0. Introduction During the academic year 1940-1941, several giants of analytic philosophy-both established and budding-congregated at Harvard University. The list is impressive: the European émigrés Bertrand Russell, Alfred Tarski, Rudolf Carnap, and C. G. Hempel were visiting the University that year. Furthermore, at this time W. V. O. Quine held his permanent professorship at Harvard, and Nelson Goodman was finishing his dissertation. This group held public meetings regularly under the name 'Logic Group,' and they had private, smaller conversations as well. Any student of the philosophical foundations of logic, mathematics, and the natural sciences would like to know what these immensely influential and innovative thinkers discussed. Such information would be valuable both for the light it could shed on the historical development of analytic philosophy, as well as for purely philosophical reasons: were interesting or compelling arguments made? Fortunately, one can almost be a 'fly on the wall' for many of these conversations, both public and private: Carnap often took very detailed discussion notes during his year at Harvard. These documents have been preserved and stored in the Rudolf Carnap Collection, part of the Archives of Scientific Philosophy (ASP) at the University of Pittsburgh. These notes cover a wide range of topics, including inductive logic and the advantages of formal languages without types over typed languages. However, a large quantity of Carnap's discussion notes during the spring semester deal with what he and his collaborators call variously 'finitistic syntax,' 'finitistic language,' and 'the total language of science, on a finitist basis,' among other names. This project attempts to answer the question: what form should logic and mathematics take if the number of physical items in the universe is finite, or at least possibly finite? Carnap, Tarski, and Quine's attempts to answer this question involve a number of issues that were-and in many cases, still are-central to analytic philosophy of logic, mathematics, and science. In my dissertation, I will focus on three such issues: nominalism, the distinction between logical and factual truth, and the unity of science.

1. Modern nominalism Much modern nominalist work consists of 'reconstructive' projects of the following sort: a certain field of natural science or mathematics is recast in a form that does not appeal to any 'abstract' entities. (Perhaps the most prominent example of such a reconstructive project is Hartry Field's Science without Numbers: A Defense of Nominalism.) The founding document of twentieth-century reconstructive nominalism is generally recognized to be Goodman and Quine's joint 1947 article "Steps Toward a Constructive Nominalism." In it, Goodman and Quine mention that their project derives its initial impetus and framing questions from the conversations of
1940-1941 with Carnap and Tarski. These conversation notes can thus be seen as a record of the 'pre-history' of modern nominalist projects. This raises interesting questions: are certain claims, assumed by current nominalists, contested in these discussions? To what extent do the argumentative strategies pursued by current nominalists part ways from those of Carnap, Tarski and Quine? Are the motivations and justifications for nominalism in 1940 and today significantly different?

2. Analytic/ synthetic distinction Carnap's treatment of the analytic/ synthetic (or 'logical/ factual') distinction has received an enormous amount of philosophical attention, both from Carnap's contemporaries and modern commentators. In print, Carnap often cites Tarski and Quine as the major critics of this distinction. This distinction has a clear connection to the conversations on the finitistic language of science: should the number of physical items in the universe (a synthetic issue) affect arithmetic and logic
(which are supposedly analytic)? And if so, how, and to what extent? In other notes from 1940-1941 the logical/ factual distinction is addressed more directly. Interestingly, we find some promising arguments concerning the distinction that never made it to print. For example, Tarski suggests to Carnap that Gödel's first incompleteness theorem furnishes evidence against Carnap's conception of analyticity. Carnap then replies that he finds some justice in Tarski's complaint. Also during 1940-1941, Carnap was finishing work on his Introduction to Semantics, which introduced formal semantics as a tool for general philosophical use. One of the central aims of that book is to re-formulate the analytic/ synthetic distinction in semantic terms, instead of syntactic ones. The ASP contains valuable material from this period, including drafts, correspondence, and notes.

3. Unity of science The 'unity of science' movement originated in Vienna in the 1920's, and has since transformed into a central topic in modern philosophy of science, under the heading of 'reductionism.' A primary aim of the movement was to construct and disseminate a single language adequate for interdisciplinary communication of all scientific knowledge. The issue arises among the philosophers gathered at Harvard in 1940-1941. For example, in a lecture given in the Logic Group, Quine explicitly addresses what form a "universal language of science" should take, and what value such a language may or may not have. Further, Carnap, Tarski, and Quine's search for a 'total language of science' can be considered as a concrete-and extreme-attempt to realize the aims of the unity of science. For they attempt to integrate not only the languages of the biological, physical, and social sciences, but also the language of mathematics. This prompts the question: what motivates and justifies the drive for such an extreme version of unified science? I suggest two answers to this question. First, for Carnap, constructing such a language would help resolve the perceived conflict between two competing philosophies of mathematics, formalism and logicism (see Logical Syntax of Language, §84). Second, the logical empiricists and their allies all harbored antipathies for speculative metaphysics, contrasting metaphysical pseudo-propositions with scientific claims, which have genuine cognitive content. One criterion for distinguishing science from metaphysics was the following: if a claim cannot be incorporated into a system of a language of science, then that claim is metaphysical. Thus, constructing a single language of science that encompasses the mathematical and natural domains would ensure that claims about mathematical entities are not on an epistemological par with Platonic metaphysics.