Abstract:Recent years have seen a resurgence of scholarly interest in the precise nature of Wittgenstein’s fateful but notoriously obscure criticisms of Russell’s multiple relation theory of judgment, levelled as Russell was furiously composing Theory of Knowledge in May–June 1913. In this paper, I place special expository focus on two controversial documents from the relevant period, whose nature and interrelationships to this point have been inadequately understood in the literature. The first document is a set of working notes composed by Russell (...) under the title “Props”—which I date as on or shortly after 26 May—while the second is a June 1913 letter from Wittgenstein to Russell, often thought to contain a “paralyzing”, if mysterious, objection to Russell’s theory. On the basis of a new interpretation of these two documents and their relationship, I revise the “standard reading” of Wittgenstein’s criticisms. The revision renders that reading invulnerable to certain seemingly devastating criticisms developed by Stevens in 2003. I defend my revised reading against various “non-standard” alternatives which have flourished in the recent literature, in part as the result of Stevens’ criticisms. (shrink)

Hans Hahn's long-neglected philosophy of mathematics is reconstructed here with an eye to his anticipation of the doctrine of logical pluralism. After establishing that Hahn pioneered a post-Tractarian conception of tautologies and attempted to overcome the traditional foundational dispute in mathematics, Hahn's and Carnap's work is briefly compared with Karl Menger's, and several significant agreements or differences between Hahn's and Carnap's work are specified and discussed.

In this article I present a summary of Bertrand Russell's protracted attempts to solve the problem of the unity of the proposition, and explain the significance of the problem for Russell's philosophy. Unlike many other accounts which take the problem to be confined to Russell's early theories of propositional content, I argue that the problem (or variants of it) is a recurring theme throughout the whole of Russell's career.

In this article I argue that Russell's multiple-relation theory of judgment is a continuation of the campaign against Frege and Meinong begun in “On Denoting” with the theory of descriptions. More precisely, I hold that the problem of false belief, to which the multiple-relation theory is presented as a solution, emerges quite naturally out of the problem context of “On Denoting” and threatens to give new life to the theories Russell purports to have laid to rest there, and that Russell's (...) solution to the much neglected third puzzle of “On Denoting” contains the gist of the multiple-relation theory. The failure of that theory to solve the problem of false belief thus signifies the failure of the theory of descriptions. (shrink)

It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there (...) is only one ultimate ontological category. This, combined with Russell's reification of propositions, ensures that he must hold concepts and objects to be of the same logical and ontological type. In this paper I argue that, while Frege's treatment of the unity of the proposition has immediate advantages over Russell's, a deeper consideration of the philosophical underpinnings and metaphysical consequences of the two approaches reveals that Frege's supposed solution is, in fact, far from satisfactory. Russell's repudiation of the Fregean position in the Principles is, I contend, convincing and Russell's own position, despite its problems, conforms to a greater extent than Frege's with common sense and, furthermore, with certain ideas which are central to our understanding of the origins of the analytical tradition. (shrink)

This paper investigates Wittgenstein's "notorious" criticism of Russell's theory of judgment. Instead of advancing a further new interpretation of it, though, I analyze and discuss some of the most promising readings of the Russell/Wittgenstein dispute put forward in the secondary literature; I aim to show that, despite their alleged reciprocal opposition, they cohere with each other because they are, at bottom, different ways of highlighting the same question. I then connect Wittgenstein's criticism of Russell to the account of the nature (...) of the proposition presented in the Tractatus, arguing that the latter can be seen as a natural development of the former. Finally, I make a quick connection between Wittgenstein's criticism of Russell and the conception of the world as the totality of facts, as presented in the Tractatus. (shrink)