Skip to main content

Modal Theories and Modal Logic

  • Living reference work entry
  • First Online:
Encyclopedia of Medieval Philosophy
  • 63 Accesses

Abstract

Early medieval thinkers were acquainted with ancient modal theories through Boethius’ commentaries on De interpretatione, which dealt with Aristotelian and other ancient modal paradigms extensively. Modal syllogistic was brought into the discussion by the recovery of Aristotle’s Prior Analytics in the twelfth century. Medieval considerations were also influenced by Augustine’s ideas, which deviated from philosophical paradigms, particularly his conception of God as acting by choice between simultaneous alternative possibilities. There were analogous discussions of philosophical and theological modalities in Arabic philosophy. Arabic modal theories influenced Latin discussions mainly through the translations of Averroes’ works.

Apart from ancient philosophical conceptions, the new idea of associating modal terms with simultaneous alternatives was discussed by Abelard and some other early medieval thinkers. While these innovations were used to some extent in thirteenth-century theology, they were not often discussed in philosophical contexts. The increasing reception of Aristotle’s philosophy in the thirteenth century gave support to traditional modal paradigms, as is seen in Robert Kilwardby’s influential commentary on Aristotle’s Prior Analytics, where modal syllogistics is treated as an essentialist theory of the structures of being.

Things became different when John Duns Scotus combined the various elements of the conception of modality as alternativeness into a detailed theory. A logically possible state of affairs is something to which to be is not repugnant, though it may not be compossible with other possibilities. Scotus’ modal semantics influenced early fourteenth-century philosophy and theology in many ways. The new modal logic which was developed by William Ockham, John Buridan, and others was based on the new modal semantics. Thirteenth-century essentialist assumptions were largely dropped from modal syllogistics, the Aristotelian version of which was regarded as a fragmentary theory without a sufficient explication of the various fine structures of modal propositions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Bibliography

Primary Sources

  • Abelard, P. (1919–1927). Philosophische Schriften I. Die Logica ‘Ingredientibus’. In B. Geyer (Ed.), Beiträge zur Geschichte der Philosophie und Theologie des Mittelalters XXI (pp. 1–3). Münster: Aschendorff.

    Google Scholar 

  • Abelard, P. (1958). Super Periermenias XII–XIV. In L. Minio-Paluello (Ed.), Twelfth century logic: Texts and studies II: Abaelardiana inedita. Rome: Edizioni di Storia e Leteratura.

    Google Scholar 

  • Albert the Great. (1890). Commentarius in librum I priorum analyticorum. In A. Borgnet (Ed.), Opera omnia (Vol. 1). Paris: Vivès.

    Google Scholar 

  • Anonymus. (1967). Dialectica Monacensis. In L. M. de Rijk (Ed.), Logica modernorum. A contribution to the history of early Terminist logic II.1–2: The origin and early development of the theory of supposition. Wijsgerige teksten en studies (Vol. 6). Assen: van Gorgum.

    Google Scholar 

  • Boethius. (1877–1880). Commentarii in librum Aristotelis Perihermeneias I–II (ed. Meiser, C.) Leipzig: Teubner.

    Google Scholar 

  • John Buridan. (1976). Tractatus de consequentiis (ed. Hubien, H.) Philosophes médiévaux 16. Louvain/Paris: Publications Universitaires/Vander-Oyez.

    Google Scholar 

  • John Buridan. (2001). Dialectica (an annotated translation with a philosophical introduction by Klima, G.). New Haven: Yale.

    Google Scholar 

  • John Duns Scotus. (1963). Opera omnia (vol. 6, ed. Balić, C., et al.). Vatican City: Typis Polyglottis Vaticanis.

    Google Scholar 

  • Robert Kilwardby. (2016). Notule libri priorum, ed. P. Thom and J. Scott. Oxford: Oxford University Press.

    Google Scholar 

  • Richard of Campsall. (1968). Quaestiones super librum priorum analyticorum. In E. A. Synan (Ed.), The works of Richard Campsall (Vol. 1). Toronto: Pontifical Institute of Mediaeval Studies.

    Google Scholar 

  • Thomas Aquinas (1962). On interpretation (trans: Oesterle, J. T.). Milwaukee: Marquette University Press.

    Google Scholar 

  • Thomas Aquinas. (1989). Expositio libri Peryermenias, cura et studio Fratrum Praedicatorum. Paris: Commissio Leonina, Rome/Vrin.

    Google Scholar 

  • William Ockham (1974). Summa logicae. In B. Ph, G. Gál, & S. Brown (Eds.), Guillelmi de Ockham Opera philosophica (Vol. 1). St. Bonaventure: St. Bonaventure University.

    Google Scholar 

Secondary Sources

  • Boh, I. (1993). Epistemic logic in the later middle ages. London: Routledge.

    Google Scholar 

  • Bydén, B., & Thomsen Thörnqvist, C. (Eds.). (2016). The Aristotelian tradition: Aristotle’s works on logic and metaphysics and their reception in the Middle Ages. Toronto: PIMS.

    Google Scholar 

  • Ebbesen, S. (1981). Analyzing syllogisms or Anonymus Aurelianensis III – The (pesumably) earliest Latin commentary on the prior analytics, and its Greek model. Cahiers de l’Institut du Moyen-Âge Grec et Latin, 37, 1–20.

    Google Scholar 

  • Knuuttila, S. (1993). Modalities in medieval philosophy. London: Routledge.

    Google Scholar 

  • Knuuttila, S. (2004). Anselm on modality. In B. Davies & B. Leftow (Eds.), The Cambridge companion to Anselm (pp. 111–131). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Knuuttila, S. (2008). Medieval modal theories and modal logic. In J. Woods & D. M. Gabbay (Eds.), Handbook of the history of logic II (pp. 505–578). Amsterdam: Elsevier.

    Google Scholar 

  • Knuuttila, S. (2012). Modality. In J. Marenbon (Ed.), The Oxford handbook of medieval philosophy (pp. 312–341). New York: Oxford University Press.

    Google Scholar 

  • Knuuttila, S., & Hallamaa, O. (1995). Roger Roseth and medieval deontic logic. Logic and Analysis, 149, 75–87.

    Google Scholar 

  • Kukkonen, T. (2000). Possible worlds in the Tahâfut al-tahâfut: Averroes on plenitude and possibility. Journal of the History of Philosophy, 38, 329–347.

    Article  Google Scholar 

  • Lagerlund, H. (2000). Modal syllogistics in the Middle Ages. In Studien und Texte zur Geistesgeschichte des Mittelalters (Vol. 70). Leiden: Brill.

    Google Scholar 

  • Martin, C. (1999). Thinking the impossible: Non-reductive arguments from impossible hypotheses in Boethius and Philoponus. Oxford Studies in Ancient Philosophy, 19, 279–302.

    Google Scholar 

  • Normore, C. (2003). Duns Scotus’s modal theory. In T. Williams (Ed.), The Cambridge companion to Duns Scotus (pp. 129–160). Cambridge: Cambridge University Press.

    Google Scholar 

  • Normore, C. (2016). Ockham and the foundations of modality in the fourteenth century. In M. Cresswell, E. Mares, & A. Rini (Eds.), Logical modalities from Aristotle to Carnap: The story of necessity (pp. 133–153). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Street, T. (2004). Arabic logic. In J. Woods & D. M. Gabbay (Eds.), Handbook of the history of logic I (pp. 471–556). Amsterdam: Elsevier.

    Google Scholar 

  • Thom, P. (2003). Medieval modal systems: Problems and concepts. Ashgate studies in medieval philosophy. Aldershot: Ashgate.

    Google Scholar 

  • Thom, P. (2007). Logic and ontology in the syllogistic of Robert Kilwardby. Leiden: Brill.

    Book  Google Scholar 

  • Yrjönsuuri, M. (Ed.). (2001). Medieval formal logic: Obligations, insolubles and consequences, The New Synthese Historical Library 49. Dordrecht: Kluwer.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Simo Knuuttila .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Science+Business Media B.V.

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Knuuttila, S. (2018). Modal Theories and Modal Logic. In: Lagerlund, H. (eds) Encyclopedia of Medieval Philosophy. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1151-5_340-2

Download citation

  • DOI: https://doi.org/10.1007/978-94-024-1151-5_340-2

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-024-1151-5

  • Online ISBN: 978-94-024-1151-5

  • eBook Packages: Springer Reference Religion and PhilosophyReference Module Humanities and Social SciencesReference Module Humanities

Publish with us

Policies and ethics