Abstract
Willard van Orman Quine (1908–2000) was an American logician and philosopher working in the analytical tradition and shaping it in various respects. Quine is well-known for his critical attitude towards modal logic, which makes their conversation about Popper’s formalization of modal logic in Popper (1947d) particularly interesting. The letter from Popper to Quine of 6 April 1948 is remarkable for an indication of the demarcation between logic and mathematics. Popper says that he has formulated inferential definitions for cardinal numbers; this would increase the scope of his approach from logic to mathematics. However, this idea has not been pursued in any of Popper’s subsequent publications, and we were not able to find definite traces of this idea in his unpublished work either.
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Goodman, N. and W. V. O. Quine (1947). Steps Toward a Constructive Nominalism. In: Journal of Symbolic Logic 12 (4), pp. 105–122.
Popper, K. R. (1947b). Logic without Assumptions. In: Proceedings of the Aristotelian Society 47, pp. 251–292. Reprinted as Chapter 2 of this volume.
– (1947d). Functional Logic without Axioms or Primitive Rules of Inference. In: Koninklijke Nederlandse Akademie vanWetenschappen, Proceedings of the Section of Sciences 50, pp. 1214–1224. Reprinted as Chapter 4 of this volume.
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Popper, K.R., Quine, W.V.O. (2022). Popper’s Correspondence with Willard Van Orman Quine. In: Binder, D., Piecha, T., Schroeder-Heister, P. (eds) The Logical Writings of Karl Popper. Trends in Logic, vol 58. Springer, Cham. https://doi.org/10.1007/978-3-030-94926-6_30
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DOI: https://doi.org/10.1007/978-3-030-94926-6_30
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