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The Historical and Cultural Context

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Book cover Thinking about Contradictions

Part of the book series: Synthese Library ((SYLI,volume 386))

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Abstract

This chapter contextualizes Vasil’ev’s work considering the state of logic in both Russia and Western Europe between the end of the nineteenth and the beginning of the twentieth century, and, above all, the ways in which Vasil’ev absorbed and re-worked input and suggestions flowing from external sources. This survey starts with the individual, Vasil’ev himself, and then moves outwards to isolate and identify the broader contexts within which his ideas developed. Among the main Russian logicians who were important for Vasil’ev there are Matvei Mikhailovich Troitsky, Mikhail I. Vladislavlev, Mikhail Ivanovich Karinsky, as well as the neo-Kantians Aleksandr Ivanovich Vvedensky and Ivan Ivanovich Lapshin. As to the Western scholars, even though Vasil’ev wrote during the years of the foundational crisis of mathematics, he placed great importance on Aristotelian logic and hence on traditional logicians like William Hamilton, John S. Mill, Rudolf Hermann Lotze, Christoph Sigwart, Benno Erdmann, and Wilhelm Wundt. At the same time, attention is focused on the work of some contemporaries like Isaac Husik, Jan Łukasiewicz, Alexius Meinong and Charles S. Peirce, whose work was relevant for the elaboration of non-classical logical ideas around the turn of the century. In particular, the reading of Peirce played an important role in Vasil’ev’s elaboration of the idea of a non-Aristotelian logic. Just as important was his acquaintance with Darwin’s evolutionary theories through the mediation of Sigwart.

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Notes

  1. 1.

    For a historical reconstruction of the fortunes of logic in Russia from the late medieval period to the nineteenth century see Anellis (1992).

  2. 2.

    On the history of philosophy in the universities see Bazhanov (1995). Stelzner & Kreiser (2004: 236–241) provide a highly synthetic picture. On the history of logic in Russia in the nineteenth century until the beginning of the twentieth century see also Bazhanov (2012; 2013: 65–67), Schumann (2014).

  3. 3.

    Cf. Cavaliere (1992–1993: 7 ff.). The Russian translations of the mentioned works are listed in the bibliography.

  4. 4.

    Cf. Vasil’ev (1910: 10 fn. 1, 34, 41 = 1989: 18–19 fn. 8, 42, 48).

  5. 5.

    Cf. Vladislavlev (1872: 54–55).

  6. 6.

    Cf. Stelzner (2001: 250–251), Stelzner & Kreiser (2004: 256–257). For more details on the problematic of contradiction in Vladislavlev see Stelzner (2001: 243–249), Stelzner & Kreiser (2004: 387–393) again.

  7. 7.

    Cf. Biryukov (2001: 220–223).

  8. 8.

    Vasil’ev (1912–1913a: 80 = 1989: 122 [1993: 351]).

  9. 9.

    In Russia, in 1901–1902, Samuil Osipovich Shatunovsky had maintained that the principle of excluded middle was not valid for infinite sets, and later, Pavel A. Florensky , in The Pillar and Ground of the Truth (1914 [1997]), spoke of degrees of belief, or faith, that go from +∞ to –∞ (cf. Bazhanov 2001: 207; 2011: 95). There is no lack of scholars who see already in Florensky a supporter of paraconsistency; cf. Guseinov & Lektorsky (2008: 13), Rhodes (2013: 20, 24 ff.). On the relationships between Vasil’ev’s imaginary logic and Florensky’s philosophy, see Biryukov & Pryadko (2010).

  10. 10.

    According to Hamilton (1861–18662: iii, 100), “all that we can positively think, that is, all that is within the jurisdiction of the law of Reason and Consequent, lies between two opposite poles of thought, which, as exclusive of each other, cannot, on the principles of Identity and Contradiction, both be true, but of which, on the principle of Excluded Middle, the one or the other must.” All this applies to anything, even to the inconceivable, hence both to the phenomenal and to the noumenal. On Hamilton’s concept of the laws of thought see Raspa (1999b: 84–89).

  11. 11.

    Cf. Biryukov (2001: 225–227), Stelzner & Kreiser (2004: 241–248).

  12. 12.

    Cf. Vasil’ev (1910: 12, 14 fn. 1, 40 fn. 1 = 1989: 20, 22 fn. 10, 47–48 fn. 22; 1912: 218–219 fn. 2, 222 = 1989: 65 fn. 6, 68–69 [2003: 137 fn. 6, 140–141]; 1912–1913a: 80 = 1989: 122 [1993: 351]).

  13. 13.

    Vasil’ev (1912: 222 = 1989: 69 [2003: 141]).

  14. 14.

    Vasil’ev (1912: 218, fn. 2 = 1989: 65, fn. 6 [2003: 137, fn. 6]).

  15. 15.

    Cf. Vasil’ev (1912–1913a: 72, fn. 1 = 1989: 114, fn. 10 [1993: 344]). In the translation, the note has been put in the text.

  16. 16.

    Cf. Biryukov (2001: 227–228).

  17. 17.

    On Kantianism in Russia see also Evtuhov (1995), who speaks about Vvedensky ’s reading of Kant and Kantianism at Kazan University. On Vvedensky ’s logical ideas and biography see Biryukov & Biryukova (2011; 2012).

  18. 18.

    Cf. Vasil’ev (1911/1989: 126; 1912: 244 = 1989: 92 [2003: 161]; 1912–1913a: 80 = 1989: 122 [1993: 350]; 1925: 107).

  19. 19.

    By ‘classical logic’ we understand, in accordance with contemporary usage, not traditional logic, which arose with Aristotle and the stoic-megarian reflection, to continue through the Medieval age down to modern times, but logical systems (classical propositional calculus and the logic of predicates of the first and second order) that are opposed to intuitionistic, many-valued, paraconsistent logics etc., i.e. ‘non-classical logics.’ Nonetheless, as should emerge from the following pages, not all non-classical logics arise in reaction to classical logic, since non-classical elements were already present in traditional logic.

  20. 20.

    Cf. Priest (2000: 144).

  21. 21.

    Cf. for example Hamilton (1861–18662: iii, 79, 100) and Heymans (1905 2: 62 ff.); see also Sect. 2.1 fn. 10, and Sect. 5.1. With regard to twentieth century exponents of traditional formal logic, cf. Freytag-Löringhoff (1955: 13–14, 20) and Luce (1958: 124).

  22. 22.

    Vasil’ev (1912–1913a: 59 = 1989: 101 [1993: 334]).

  23. 23.

    Cf. Vasil’ev (1912: 208, 223 = 1989: 55, 69 [2003: 128, 141]; 1925: 108).

  24. 24.

    Vasil’ev (1912–1913a: 59 = 1989: 101–102 [1993: 334]).

  25. 25.

    Cf. Bazhanov (1990a: 334; 1998: 17).

  26. 26.

    Cf. Bazhanov (1992a: 46; 1998: 18–19; 2001: 209 ff.).

  27. 27.

    Vasil’ev (1912–1913a: 79 = 1989: 122 [1993: 350]).

  28. 28.

    Sigwart (19043: ii, § 94, pp. 462–463 [1895: ii, 328–329]).

  29. 29.

    Vasil’ev (1912–1913a: 74 = 1989: 116 [1993: 346]). Cf. also Vasil’ev (1909c), with reference to which see Bazhanov (1990c).

  30. 30.

    Cf. Bazhanov (1992a: 46–47).

  31. 31.

    Peirce quoted in Carus (1910a: 45).

  32. 32.

    Cf. Peirce quoted in Carus (1910b: 158): “It does not seem to me to have been a lunatic study. On the contrary, perhaps if I had pursued it further, it might have drawn my attention to features of logic that had been overlooked. However, I came to the conclusion that it was not worth my while to pursue that line of thought further. In order to show what sort of false hypotheses they were that I traced out to their consequences, I will mention that one of them was that instead of the form of necessary inference being, as it is, that from A being in a certain relation to B, and B in the same relation to C, it necessarily follows that A is in the same relation to C, I supposed, in one case, that the nature of Reason were such that the fundamental form of inference was, A is in a certain relation to B and B in the same relation to C, whence it necessarily follows that C is in the same relation to A; and I followed out various other similar modifications of logic.”

  33. 33.

    Cf. Bazhanov (1992a: 48; 2001: 207); on Vasil’ev’s reading of Carus ’s essay see also Bazhanov (1988a: 68–70; 2009a: 108–111).

  34. 34.

    Cf. Carus (1910a: 37): “Every contradiction is a problem and every solution of a problem becomes a renewed justification of our belief in the consistency of existence. [...] If there were no consistency there would be no science, reason would be a mere coincidence of haphazard regularities, and a trust in the efficiency of reason should be branded as a vagary of deluded dreamers. The very existence of reason is an evidence that the universe is consistent throughout, and human reason is an instinctive comprehension of this most remarkable feature of existence, while science is simply the methodical application of reason.”

  35. 35.

    Kant (17811–17872: A 651 = B 679 [1998: 595]).

  36. 36.

    Cf. Peirce (1892: CP 6.39; W 8, 113).

  37. 37.

    Carus (1910a: 39).

  38. 38.

    Carus (1910a: 44).

  39. 39.

    Carus (1910a: 46).

  40. 40.

    Cf. Bazhanov (1992a: 50).

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  1. Dipartimento di Studi Umanistici, Università degli Studi di Urbino Carlo Bo, Urbino, Italy

    Venanzio Raspa

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Raspa, V. (2017). The Historical and Cultural Context. In: Thinking about Contradictions. Synthese Library, vol 386. Springer, Cham. https://doi.org/10.1007/978-3-319-66086-8_2

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