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On logical ‘relativism’ (1937)

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References

  1. [Bocheński is answering some objections raised in the meeting held in 1936 at the Cracow Catholic Scientific Institute. Transl. note: TN].

  2. See C. Prantl,Geschichte der Logik im Abedlande, Leipzig 1927, bd. I, 370 ff; A. Becker,Die Aristotelische Theorie der Möglichkeitsschlüsse, Berlin 1933, 66 ff. The undersigned has written an essay on that question and is going to publish it soon [Z historii logiki zdań modalnych [On the history of modal logic], Lvov 1938. TN].

  3. See J. Łukasiewicz, “Zur Geschichte der Aussagenlogik”,Erkenntnis, 5 (1935), 116 ff.

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  4. See above, 126.

  5. A.N. Whitehead, B. Russell,Principia Mathematica, Cambridge 1935, vol. I, 96 ff.

  6. D. Hilbert, W. Ackermann,Grundzüge der theoretischen Logik, Berlin 1928, 22.

  7. J. Łukasiewicz,Elementy logiki matematycznej [Elements of mathematical logic], Warszawa 1929, 45.

  8. See above, 83.

  9. B. Sobociński, “Z badań nad teorią dedukcji” [Investigations on the theory of deduction], Odbitka z Księgi Pamiątkowej Koła Filozoficznego Słuchaczów Uniwersytetu Warszawskiego, Warszawa 1932 (see alsoPrzegląd Filozoficzny, 35 (1932).

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  10. See the article in note 5, in which Łukasiewicz deduces from his assumptions both Frege's axiomatic (80) and the axiomatic ofPrincipia (87). It is equally possible to deduce on the basis of this system Hilbert's axiomatic and the axioms of dr. Sobociński — the contrary process is obviously also possible.

  11. See the excellent article E.J. Nelson, “Deductive systems and the absolutness of logic”,Mind, 92 (1933), 30–42. The author discusses with the conventionalist C.J. Lewis proving that his ‘various’ logics are different ways of writing the same true logic. C.J. Lewis is, moreover, an ‘outsider’ of classic logic also on other points.

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  12. In classic treatises of modern formal logic it is difficult to find a clear declaration of this point — facts seem clearly obvious to the authors. It is enough to read e.g. the preface toPrincipia or the articles of Ł ukasiewicz, “O znaczeniu i potrzebach logiki matematycznej” [On the meaning and needs of mathematical logic],Nauka Polska, 10 (1929), 604–20 and “Logistyka a filozofia” [Logistic and philosophy],Przegląd Filozoficzny, 39 (1936), 115–31 in order to convince oneself of how these two prominent modern logicians see our problem. G.H. Luquet (Logique formelle, Paris 1925, V) says clearly: “La logique a pour rôle de déterminer les moyens d'atteindre la vérité”.

  13. For this question, see A. Tarski, “O logice matematycznej i metodzie dedukcyjnej” [On mathematical logic and deductive method], Warszawa (bez daty) [Warsaw, no date], 88 ff. The author — not suspicious of absolutism — warns us of regarding modern formal logic as a game.

  14. See Z. Zawirski, “Über das Verhältnis der mehrwertigen Logik zur Wahrscheinlichkeitsrechnung”,Studia Philosophica, 1 (1935), 407–442.

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  15. [The Author is referring here to the ideas of C.I. Lewis. See note 13. TN].

  16. H. Reichenbach, “Die logischen Grundlagen des Wahrscheinlichkeitsbegriffs”,Erkenntnis, 3 (1933), 401 ff.

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  17. See C.I. Lewis, C.H. Langford,Symbolic Logic, New York — London 1932, 229 ff.

  18. See Joannis a S. Thoma,Ars Logica, ed. B. Reiser, Taurini 1930, 777a.

  19. A similar logical apprehension of indeterminism can be found in Aristotle (De Interpretatione, 9) and, under Aristotle's influence, it has been discussed also by Middle-age philosophers (ed. note).

  20. Łukasiewicz perfectly explained this point it in his article “Logistyka a filozofia” [Logistic and philosophy] (see note 14). Also H. Scholz, one of the most famous German logicians, forms an entirely clear opinion in that question. It is worth citing some sentences from his work: “In keinen Falle steht es so, das ein überzeugter Logistiker nicht zugleich Metaphysiker sein kann in dem streng determinierten Leibnizischen Sinne eines denkenden Menschen, für welchen sogar die Gottesfrage als ein durch keinen noch so charaktervollen Positivismus totzumachendes philosophisches Problem mit dem ganzen Gewicht eines solchen existiert. Man hüte sich also die von uns mit Leibniz bahauptete zentralphilosophische Leistungsfähigkeit der Logistik dadurch zu welcher die neue Logik allerdings in einiger ihrer stärksten Vertreter mit einem extremen Positivismus gegenwartig existiert” (Geschichte der Logik, Berlin 1931, 65).

  21. See R. Carnap,Abriss der Logistik, Wien 1929, 70 ff.

  22. As to the pragmatistic views of formal logic see A. Reymond,Les principes de la logique et la critique contemporaine, Paris 1932, 49 ff. We should beware that authors like L. Rougier (La structure des théories déductives, Paris 1921) do not know sufficiently well the thomism against which they oppose modern formal logic. They should be warned of the acceptance of their conclusion concerning the contradiction between these two doctrines. In fact no contradiction on account of the, here mentioned, facts arises — moreover we could easily show that a thomistic philosophy of logic can serve to a philosophical establishment of modern formal logic easier than to a logic called ‘classic’ (the point concerms especially the analysis of the sentence of the form: for every x: if x is A, then x is B).

  23. See R. Carnap,Abriss der Logistik, Wien 1929, 107, n. 47, 3 A.

  24. G.H. Luquet,Logique formelle, Paris 1925.

  25. See J. Łukasiewicz,Elementy logiki matematycznej [Elements of mathematical logic], Warszawa 1929, 1–7.

  26. On the evolution of Aristotle's logic, see F. Solmsen,Die Entwicklung der Aristotelischen Logik und Rhetorik, Berlin 1929. This work, excellent for many reasons, is a proof of the necessity of some education in modern formal logic for historians of philosophy: the author does not possess it and in consequence he simply does not see many significant things.

  27. E.g.Analytica priora A 15, 34a, 27–33.

  28. J. Łukasiewicz,Elementy logiki matematycznej [Elements of mathematical logic], Warszawa 1929, 99 ff.

  29. J. Salamucha, “Dowód ‘ex motu’ na istnienie Boga”,Collectanea Theologica, 15 (1934), fasc.1–2. [See its English translation: J. Salamucha, “The Proof ‘ex motu’ for the Existence of God. Logical Analysis of St. Thomas' Arguments”, transl. T. Gierymski, M. Heitzmann,New Scholasticism, 32 (1958), fasc. 3, 334–72. TN].

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  30. Met. II, 3, 995a 14–17. “tèn d'akribologhían tèn mathematikèn ouk en hápasin apaitetéon, all'en toł s mè échousin húlen. Dióper ou physikòs ho trópos hápasa gàr ísos he phúsis échei húlen” (Mathematical accuracy is not to be demanded in everything, but only in things which do not contain matter. Hence this method is not that of natural science, because presumably all nature is concerned with matter. — Translation of H. Tredennick).

  31. S. Thomae Aquinatis,In Metaphysicam Aristotelis commentaria, ed. M.R. Cathala, Taurini 1926, lib. II, lect. V, N. 336. It is worthwhile to be aware that St. Thomas does not speak of exactness (exactitudo), but of certainty (certituto, certa ratio).

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“Tradycja myśli katolickiej a ścisłość”, in K. Michalski,Myśl katolicka wobec logiki współczesnej [Catholic mind in relation to modern logic], Poznań. [This paper was written more than half a century ago. Several statements it contains are no longer upheld by the author. J.M.B.].

[Translated by Ryszard Puciato]

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Bocheński, J.M. On logical ‘relativism’ (1937). Axiomathes 4, 193–209 (1993). https://doi.org/10.1007/BF02229795

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