During the academic year 1940-1941, several giants of analytic philosophy congregated at Harvard: Russell, Tarski, Carnap, Quine, Hempel, and Goodman were all in residence. This group held both regular public meetings as well as private conversations. Carnap took detailed diction notes that give us an extensive record of the discussions at Harvard that year. Surprisingly, the most prominent question in these discussions is: if the number of physical items in the universe is finite (or possibly finite), what form should the logic and mathematics in science take? This question is closely connected to an abiding philosophical problem, one that is of central philosophical importance to the logical empiricists: what is the relationship between the logico-mathematical realm and the natural, material realm? This problem continues to be central to analytic philosophy of logic, mathematics, and science. My dissertation focuses on three issues connected with this problem that dominate the Harvard discussions: nominalism, the unity of science, and analyticity. I both reconstruct the lines of argument represented in Harvard discussions and relate them to contemporary treatments of these issues.
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