Skip to main content Skip to main navigation menu Skip to site footer
  • Register
  • Login
  • Language
    • English
    • Język Polski
  • Menu
  • Home
  • Current
  • Archives
  • Online First Articles
  • About
    • About the Journal
    • Submissions
    • Editorial Team
    • Advisory Board
    • Peer Review Process
    • Logic and Logical Philosophy Committee
    • Open Access Policy
    • Privacy Statement
    • Contact
  • Register
  • Login
  • Language:
  • English
  • Język Polski

Logic and Logical Philosophy

Compatibility and relevance: Bolzano and Orlov
  • Home
  • /
  • Compatibility and relevance: Bolzano and Orlov
  1. Home /
  2. Archives /
  3. No. 10 (2002) /
  4. Articles

Compatibility and relevance: Bolzano and Orlov

Authors

  • Werner Stelzner University of Bremen

DOI:

https://doi.org/10.12775/LLP.2002.009

Abstract

For a dozen years the Russian engineer and logician I.E. Orlov has been recognized as the founder of the first precisely elaborated modern system of relevance logic.

Author Biography

Werner Stelzner, University of Bremen

FB 9/Philosophy

References

Anderson, A.R., and Belnap Jr., N.D. (1975), Entailment, vol. 1, University Press: Princeton.

Anderson, A.R., Belnap Jr., N.D., and Dunn, J.M. (1992), Entailment, vol. 2, University Press: Princeton.

Bammel, G. (1925), “The question of the logical fates of the theory of sets”, Under the banner of marxism, n. 3, 7

Bazhanov, V.A. (2000), Scientist and the “century of wolfdogs”. The fate of I.E. Orlov in logic, philosophy and science. Ulyanovsk, 30 p.

Becker, O. (1930), “Zur Logik der Modalitäten”, Jahrbuch für Philosophie und Phänomenologische Forschung 11, 497–548. Partial reprint in: K. Berka, L. Kreiser (1971), Logik-Texte, Akademie-Verlag: Berlin, 152–160.

Berg, J. (1962), Bolzano’s Logic, Alquist & Wiksell: Stockholm. Berg, J. (1981), “A Requirement for the logical basis of scientific theories implied by Bolzano’s logic of variation”, Acta Historiae Rerum Naturalium Necnon Technicarum Special Issue 13, 415–424.

Berg, J. (1987), Introduction to: Bolzano (1837).

Bolzano, B. (1837), Wissenschaftslehre, Seidel: Sulzbach, newly ed. by Jan Berg, in: Bernard Bolzano-Gesamtausgabe, I. Schriften: vols. 11/1 (§§1–45) (1985), 11/2 (§§46–90) (1987) , 11/3 (§§91–120) (1987), 12/1 (§§121–163) (1988), 12/2 (§§164–222) (1988), 12/3 (§§223–268) (1988), Frommann-Holzboog: Stuttgart/Bad Cannstatt.

Buhl, G. (1961), Ableitbarkeit und Abfolge in der Wissenschaftstheorie Bolzanos (Kantstudien Ergänzungshefte 83), Köln 1961.

Church, A. (1951), “The weak theory of implication”. In: A. Menne, A. Wilhelmy, H. Angsil (Hg.), Kontrolliertes Denken. Untersuchungen zum Logikkalkül und zur Logik der Einzelwissenschaften, Alber: München.

Došen, K. (1990), “The first axiomatization of a relevant logic”, Konstanzer Berichte Logik & Wissenschaftstheorie 9–90. 17 S.

Dunn, J.M. (1986), “Relevance logic and entailment”. In: D. Gabbay, F. Guenthner (eds.), Handbook of Philosophical Logic, vol. III: Alternatives to Classical Logic, Reidel: Dordrecht, 117–224.

Frege, G. (1879), Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Nebert: Halle a. S.

Frege, G. (1893/1903), Grundgesetze der Arithmetik, vol. I and II, Pohle: Jena.

George, R. (1972), “Enthymematic consequence”, American Philosophical Quarterly 9, 113–116.

George, R. (1981), “Review of Kambartel (1978)”, History and Philosophy of Logic 2; 1981, 176 f.

George, R. (1983), “Bolzano’s consequence, relevance, and enthymemes”, Journal of Philosophical Logic 12; 1983, 299–318.

George, R. (1983), “A postscript on fallacies”, Journal of Philosophical Logic 12, 319–325.

George, R. (1986), “Bolzano’s concept of consequence”, The Journal of Philosophy 83, 558–564.

George, R. (1992), “Concepts of consequence”. In: Bolzano’s Wissenschaftslehre 1837–1987. International Workshop (Biblioteca di Storia della Scienza 31), Olschki: Florenz, 3–26.

Gödel, K. (1933), “Eine Interpretation des intuitionistischen Aussagenkalküls”, Ergebnisse eines mathematischen Kolloquiums 4, 39–40 (Reprint in: K. Berka, L. Kreiser (1971), Logik-Texte, Akademie-Verlag: Berlin, 187–188 (reprinted with English translation in: K. Gödel, Collected Works, vol. 1: Publications 1929–1936”, Oxford University Press: New York, 1986).

Herbart, J.F. (1884 ff.), Sämmtliche Werke, hrsg. von Karl Kehrbach, Leipzig.

Hilbert, D. (1923), “Die logischen Grundlagen der Mathematik”, Mathematische Annalen 88, 151–165.

Kambartel, F. (1978), Bernard Bolzanos Grundlegung der Logik, Meiner: Hamburg 2 1978.

Leibniz, G.W. (1765), “Nouveaux essais sur l’entendement humain”. In: Œuvres philosophiques latines & françaises de feu M. de Leibnitz, ed. by E. Raspe, Amsterdam and Leipzig, 1–496.

Leśniewski, S. (1929), “Grundzüge eines neuen Systems der Grundlagen der Mathematik”, Fundamenta Mathematicæ 14, 1–81. (English translation in: J. van Heijenoort (ed.), From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Harvard University Press: Cambridge, Mass. 1967).

Lotze, R.H. (1843), Logik, Weidmann: Leipzig.

Lotze, R.H. (1874), Logik: Drei Bücher vom Denken, vom Untersuchen und vom Erkennen, Hirzel: Leipzig.

Łukasiewicz, J. (1970), “On variable functors of propositional arguments”. In: J. Łukasiewicz, Selected Works. North-Holland Publ. Company: Amsterdam – London, 311–324.

Massey, G. (1981), “The fallacy behind fallacies”. In: P.A. French, T.E. Vehling, Jr., H.K. Wettstein (eds.), The Foundation of Analytic Philosophy, University Press: Minneapolis, 489–500.

Max, I. (1988), “Vorschläge zur logischen Explikation von Negationen mittels Funktorenvariablen”, Linguistische Studien, Reihe A, Berlin, 182, 105–161.

Moh, S.K. (1950), “The deduction theorems and two new logical systems”. Methodos 2, 56–75.

Orlov, I.E. (1916), “About the inductive proof”, Voprosy Filosofii i Psikhologii, kn. 135, 356–388.

Orlov, I.E. (1916), “Realism in natural science and inductive method”, Voprosy Filosofii i Psikhologii, kn. 131, 1–35.

Orlov, I.E. (1923), “Pure geometry and reality”, Pod znamenem marksizma, N. 12, 69–74.

Orlov, I.E. (1924), “Formal logic, logic of natural science and dialectics”, Pod znamenem marksizma, Nr. 6–7, 69–90.

Orlov, I.E. (1925), “Logical calculus and traditional logic”, Pod znamenem marksizma, M. Nr. 4, 69–78.

Orlov, I.E. (1925b), “Logic of infinity and the theory of G. Cantor”, Pod znamenem marksizma, n. 3.

Orlov, I.E. (1925c), Logic of natural science, Gosud. Izdat.: M[oscow].-L[eningrad].

Orlov, I.E. (1926), “On the rationalization of mental work”, Pod znamenem marksizma, 12.

Orlov, I.E. (1928), “Calculus of the compatibility of sentences”, Matematicheskij sbornik, M. 35, 263–286.

Popov, V.M. (1978), “Decidibility of the relevant system RA0”. In: Modal’nye I intensional’nye logiki, AN SSSR, Moskva.

Routley, R., Meyer, R.K., et al. (1982), Relevant Logics and their Rivals, I: The Basic Philosophical and Semantical Theory, Ridgeview, Atascadero.

Scholz, H. (1953) “Rezension von Bar-Hillel [3]”; in: Zentralblatt für Mathematik und ihre Grenzgebiete 47; 1953; S. 12 f.

Siebel, M. (1996), Der Begriff der Ableitbarkeit bei Bolzano [Beiträge zur Bolzano-Forschung 7], Academia Verlag: Sankt Augustin.

Sigwart, C. (1871), Beiträge zur Lehre vom hypothetischen Urteil, Laupp: Tübingen.

Sigwart, C. (1873), Logik, Bd. I: Die Lehre vom Urteil, vom Begriff und vom Schluss, Vol. II: Die Methodenlehre, Laupp: Tübingen 1 1873 and 1878, 4 1911.

Simons, P. (1987), “Bolzano, Tarski, and the Limits of Logic”, Philosophia Naturalis 24, 378–405.

Smiley, T.J. (1959), “Entailment and deducibility”, Proceedings of the Aristotelian Society, n.s. 59, 233–254.

Stelzner, W. (1980), “Funktorenvariable, Funktionenvariable und nichtklassische Logik”, Wissenschaftliche Zeitschrift der KMU Leipzig, Ges. u. spr. Reihe 28, 313–318.

Stelzner, W. (2001), “Zur Behandlung von Widerspruch und Relevanz in der russischen traditionellen Logik und bei C. Sigwart”. In: W. Stelzner, M. Stöckler, Zwischen traditioneller und moderner Logik. Nichtklassische Ansätze, mentis: Paderborn, 239–296.

Vasil’ev, N.A. (1910), “On particular judgments, on the triangle of contraries, on the law of excluded fourth”. In: Uchennye zap. Kazan. un-ta 77, kn. 10, 1–47 Compatibility and relevance: Bolzano and Orlov 171

Vasil’ev, N.A. (1912), “Imaginary (non-Aristotelian) logic”. In: Zhurnal m-va nar. prosveshcheniya, Nov. ser. 40, 207–246

Vasil’ev, N.A. (1912/13), “Logic and metalogic”, Logos, Nr. 1–2, 53–81.

Vasil’ev, N.A. (1925), “Imaginary (non-Aristotelian) logic”. In: Estratto dagli Atti dei V Congresso internationale di Filosofia, 5–9 maggio, 1924, Napoli. Naples, 107–109.

Vladislavlev, M.I. (1872), Logic. Survey on inductive and deductive procedures of thinking and historical sketches: the logic of Aristotle, Scholastic dialectics, formal and inductive logic, Demakov: Sankt Petersburg, 2 1881.

Downloads

  • PDF

Published

2004-01-19

How to Cite

1.
STELZNER, Werner. Compatibility and relevance: Bolzano and Orlov. Logic and Logical Philosophy. Online. 19 January 2004. Vol. 10, no. 10, p. 137–171. [Accessed 4 July 2025]. DOI 10.12775/LLP.2002.009.
  • ISO 690
  • ACM
  • ACS
  • APA
  • ABNT
  • Chicago
  • Harvard
  • IEEE
  • MLA
  • Turabian
  • Vancouver
Download Citation
  • Endnote/Zotero/Mendeley (RIS)
  • BibTeX

Issue

No. 10 (2002)

Section

Articles

Stats

Number of views and downloads: 749
Number of citations: 0

Crossref
Scopus
Google Scholar
Europe PMC

Search

Search

Browse

  • Browse Author Index
  • Issue archive

User

User

Current Issue

  • Atom logo
  • RSS2 logo
  • RSS1 logo

Information

  • For Readers
  • For Authors
  • For Librarians

Newsletter

Subscribe Unsubscribe

Language

  • English
  • Język Polski
Up

Akademicka Platforma Czasopism

Najlepsze czasopisma naukowe i akademickie w jednym miejscu

apcz.umk.pl

Partners

  • Akademia Ignatianum w Krakowie
  • Akademickie Towarzystwo Andragogiczne
  • Fundacja Copernicus na rzecz Rozwoju Badań Naukowych
  • Instytut Historii im. Tadeusza Manteuffla Polskiej Akademii Nauk
  • Instytut Kultur Śródziemnomorskich i Orientalnych PAN
  • Instytut Tomistyczny
  • Karmelitański Instytut Duchowości w Krakowie
  • Ministerstwo Kultury i Dziedzictwa Narodowego
  • Państwowa Akademia Nauk Stosowanych w Krośnie
  • Państwowa Akademia Nauk Stosowanych we Włocławku
  • Państwowa Wyższa Szkoła Zawodowa im. Stanisława Pigonia w Krośnie
  • Polska Fundacja Przemysłu Kosmicznego
  • Polskie Towarzystwo Ekonomiczne
  • Polskie Towarzystwo Ludoznawcze
  • Towarzystwo Miłośników Torunia
  • Towarzystwo Naukowe w Toruniu
  • Uniwersytet im. Adama Mickiewicza w Poznaniu
  • Uniwersytet Komisji Edukacji Narodowej w Krakowie
  • Uniwersytet Mikołaja Kopernika
  • Uniwersytet w Białymstoku
  • Uniwersytet Warszawski
  • Wojewódzka Biblioteka Publiczna - Książnica Kopernikańska
  • Wyższe Seminarium Duchowne w Pelplinie / Wydawnictwo Diecezjalne „Bernardinum" w Pelplinie

© 2021- Nicolaus Copernicus University Accessibility statement Shop