Gerland’s Dialectica and Paraconsistency

• Authors: Loffredo D’Ottaviano Itala M. , Gomes Evandro Luís
• Languages of publication: EN

Abstracts

EN

An analysis of positions for and against the principle of ex falso sequitur quodlibet is essential to the history of a paraconsistent approach in scholastic logic and in Western thought. In this paper we analyze the role that the Dialectica of Gerland of Besançon played in initiating the discussion about the ex falso in the 12th century, and we interpret his position as contrary to the acceptance of the principle. We consider Gerland one of the earliest authors to prepare the path and examine properly the role of the ex falso sequitur quodlibet principle, making it central in the philosophical context of the time. We adopt the thesis of Józef Maria Bocheński, according to which the formal aspects of logical theory are essential, decisive, and indispensable to a good historiography of logic.

Keywords

EN

theory of topics; logical implication; consequence; logica vetus; early scholastic logic; Gerland of Besançon; paraconsistency

• Publisher: University of Warsaw, Institute of Philosophy
• Journal: Edukacja Filozoficzna
• Year: 2020
• Issue: 70
• Pages: 143-170

Contributors

author

Loffredo D’Ottaviano Itala M.

author

Gomes Evandro Luís

References

• Anderson A.R., Belnap Jr N.D., Entailment: The Logic of Relevance and Necessity, Vol. 1, Princeton, NJ 1975.
• Aristotle, The Complete Works of Aristotle: The Revised Oxford Translation, 2 vols., ed. J. Barnes, Princeton, NJ 1985.
• Barth E.M., Krabbe E.C., From Axiom to Dialogue, Berlin 1982, https://doi.org/10.1515/9783110839807.
• Bobenrieth Miserda A., Inconsistencias ¿Por qué no? Un estudio filosófico sobre la lógica paraconsistente, Bogotá 1996.
• Bocheński J.M., A History of Formal Logic, trans. I. Thomas, New York, NY 1970.
• Boethius’s “In Ciceronis Topica”, trans., notes, and essays on the text E. Stump, Ithaca, NY–London 2004.
• Boh I., Epistemic Logic in the Later Middle Ages, London 1993.
• Cameron M., Abelard’s Early Glosses: Some Questions, in: Arts du langage et théologie aux confins des XIe–XIIe siècles: textes, maîtres, débats, ed. I. RosierCatach, Turnhout 2011, pp. 647–662.
• Cicero, On Invention, The Best Kind of Orator, Topics, trans. H.M. Hubbell, Loeb Classical Library 386, Cambridge, MA 1949.
• da Costa N.C.A., Krause D., Bueno O., Paraconsistent Logics and Paraconsistency, in: Philosophy of Logic, ed. D. Jacquette, Amsterdam 2006, pp. 791–911.
• Dalla Chiara M.L., Logica, Milano 1974.
• D’Ottaviano I.M.L., On the Development of Paraconsistent Logic and da Costa’s Work, “The Journal of Non-Classical Logic” 1990, Vol. 7, No. 1–2, pp. 89–152.
• Dunn J.M., Restall G., Relevance Logic, in: Handbook of Philosophical Logic, Vol. 6, 2nd ed., eds. F. Guenthner, D. Gabbay, Dordrecht 2002, pp. 1–128.
• Garlandus Compotista, Dialectica, ed. L.M. De Rijk, Assen 1959.
• Gili L., Podolak P., Hugh Eterianus, Alexander of Aphrodisias and Syllogistic Demonstrations: A Newly Discovered Fragment of Alexander of Aphrodisias’ "Commentary on Aristotle’s Posterior Analytics”, “Documenti e Studi sulla Tradizione Filosofica Medievale” 2018, Vol. 29, pp. 137–154.
• Gomes E.L., D’Ottaviano I.M.L., Para além das colunas de Hércules, uma história da paraconsistência: de Heráclito a Newton da Costa [Beyond the Columns of Hercules, a History of Paraconsistency: From Heraclitus to Newton da Costa], Campinas 2017.
• Ioannis Saresberiensis, Metalogicon (Metalogicus), in: Patrologia Latina, Vol. 199, ed. J.-P. Migne, Paris 1815–1875.
• Iwakuma Y., “Vocales,” or Early Nominalists, “Traditio” 1992, Vol. 47, pp. 37–111, https://doi.org/10.1017/S0362152900007200.
• Martin C.J., A Note on the Attribution of the “Literal Glosses” in Paris, BnF, lat. 13368 to Peter Abaelard, in: Arts du langage et théologie aux confins des XIe–XIIe siècles: textes, maîtres, débats, ed. I. Rosier-Catach, Turnhout 2011, pp. 605–646.
• Martin C.J., William’s Machine, “The Journal of Philosophy” 1986, Vol. 83, No. 10, pp. 564–572, https://doi.org/10.2307/2026432.
• Minio-Paluello L., Twelfth Century Logic: Texts and Studies, Vol. 1: Adam Balsamiensis Parvipontani Ars Disserendi (Dialectica Alexandri), Roma 1956.
• Moody E.A., Truth and Consequence in Mediaeval Logic, Amsterdam 1953.
• Mortensen C.E., Inconsistent Mathematics, Dordrecht 1995, https://doi.org/10.1007/978-94-015-8453-1.
• Parsons T., Articulating Medieval Logic, Oxford 2014, https://doi.org/10.1093/acprof:oso/9780199688845.001.0001.
• Peter of Spain (Petrus Hispanus Portugalensis), Peter of Spain: Summaries of Logic, text, trans., intr., and notes by B.P. Copenhaver, C. Normore, T. Parsons, Oxford 2014.
• Petrus Abaelardus, Dialectica, 2nd ed., ed. L.M. de Rijk, Assen 1970.
• Routley R., Plumwood V., Meyer R.K., Brady R., Relevant Logics and Their Rivals, Atascadero, CA 1982.
• Stump E., Dialectic in the Eleventh and Twelfth Centuries: Garlandus Compotista, “History and Philosophy of Logic” 1980, Vol. 1, pp. 1–18.
• Thom P., Robert Kilwardby’s Science of Logic: A Thirteenth-Century Intensional Logic, Leiden–Boston, MA 2019