Abstract
A proposition is presented by a complete, self-contained statement which, taken as a whole, will be true or false: The cat is on the mat, for example. When such a proposition is itself made subject to some further qualification of such a kind that the entire resulting complex is itself once again a proposition, then this qualification is said to represent a modality to which the original proposition is subjected. The classical modalities, treated by logicians at least since the time of Aristotle (b. 384 B.C.)1, revolve around the notion of truth itself:
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It is necessarily true (or: false) that p.
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It is actually true (or: false) that p.
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It is possibly true (or: false) that p.
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References
Actually, in Aristotle himself one does not find the term modality (Greek: tropos = mode) at all, although the idea is explicitly present in his writings. In many of the Aristotelian commentators (especially Ammonius and Philoponus), a ‘mode’ can be presented by using any adverb to qualify the verb of a simple statement - e.g., by changing ‘Socrates discourses’ to ‘Socrates discourses well’. See O. Hamelin, Le système d’Aristote (publié par L. Robin, Paris, 1920), p. 190.
A fine introduction to modal logic is G. H. von Wright’s book, An Essay in Modal Logic (Amsterdam, 1951 ).
Von Wright’s system was first presented in his paper ‘A New System of Modal Logic’, Proceedings of the Xlth International Congress of Philosophy (Brussels, 1953), V, 59–63. A much expanded version of this paper is presented under the same title in von Wright, Logical Studies (London, 1957), pp. 89–126.
Von Wright employs ‘M’ (for möglich) in place of ‘P’ (for possible).
Here, and throughout, quotation-marks are omitted, and symbols used autonymously, where confusion cannot result.
A. W. Burks, ‘The Logic of Causal Propositions’, Mind 60 (1951) 363–382 (see also the author’s review of this in The Journal of Symbolic Logic 16 (1951) 277–278) and ‘On the Presuppositions of Induction’, The Review of Metaphysics 8 (1955) 574–611.
A. W. Burks (op. cit.),pp. 368–382.
This is readily shown by means of the probabilistic interpretation of modalities shortly to be discussed.
See P. R. Halmos, ‘The Foundations of Probability’, American Mathematical Monthly 51 (1944) 493–510.
See Burks’ papers cited above. I have already tried to set forth in Section 3 the grounds of my view that Burks’ analysis cannot be accepted as it stands.
A Theory of Evidence’, Philosophy of Science 25 (1958) 83–94.
This chapter is a revised version of a paper of the same title published in The Review of Metaphysics 12 (1958) 186–199.
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Rescher, N. (1968). A Contribution to Modal Logic. In: Topics in Philosophical Logic. Synthese Library, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3546-9_4
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