Third Annual Early Analytic Philosophy Conference
Purdue University
April 9-10, 2004

• Carnap's Dream: Wittgenstein, Gödel, and Logical Syntax
  André Carus (Chicago)
  Abstract: In January 1931 Rudolf Carnap had a "vision" during a sleepless night. Years later, in his autobiography, he reports that "the whole theory of language structure and its possible applications in philosophy" became clear to him, in a flash, and he wrote it all down in shorthand the next day. He gave these notes the title "Attempt at a Metalogic". They became the germ of Logical Syntax of Language, he tells us. But wherein did this momentous insight actually consist? What was that "germ"? Using Carnap's shorthand manuscript of the "Attempt at a Metalogic", and other notes from this period, we try to answer this question. The punch line, somewhat oversimplified, is this: Carnap uses Gödel's then-recent logical discoveries to overcome the conception of meaning he had derived from Wittgenstein's Tractatus, and which had turned out to be incompatible with other Vienna Circle goals. The "vision" was Carnap's liberation from the notion of meaning. This is joint work with Steve Awodey.
• Quine and Carnap on Truth by Convention
  Gary Ebbs (Illinois)
  Abstract: My goal in this paper is to explain why Quine believed that his criticisms of the thesis that logic is true by convention shed light on what is wrong with Carnap's conception of logic, even though Quine knew that Carnap was not committed to that thesis. I argue that Quine was led by a principle of interpretive charity to search for some way to view Carnap's contributions to logic as part of natural science. Quine viewed the thesis that logic is true by convention as an initially plausible but ultimately empty attempt to show how logic makes an explanatory contribution to science, and so he thought it both charitable and illuminating to see Carnap's explications of logical truth as attempts to explain logical truth in terms of conventions we adopt for using our words. Carnap's official characterization of logic is not even initially plausible according to Quine, because it was expressly designed to yield "logical truths" that make no explanatory contribution to natural science.
• Quine and the Aufbau: The Possibility of Objective Knowledge
  Peter Hylton (Illinois, Chicago)
  Abstract: In this essay I consider the relation between the Carnap's epistemological project in his Logischer Aufbau der Welt and Quine's work, in the light of the new interpretation of that work of Carnap's put forward by (among others) Michael Friedman and Alan Richardson. This new interpretation sees Carnap as primarily motivated by the question: How is objective knowledge possible on the basis of subjective experience? I argue that this question, or at any rate a question that can be phrased in that way, receives an answer in Quine's mature work, although answering it is not the motivation for that work. This point of similarity then provides the basis for a discussion of the differences between Quine and Carnap.
• Russell's Logical Atomism and the Thesis that Ontology is Sinnlos
  Gregory Landini (Iowa)
  Abstract: This paper investigates Russell's logical atomist views on the nature of ontology and compares them with those of Wittgenstein, Carnap and Quine. It is argued that although Russell rejected Wittgenstein's thesis that ontology is sinnlos, his conception of philosophy as an eliminativistic analysis provides a new perspective on Wittgenstein's thesis and on the debate between Carnap and Quine on ontology.
• On the Prehistory of Mathematical Incompleteness: Paul du Bois-Reymond
  D. C. McCarty
  Abstract: Paul du Bois-Reymond was a significant mathematician and philosopher of the late 19th Century, publishing in differential equations, analysis and the foundations of mathematics. His magnum opus, "General Function Theory," which appeared in 1882, contained what its author claimed to be a demonstration that mathematics is absolutely incomplete, that is, that there is a mathematically meaningful proposition (indeed, a large number of mathematical important propositions) A such that neither A nor not-A will ever be proven true by mathematicians. His intended demonstration is not, of course, based on the notion of a formal system, but on a detailed analysis of mathematical cognition. We will describe that analysis and assess du Bois-Reymond's incompleteness argument for its cogency.
• Russell's Changing Beliefs
  Christopher Pincock (Purdue)
  Abstract: This paper articulates and defends a new interpretation of why Russell set aside his multiple relation theory of judgment and the 1913 Theory of Knowledge manuscript. I focus on the difficulties with spelling out the correspondence relations between states of understanding and facts. In the end, Wittgenstein convinced Russell that the multiple relation approach to states of understanding precluded defining correspondence. I emphasize Russell's discussion of these issues in the Theory of Knowledge as well as in some of his later published and unpublished writings.
• Truth, Assertion, and the Horizontal: Frege on "the essence of logic"
  William Taschek (Ohio State)
  Abstract: In the opening to his late essay, "Thoughts" (1918-19), Frege asserts without qualification that the word "true" points the way for logic. But in a short piece from his Nachlass entitled, "My Basic Logical Insights" (to which the editors assign the date 1915), Frege writes that the word "true" makes "an abortive attempt to point to the essence of logic," asserting instead that "what logic is really concerned with lies not in the word 'true' but in the assertoric force with which the sentence is uttered." Properly understanding what Frege takes to be at issue here is crucial for understanding his conception of logic. In this paper I attempt to clarify this matter, focusing especially on the latter claim and Frege's motivations for making it. Along the way, I will address some peculiarities about the role of the horizontal and its relation to the judgement-stroke in Frege's mature Begriffsschrift (i.e., after the changes introduced in "Function and Concept").
• Rediscovering the C-Series: McTaggart's Lost Insight
  David Taylor (Iowa)
  Abstract: That McTaggart's famous argument for the unreality of time, and in particular his distinction between the A-series and the B-series, shaped the agenda of analytic philosophy of time is well-known. What is less-known is McTaggart's own positive account of why we hold the mistaken belief that time exists. After arguing that the concepts associated with the A-series and B-series cannot refer to objective features of the world, he offers an "error theory", which involves the claim that we in fact mistake certain objective features of the world, in particular what he calls the "C-series", for temporal series. In this paper I argue that in his quest for a relation that can serve as the grounding for our erroneous belief in the existence of time, he makes a significant discovery concerning the nature of temporal relations, namely its formal indistinguishability from certain mereological relations. Even if we reject his arguments against the reality of time, we can gain a deeper understanding of the temporal series from his thorough analysis of the features that must be had by a series that can underlie our belief in time.
• Wittgenstein and the Algebraic Tradition
  Chris Tillman (Indiana)
  Abstract: Both the Tractarian Wittgenstein and the algebraists of the 19th century conceived the principal method of mathematics as calculatory. I will here argue for the conceptual cogency of both adopting the calculatory view and yet rejecting the idea that calculation is mere manipulation of signs according to rules that are arbitrary, stipulated, or conventional. It follows that the role calculation plays in Wittgenstein's early thought on mathematics does not commit him to this sort of formalism. Furthermore, I would like to demonstrate that, for Wittgenstein, as for a variety of algebraists who applied the algebraic method to logic, calculation rules are not arbitrarily determined. I hope this paper shows the 19th century algebraic perspective on the nature of mathematics and logic to be a revealing perspective on Wittgenstein's thought at the time of Tractatus.

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