an accident. One key claim of the picture theory of meaning is that elementary propositions are capable of being true and capable of being false independently of one another. If it is a matter of debate whether or not Wittgenstein adhered to a deflationary account of truth at the time of the Tractatus, it is clear that he later espoused deflationary views about truth. One problem for deflationary accounts of truth along the lines of Prior has been the treatment of propositions in which we seem to be faced with an ascription of truth to a named proposition.

Gilbert Ryle is acknowledged as a major figure in twentieth-century philosophy and yet discussions of Ryle's own writings are rare. This is a great pity, since his work is philosophically rich and the arguments and positions he develops are often subtler and more persuasive than those ascribed to him. In this collection, leading scholars engage with Ryle's writings on topics such as the concept of thinking, the explanation of action, the notion of a category mistake, and the analysis of hypotheticals. Together the essays demonstrate the continuing relevance of Ryle's arguments to these areas of philosophy. The contributors are Maria Alvarez, Jonathan Dancy, Hans-Johann Glock, Christoph Pfisterer, Bede Rundle, Paul Snowdon, Rowland Stout, Julia Tanney, and Roger Teichmann.

It is often maintained that co-referential terms can be substituted for one another whilst preserving truth-value in extensional contexts, and preserving grammaticality in all contexts. Crispin Wright calls this claim ‘The Reference Principle’. Since Wright defines extensional contexts as those in which truth-value is determined only by reference, it is the assertion about substitution salva congruitate that is significant. Wright argues that RP is the key to understanding how Frege came to hold, paradoxically, that the concept horse is not a concept, and to providing a resolution to the paradox.RP and Wright's application of it to Frege's Paradox have recently been criticized by Oliver. 1 Oliver argues that the syntax of natural languages is too complicated for the failure of two terms to fit into the same forms of speech to indicate a difference in semantic significance: RP is, he claims, an empirical falsehood.I shall argue that, although Oliver's arguments show that RP is false as it stands, a revised version of the principle, employing a more robust notion of substitution, is nevertheless correct. I shall end by outlining the implications of this revision for the appeal to RP and for Wright's resolution of Frege's Paradox.1. Referring terms and referential positionOliver's case against RP appeals to an impressive array of counter-examples. For our purposes it will be useful to regard these as being of three sorts. The first sort can be dealt with relatively swiftly: examples of the second and third sorts are more challenging.The first sort of counter-example involves referring terms that feature as parts of complex referring expressions. Oliver's examples include ‘William’ in the complex expression ‘William the Conqueror’. The substitution of expressions co-referential with ‘William’ into sentences employing the complex referring expression often results in ungrammatical ….

This book offers a detailed account and discussion of Ludwig Wittgenstein's philosophy of mathematics. In Part I, the stage is set with a brief presentation of Frege's logicist attempt to provide arithmetic with a foundation and Wittgenstein's criticisms of it, followed by sketches of Wittgenstein's early views of mathematics, in the Tractatus and in the early 1930s. Then (in Part II), Wittgenstein's mature philosophy of mathematics (1937-44) is carefully presented and examined. Schroeder explains that it is based on two key ideas: the calculus view and the grammar view. On the one hand, mathematics is seen as a human activity - calculation - rather than a theory. On the other hand, the results of mathematical calculations serve as grammatical norms. The following chapters (on mathematics as grammar; rule-following; conventionalism; the empirical basis of mathematics; the role of proof) explore the tension between those two key ideas and suggest a way in which it can be resolved. Finally, there are chapters analysing and defending Wittgenstein's provocative views on Hilbert's Formalism and the quest for consistency proofs and on Gödel's incompleteness theorems.

Objectual interpretations of non-nominal quantification seems to offer a non-substitutional treatment of quantification which respects differences of grammatical category in the object language whilst only employing nominal quantification in the metalanguage. I argue that the satisfaction conditions of such interpretations makes use concepts that must themselves be explained through non-nominal quantification. As a result, the interpretation misrepresents the structure of non-nominal quantification and the relationship between nominal and non-nominal forms of generality.