world does not have a finite number of positions, it is an empirical fact that it does not have this spatiotemporal structure; thus, the position-based interpretation cannot make the axiom of infinity analytic. Therefore, I think Lavers’ concern that the position-based interpretation does not make the axiom of infinity analytic is justified, although I demur from his reasons for this conclusion offered in this symposium. REFERENCES Carnap, Rudolf (1932/1959). of Metaphysics through the Logical “Elimination Analysis of Language,” in Logical Positivism, A. J. Ayer (ed.). New York: Free Press, 60-81. Carnap, Rudolf (1934/1937). Logical Syntax of Language, A. Smeaton (trans.). Chicago: Open Court. Carnap, Rudolf (1939). of and Mathematics,” in International “Foundations Encyclopedia of Unified Science, O. Neurath, R. Carnap, and C. Morris (eds.). Chicago: University of Chicago Press, 139-214. Carnap, Rudolf (1963). Autobiography,” in The Philosophy of Rudolf “Intellectual Carnap, P. Schilpp (ed.). LaSalle: Open Court. Creath, Richard (1990). Dear Carnap, Dear Van. Berkeley: University of California. Frost-Arnold, Greg (2013). Chicago: Open Carnap, Tarski, and Quine at Harvard. Court. Lavers, Gregory (forthcoming). on Abstract and Theoretical Entities,” in “Carnap Ontology After Carnap, Blatti and Lapointe (eds.). New York: Oxford University Press. Mancosu, Paolo (2004). 1940-41: Carnap, Tarski and Quine on a Finitistic “Harvard Language of Mathematics for Science,” History and Philosophy of Logic 26: 327-357. Quine, W. V. (1953). Dogmas of Empiricism,” in From a Logical Point of View. “Two Cambridge: Harvard University Press.
world does not have a finite number of positions, it is an empirical fact that it does not have this spatiotemporal structure; thus, the position-based interpretation cannot make the axiom of infinity analytic. Therefore, I think Lavers’ concern that the position-based interpretation does not make the axiom of infinity analytic is justified, although I demur from his reasons for this conclusion offered in this symposium. REFERENCES Carnap, Rudolf (1932/1959). “Elimination of Metaphysics through the Logical Analysis of Language,” in Logical Positivism, A. J. Ayer (ed.). New York: Free Press, 60-81. Carnap, Rudolf (1934/1937). Logical Syntax of Language, A. Smeaton (trans.). Chicago: Open Court. Carnap, Rudolf (1939). “Foundations of and Mathematics,” in International Encyclopedia of Unified Science, O. Neurath, R. Carnap, and C. Morris (eds.). Chicago: University of Chicago Press, 139-214. Carnap, Rudolf (1963). “Intellectual Autobiography,” in The Philosophy of Rudolf Carnap, P. Schilpp (ed.). LaSalle: Open Court. Creath, Richard (1990). Dear Carnap, Dear Van. Berkeley: University of California. Frost-Arnold, Greg (2013). Carnap, Tarski, and Quine at Harvard. Chicago: Open Court. Lavers, Gregory (forthcoming). “Carnap on Abstract and Theoretical Entities,” in Ontology After Carnap, Blatti and Lapointe (eds.). New York: Oxford University Press. Mancosu, Paolo (2004). “Harvard 1940-41: Carnap, Tarski and Quine on a Finitistic Language of Mathematics for Science,” History and Philosophy of Logic 26: 327-357. Quine, W. V. (1953). “Two Dogmas of Empiricism,” in From a Logical Point of View. Cambridge: Harvard University Press.
MetascienceResponseFrost-Arnold.docx