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  • Mark Wilson  “Frege's Mathematical Setting”, forthcoming in T. Ricketts ed., The Cambridge Companion to Frege, Cambridge University Press. This article was written in circa 1997.

This survey article describes Frege's celebrated foundational work against the context of other late nineteenth century approaches to introducing mathematically novel "extension elements" within both algebra and geometry.

  • ditto   “Ghost World: A Context for Frege's Context Principle”, in M. Beaney and E. Reck ed., Gottlob Frege. Critical Assessments of Leading Philosophers, vol. 3, Routledge, 2005

There is considerable likelihood that Gottlob Frege began writing his Foundations of Arithmetic with the expectation that he could introduce his numbers, not with sets, but through some algebraic techniques borrowed from earlier writers of the Gottingen school. These rewriting techniques, had they worked, would have required strong philosophical justification provided by Frege's celebrated "context principle," which otherwise serves little evident purpose in the published Foundations.

  • Steve Awodey and Erich H. Reck   “Completeness and Categoricity. Part I: 19th Century Axiomatics to 20th Century Metalogic”, in: History and Philosophy of Logic, vol. 23, no. 1, 2002
  • ditto           “Completeness and Categoricity. Part II: 20th Century Metalogic to 21st Century Semantics”, in: History and Philosophy of Logic, vol. 23, no. 2, 2002
  • Gary Hardcastle  “Quine’s 1934 “Lectures on Carnap””, in: GAP.6 Workshop on Rudolf Carnap, Berlin, September 2006

In November of 1934, over successive Thursdays, the 26-year-old Willard van Orman Quine gave three “Lectures on Carnap” at Harvard University, the ostensive aim of which was a presentation of the “central doctrine” of Carnap’s Logische Syntax der Sprache, “that philosophy is syntax.” These were among Quine’s very first public lectures, and they constituted the American premier of Carnap’s logische Syntax program. As such, these lectures are of considerable significance to the history of analytic philosophy. They show, for example, one way Carnap’s syntactical program was presented and understood in the 1930s, and indeed they show how Quine, emerging even in 1934 as one of America’s brightest logicians, understood that particular project. Moreover, they promise to tell something about how Quine himself was thinking about central philosophical issues—the a priori, analyticity, and philosophy itself—early in his career, before he wrote the papers and books on those topics that established his reputation. This paper takes up this last topic. My aim is to reconstruct and understand how Quine was thinking about the a priori, analyticity, and philosophy itself in 1934, what he aimed to accomplish in the “Lectures on Carnap,” and the considerable extent to which he accomplished that aim. What Quine accomplished, in short, was the outline of a fascinating and original anti-metaphysics, with conventionalism (specifically, implicit definition) at its heart. This was an anti-metaphysics that invited (but, significantly, could not demand) adoption of a particular conception of philosophy.

  • Lieven Decock  “True by virtue of Meaning: Carnap and Quine on Some Analytic-Synthetic Distinctions”, in: GAP.6 Workshop on Rudolf Carnap, Berlin, September 2006, under construction.

I want to analyse the Quine-Carnap discussion on analyticity with regard to logical, mathematical and set-theoretical statements. In recent years, the renewed interest in Carnap’s work has shed a new light on the analytic-synthetic debate. If one fully appreciates Carnap’s conventionalism, one sees that there was not a metaphysical debate on whether there is an analytic-synthetic distinction, but rather a controversy on the expedience of drawing such a distinction.
However, on this view, there can be no longer a single analytic-synthetic distinction, because several kinds of statements could be regarded as analytic (L-determinate). L-equivalence between extra-logical linguistic predicates has already been heavily debated. The recent consensus states that Quine’s rejection of this analytic-synthetic is pragmatically grounded in his linguistic behaviorism. However, Carnap’s logical frameworks also contain other kinds of statements, and it is worthwhile to compare both Quine and Carnap’s grounds for considering these statements as analytic or not analytic.
First, I will discuss logical statements. I will argue that Quine draws a very sharp distinction between first order logic and set theory, which should be regarded as a (pragmatic) analytic-synthetic distinction (as Quine admits in an interview, see Theoria, 40, 1994, p. 199). In fact, Quine’s major worry is whether identity statements are analytic. Second, I will discuss mathematical statements. In Carnap’s Foundations of Logic and Mathematics, it is clear that mathematical statements are analytic. For Quine, all mathematical statements are reducible to set-theoretical statements. Third, I discuss the analyticity of set-theoretical statements. For Quine, the membership predicate should be regarded as an interpreted extra-logical predicate. Quine’s work in set theory and his later philosophy of set theory naturally lead to the view that set-theoretical statements cannot be analytic. A major complication for the Quine-Carnap comparison is that Carnap has no elaborate reflections on set theory, while the influence of set theory on Quine’s views can hardly be underestimated. I conclude with some lessons for the contemporary debate on analyticity.

Wilsonさんの2本目とAwodey and Reck論文の2本は既に持っていたかと思うが、念のため入手。