References
- Formal Logic 185 – 186 . The distinction goes back to a puzzle in Aristotle's De Sophisticis Elenchis.
- The use of the symbol H for alternation is a departure from the usual Polish notation, which here uses the symbol A. I have to make this departure since I want a little later on to introduce the Aristotelian syllogistic operators. I prefer to symbolise alternation in another way, now explained, so as to retain the symbol A for the universal affirmative of Aristotelian syllogistic. For the same reason, equivalence is symbolised by Q rather than the more usual E. This usage follows that of Lukasiewicz Aristotle's Syllogistic himself in as well as others working in this field.
- That one can make such a re-interpretation might perhaps explain the confusion between predication and assertion as it applies to the question of truth Geach P. Three Philosophers 133 133 Cf. considers that Frege in his early work, Begriffsschrift, had not fought his way out of this confusion and writes as if his introduction of the assertion-sign were a reduction of all predicates to the single predicate “is the case” or “is true”.
- On this point cf. Logico-Philosophical Studies Menne A. 31 31 n.1.
- This account owes much to Thomas I. CS(n): An Extension of CS Logico-Philosophical Studies 40ff 40ff
- For an investigation of this see Bochenski I.M. On the Categorical Syllogism Logico-Philosophical Studies and the extension of this by I. Thomas (op. cit.) in the same volume. Bochenski's study provides the basis for much of what immediately follows.
- Out of the twenty-four modes of the traditional categorical syllogism, nine are now invalid. Cf. Bochenski On the Categorical Syllogism Logico-Philosophical Studies 28 28
- Shepherdson , J.C. 1956 . “ On the Interpretation of Aristotelian Syllogistic ” . In JSL 137 – 147 . maintains that I is not a truth-operator at all. Cf. Logico-Philosophical Studies, p. 31, n.1.
- This approach is that of von Wright G. An Essay in Modal Logic ch. 3 and Appendix II.
- For this, cf. von Wright An Essay in Modal Logic 25ff 25ff
- An Essay in Modal Logic 27 – 27 .
- Formal Logic 211 – 211 .
- Formal Logic 27 – 27 .
- Formal Logic 28 – 28 .
- Cf Formal Logic 212 213 for the proof of this.