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References
See F. Graf Hoensbroech, “Beziehungen zwischen Inhalt und Umfang von Begriffen”,Erkenntnis 1931, 231–300.
It is true that this principle looks like the one given, with unsteady terminology, by G. Sanseverino (Philosophia Christiana cum antiqua et nova comparata, 3 vols., Neapol, 1862–66) and without any objection by C. Gutberlet (Lehrbuch der Philosophie, 6 vols., Münster, 1901–13 (4th ed.)), but we cannot find it in J. Kleutgen (Die Philosophie der Vorzeit, 2 vols., Innsbruck, 1878), M. Liberatore (Institutiones philosophicae, 3 vols., Prati, 1889), J.J. Urraburu (Compendium philosophiae scholasticae, 5 vols., Madrid, 1902–4), M. De Maria (Philosophia peripatetico-scholastica ex fontibus Aristotelis at S. Thomae Aquinatis expressa et ad adolescentium institutionem accomodata, 2 vols., Romae, 1904 (3rd ed.)). T. M. Zigliara (Summa philosophica in usum scholarum, 3 vols., Parisiis 1926 (17th ed.)); we cannot even find it in J. Geyser. I stress that I have got exactly in my mind the principle of converse relation between extensions and contents of notions; some sound opinions, contained in these principle, owing to which this principle is so suggestive, can be found in the Middle-Age logicians.
See Carolus Boyer,Cursus Philosophiae, Parisiis, s.a., vol. 1, 72. He calls that principlelex fundamentalis.
See Dr. Georg Grunwald, “Geschichte der Gottesbeweise im Mittelalter”,Beiträge zur Geschichte der Philosophie des Mittelalters, VI, 3, 136–40.
The correctness of the reasoning, a disputable part of which I discussed above, I showed in the article “Dowód ‘ex motu’ na istnienie Boga. Analiza logiczna argumentacij św. Tomasza z Akwinu”,Collectanea theologica, 15 (1934), fasc. 1–2, 73–76 [Engl. transl.: “The proof ‘ex motu’ for the existence of God. Logical analysis of St. Thomas' argument”,New Scholasticism, 32 (1958), fasc. 3, 334–72. TN]. I showed there that the assumption of St. Thomas is very strong, because it is inferentially equivalent to the assumption: ∏xaCPaxNMxx [∀xa(Pax → ¬Mxx). TN] (see the paper quoted above, 76, note 23). More intuitive, as it seems to me, could be the assumption that corresponds to the interpretation expressed in thesis 1.2 and thesis 2 apart from thesis 3 (see the paper quoted above, 77), but that assumption is not enough — we can prove it by means of the following interpretation, where x and y are real numbers: Mxy − x = y, Pax − 2 < x, ϕ(x): it is easy to see that on this interpretation, the assumptions 1.1, 1.3, 1.4 and the above weaker assumptions (see the paper quoted above, 74–77) will be true, but the conclusion will be false (75, 3): ∏xCϕ(x)∑tKMtxNMtx [∀ x(ϕ(x) → ∃t(Mtx ⁁ ¬Mtx). TN]. It is possible that this weaker assumption has been the cause of various manuscript variants: people tried, under the influence of the imposed intuitions, to ‘improve’ the text of St. Thomas, but using a weaker logical tool they could neither express their intuitions, nor control them. It is very positive that, after all, they did not deform the text as to its logical aspect.
See J. Łukasiewicz, “Znaczenie analizy logicznej dla poznania” [The meaning of logical analysis for knowledge],Przegląd Filozoficzny, 37 (1934), and “Logistyka i filozofia” [Logistic and philosophy],Przeglą d Filozoficzny, 39 (1936).
See H. Scholz,Geschichte der Logik, Berlin 1931.
Additional information
“Zestawienie scholastycznych narzędzi logicznych z narzędziami logistycznymi”, in K. Michalski,Myśl katolicka wobec logiki współczesnej [Catholic mind in relation to modern logic], Poznań.
[Translated by Ryszard Puciato]
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Salamucha, J. Comparisons between scholastic logical tools and modern formal logic (1937). Axiomathes 4, 210–219 (1993). https://doi.org/10.1007/BF02229796
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DOI: https://doi.org/10.1007/BF02229796