Abstract
The calculus of partial propositional functions has been introduced in [2]. It is a variant of the classical propositional calculus, a variant which takes into account that pairs of propositions may be “incompatible” and cannot therefore be connected. As is well known, such pairs are considered in Quantum Theory; but they may also be said to occur in natural languages. Difficulties arising from propositions of the type “If two times two are five, then there exist centaurs” seem to be due as much to incompatibility as to material implication.
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Bibliography
Church, A., Introduction to Mathematical Logic, vol. 1, Princeton University Press, Princeton, 1956.
Kochen, S. and Specker, E. P., ‘Logical Structures Arising in Quantum Theory’, to appear in the Proc. of the Model Theory Symp. held in Berkeley, June-July 1963.
Specker, E., ‘Die Logik nicht gleichzeitig entscheidbarer Aussagen’, Dialectica 13 (1960), 239–246.
Wajsberg, M., ‘Metalogische Beiträge II’, Wiadomości Matematyczne 47 (1939), 119–139.
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© 1975 D. Reidel Publishing Company, Dordrecht, Holland
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Kochen, S., Specker, E.P. (1975). The Calculus of Partial Propositional Functions. In: Hooker, C.A. (eds) The Logico-Algebraic Approach to Quantum Mechanics. The University of Western Ontario Series in Philosophy of Science, vol 5a. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1795-4_16
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DOI: https://doi.org/10.1007/978-94-010-1795-4_16
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