Abstract
A somewhat fictionalized account of several interpretations of implication is presented together with comparisons between classical modal, tense, and intuitionistic logics.
It was through a very curious chain of circumstances that the present manuscript came into my possession. I am afraid that at the moment I am not at liberty to reveal its true authorship. Hence, if one wishes, he may regard it purely as a piece of fiction. This explains the title: I have called it a parable under the somewhat old fashioned idea (which is fast losing ground these days) that even a work of fiction can convey a message. The original title of the paper was, simply: ‘Semantical Archaeology’.
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References
For more information on this and other kinds of implication, see A. N. Prior, Formal Logic, 2nd ed., Clarendon Press, Oxford, 1962.
For this result one must combine theorems of A. Tarski and H. Läuchli. Cf. A. Tarski, ‘Der Aussagenkalkül und die Topologie’, Fundamenta Mathematicae 31 (1938) 103–134; reprinted in translation in Logic, Semantics, Mathematics (ed. by J. H. Woodger), Clarendon Press, Oxford, 1955. Also, H. Läuchli, ‘An Abstract Notion of Realizability for Which Intuitionistic Predicate Calculus Is Complete’ to appear in the proceedings of the Buffalo Conference 1968. The idea of the interpretation through transformations is due to Läuchli though it derives from the well-known work by Kleene on intuitionism.
For more details and references see A. R. Anderson, ‘Some Open Problems Concerning the System E of Entailment’, Acta Philosophica Fennica 16 (1963) 7–18.
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© 1972 D. Reidel Publishing Company, Dordrecht-Holland
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Scott, D. (1972). Semantical Archaeology: A Parable. In: Davidson, D., Harman, G. (eds) Semantics of Natural Language. Synthese Library, vol 40. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2557-7_20
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DOI: https://doi.org/10.1007/978-94-010-2557-7_20
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