Abstract
Kalman Joseph Cohen (1931–2010) was an American economist. Before his Ph.D. in economics at the Carnegie Institute of Technology (cf. Reed Magazine, 2011), he completed a B.Litt. in mathematical logic at Oxford University, which was supervised by Popper. In Cohen (1953b) he investigates various deductive systems, in particular sequent calculi, for logics which are dual to intuitionistic logic. Although a precursor to more modern treatments of dual-intuitionistic logics, it has not been recognized or discussed much in the literature (cf. Kapsner, A., D. Miller, and R. Dyckhoff (2014). Report on Kalman Cohen’s 1954 Oxford Thesis on Alternative Systems of Logic. In: Handbook of the 5th World Congress on Paraconsistent Logic. Ed. by J.-Y. Beziau, M. Chakraborty, and S. Dutta, pp. 61–62. url: http://www.paraconsistency.org/book/Handbook-WCP5.pdf., and this volume, Chapter 1, § 2). The correspondence is notable for Popper’s semantic explanation of dual consequence, that is, of a.1b1..... bmo. Popper writes that he intends to publish on this subject, which shows that as late as 1953 he was still working on these topics.
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Cohen, K. J. (1953a). A Remark on Łukasiewicz’s ‘On the Intuitionistic Theory of Deduction’. In: Indagationes Mathematicae 56, pp. 111–112.
– (1953b). Alternative Systems of Logic. B.Litt. thesis. Faculty of Literae Humaniores, University of Oxford.
Kapsner, A., D. Miller, and R. Dyckhoff (2014). Report on Kalman Cohen’s 1954 Oxford Thesis on Alternative Systems of Logic. In: Handbook of the 5th World Congress on Paraconsistent Logic. Ed. by J.-Y. Beziau, M. Chakraborty, and S. Dutta, pp. 61–62. url: http://www.paraconsistency.org/book/Handbook-WCP5.pdf.
Popper, K. R. (1947b). Logic without Assumptions. In: Proceedings of the Aristotelian Society 47, pp. 251–292. Reprinted as Chapter 2 of this volume.
– (1947c). New Foundations for Logic. In: Mind 56 (223), pp. 193–235. Reprinted as Chapter 3 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.
– (1948a). On the Theory of Deduction, Part I. Derivation and its Generalizations. In: Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings of the Section of Sciences 51, pp. 173–183. Reprinted as Chapter 5 of this volume.
– (1948c). On the Theory of Deduction, Part II. The Definitions of Classical and Intuitionist Negation. In: Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings of the Section of Sciences 51, pp. 322–331. Reprinted as Chapter 6 of this volume.
Reed Magazine (2011). Cohen Obituary. Accessed 18 August 2021. url: https: //www.reed.edu/reed-magazine/in-memoriam/obituaries/march2011/kalmanjoseph-cohen-1951.html
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Popper, K.R., Cohen, K.J. (2022). Popper’s Correspondence with Kalman Joseph Cohen. 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_25
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