University of St Andrews

Department of Philosophy

Arché Research Centre

Theories of Paradox in Fourteenth-Century Logic: Edition and Translation of Key Texts

St Andrews Institute of Mediaeval Studies
Leverhulme Trust

Medieval Logic Research Group

Principal Investigator: Stephen Read

Research Fellow: Barbara Bartocci

  Paul of Venice

  Walter Segrave

  John Dumbleton

  Source Material

  References

Summary

The project was funded by a Leverhulme Research Project grant to Professor Read, which ran from 1 August 2017 until 31 July 2021. The project continues as we complete the planned volumes.

The main and most direct aim is scholarly and historical, to provide scholars and students with access to important and interesting texts from the 14th century on the logical paradoxes. The logical paradoxes have played a significant role in the development of philosophical ideas, not just in logic but also in philosophy of language, epistemology, metaphysics and even ethics and political philosophy, throughout the 20th and 21st centuries. They played a no less significant role in later medieval philosophy and were the subject of much debate and the spur to original ideas, arguably reaching their zenith in the 14th century. Much has been learned about the medieval debate in the past fifty years, in the writings of John Buridan, Thomas Bradwardine and others. But other interesting treatises remain unedited, many only surviving in contemporary manuscripts. We have now completed and published the treatise on insolubles (logical paradoxes) by Paul of Venice, summarizing and developing theories and solutions from his predecessors in the 14th century, constituting the final treatise of his Logica Magna. Seven of the treatises from this huge work were edited and translated into English between 1978 and 1991. But the treatise on insolubles was not among them. It has now appeared in print, consisting of an edition of the Latin text, together with an English translation and commentary (October 2022). We continue to prepare editions and English translations of two treatises on insolubles from earlier in the 14th century, those by Walter Segrave and John Dumbleton, writing in Oxford in the second quarter of the century. Paul mentions them, and they contain rich ideas about alternative solutions, restrictio and cassatio respectively. Publication of these texts will allow a better overview of the development of solutions to the paradoxes through the 14th century, as well as giving further insight into the nature of the paradoxes and their possible solution.

Paul of Venice

Paul of Venice was in Oxford from 1390 t0 1393 and wrote his Logica Magna on his return to Padua in around 1400.

The volume on Paul has now been published:

Walter Segrave

Walter Segrave was writing in Oxford in the 1320s or ’30s, defending a restrictivist theory explicitly in response to Bradwardine’s criticisms. His treatise is preserved in three mss, one incomplete (Spade 1975, pp.113-15). It constitutes an extensive and detailed response to Bradwardine, defending restrictivism by presenting a well-thought out reason for the restriction of supposition required to avoid contradiction. Where Burley, and Bradwardine, both attributed the fallacy in insolubles to what Aristotle described as the fallacy of the conditional and the unconditional (simpliciter et secundum quid), Segrave attributed it to the fallacy of accident, turning on a variation in the supposition of the middle term and the extremes in what might otherwise appear to be a sound syllogism.

Walter Segrave's Insolubles has now been published: Walter Segrave, Insolubles

John Dumbleton

John Dumbleton was, like Bradwardine, one of the famous Oxford Calculators, whose main interest was in mathematical physics. His discussion of insolubles occurs as the second chapter of Part I (Summa Logicae) of his magnum opus, Summa Logicae et Philosophiae Naturalis, a huge work running to some 400,000 words (Spade 1975, pp.63-65). The whole work was transcribed by James Weisheipl from a single ms (Vat.lat. 6750) in the early 1950s when preparing his Oxford D.Phil. thesis on Dumbleton’s natural philosophy, but that transcription was never published, and exists, it seems, in a single copy in the Library of the Pontifical Institute of Medieval Studies in Toronto. Useful as it is, it is in a very preliminary state, with many insecure, and arguably mistaken, readings, and needs comparison with the texts of the other extant mss of Dumbleton’s Summa which also contain this early section on insolubles. (Two mss are incomplete in lacking Part I; all are incomplete in lacking Part X, which Dumbleton refers to but arguably never completed before he succumbed to the Black Death in 1348 or 1349.) The 19 chapters on insolubles are preceded by an extended discussion of signification in 5 chapters, which is important for understanding Dumbleton’s solution to the insolubles and so needs to be included in the edition. The chapters on insolubles are followed by two chapters on knowledge and doubt, the whole comprising the first article of Part I, the Summa Logicae. Thus it makes sense to the first article as a whole. In his theory of insolubles, Dumbleton revives a solution much criticised by Bradwardine and others, cassationism, otherwise advocated only in a single treatise from the early 13th century (De Rijk 1966), which claims that insolubles are not in fact propositions at all.

In addition, five of the mss contain five further chapters, one on Insolubles, the others making up a short introduction to supposition theory, obligations and other logical issues, a Summulae as it is often known. (The treatise on Obligations was edited by Kretzman and E.Stump from one manuscript, in ‘The anonymous De Arte Obligatoria in Merton College Ms.306’, in E. P. Bos (ed.), Mediaeval Semantics and Metaphysics, Studies Dedicated to L. M. de Rijk, Ph.D. on the Occasion of his 60th Birthday, Ingenium, Nijmegen, 239–80.) The additional chapters are arguably by Dumbleton himself, or by a follower of his, for the doctrine is consistent with the Summa Logicae itself.

Paul Spade argues (Heytesbury 1979, p.73) that Cajetan’s identification (in his 15th-century commentary on Heytesbury’s Insolubles) of the second view criticised by Heytesbury, and consequently the eighth discussed by Paul of Venice, as Dumbleton’s cannot be right, since Dumbleton’s treatise itself argues against Heytesbury’s view. But this is a weak argument, for Heytesbury, Swyneshed, Dumbleton and others were all working together in Oxford in the 1330s and would have been aware of each others’ ideas and so could easily end up criticising each other.

The Source Material

The known manuscripts and early printed texts to be used are as follows:

References

  1. Albert of Saxony. ‘Insolubles’. In The Cambridge Translations of Medieval Philosophical Texts, vol. I: Logic and the Philosophy of Language, trans. N. Kretzmann and E. Stump. Cambridge: Cambridge University Press, 1988, 338-68.
  2.   Albert of Saxony. Logik: Lateinisch-Deutsch (Perutilis Logica), ed. and tr. H. Berger. Hamburg: Meiner 2010.
  3.   Anderson, C.A. 1983. 'The Paradox of the Knower', The Journal of Philosophy 80, 338–355.
  4.   Aristotle, 1938. Categories, On Interpretation, Prior Analytics. (The Loeb Classical Library: Heinemann). Categories and On Interpretation ed. and tr. Harold P. Cooke, Prior Analytics ed. and tr. Hugh Tredennick.
  5.   Aristotle. De Sophisticis Elenchis, Translatio Boethii, Fragmenta Translationis Iacobi et Recensio Guillelmi de Moerbeke (Aristoteles Latinus VI 1-3), ed. B. Dod. Leiden: Brill 1975. 
  6.   Ashworth, E. Jennifer. ‘Paul of Venice on Obligations: The Sources for both the Logica Magna and the Logica Parva Versions’, in Knowledge and the Sciences in Medieval Philosophy, Vol. 2, ed. Simo Knuuttila et al. Publications of Luther-Agricola Society 1990, 407-415. 
  7.   Bochenski, 1970. History of Formal Logic, translated by Ivo Thomas (Chelsea Pub.Co.), second edition.
  8.   Bos, E.P., 1985. John of Holland: Four Tracts on Logic (Suppositiones, Fallacie, Obligationes, Insolubilia). Artistarium 5 (Ingenium).
  9.   Bottin, F, 1976. Le Antinomie Semantiche nella Logica Medievale (Editrice Antenore).
  10.   Bradwardine, Thomas.2010. Insolubilia. Edition, English translation and Introduction by Stephen Read. (Dallas Medieval Texts and Translation 10.) Leuven: Peeters.
  11.   Buridan, John. 1994. Quaestiones Elencorum, ed. R. van der Lecq and H.A.G. Braakhuis (Ingenium).
  12.   Buridan, John. 2001. Summulae de Dialectica, tr. G. Klima (Yale UP).
  13.   Buridan, John. 2004. Summulae de Practica Sophismatum, ed. F. Pironet (Brepols).
  14.   Conti, Alessandro, ‘Paul of Venice’, The Stanford Encyclopedia of Philosophy. Ed. E. N. Zalta (Summer 2017 Edition)
  15.   De Rijk, Lambertus M. ‘Some Notes on the Mediaeval Tract De insolubilibus, with the Edition of a Tract Dating from the End of the Twelfth Century.’ Vivarium 4 (1966), 83-115.
  16.   De Rijk, Lambertus M. Logica Modernorum: A Contribution to the History of Early Terminist Logic. Vol. 1: On the Twelfth Century Theories of Fallacy. Assen: Van Gorcum 1962.
  17.   De Rijk, Lambertus Marie, 1977. ‘Logica Oxoniensis: an attempt to reconstruct a fifteenth-century Oxford manual of logic’, Medioevo 3, 121-64.
  18.   Heytesbury, William. On “Insoluble” Sentences: Chapter One of His Rules for Solving Sophisms. Tr. Paul Vincent Spade. “Mediaeval Sources in Translation,” vol. 21. Toronto: Pontifical Institute of Mediaeval Studies, 1979.
  19.   Heytesbury, William, 1987. Insolubilia, in Il Mentitore e il Medioevo, ed. L.Pozzi (Edizioni Zara), 201-57.
  20.   Klima, Gyula, 2009. John Buridan (OUP).  
  21.   Martin, Christopher J. ‘Obligations and Liars.’ In Sophisms in Medieval Logic and Grammar. Ed. Stephen Read. Dordrecht: Kluwer 1993, 357-81; reprinted in Medieval Formal Logic. Ed. M. Yrjönsuuri, Kluwer 2001, 63-94.
  22.   Paul of Venice. Logica Magna. Venice 1499.
  23.   Paul of Venice. Quadratura. Venice 1493.
  24.   Paul of Venice, 1483. Sophismata Aurea (Pavia, Nicolaus Girardengus, de Novis). [repr. Venice: Bonetus Locatellus, for Octavianus Scotus, 1493] 
  25.   Paul of Venice. Logica Parva. Tr. A.R. Perreiah. Munich/Vienna: Philosophia Verlag 1984.
  26.   Paul of Venice. Logica Parva. Ed. A.R. Perreiah. Leiden: Brill 2002.
  27.   Paul of Venice. Logica Magna, Secunda Pars: Tractatus de Veritate et Falsitate Propositionis et Tractatus de Significato Propositionis. Ed. F. del Punta and tr. M.M. Adams. Oxford UP for the British Academy, 1978.
  28.   Paul of Venice. Logica Magna, Prima Pars: Tractatus de Terminis. Ed. N. Kretzmann. Oxford UP for the British Academy, 1979.
  29.   Paul of Venice. Logica Magna, Prima Pars: Tractatus de Scire et Dubitare. Ed. P. Clarke. Oxford UP for the British Academy, 1981.
  30.   Paul of Venice. Logica Magna, Secunda Pars: Tractatus de Obligationibus. Ed. E.J. Ashworth. Oxford UP for the British Academy, 1988.
  31.   Paul of Venice. Logica Magna, Secunda Pars: Capitula de Conditionali et de Rationali. Ed. G. Hughes. Oxford UP for the British Academy, 1990.
  32.   Paul of Venice. Logica Magna, Secunda Pars: Tractatus de Hypotheticis. Ed. A. Broadie. Oxford UP for the British Academy, 1990.
  33.   Paul of Venice. Logica Magna, Prima Pars: Tractatus de Necessitate et Contingentia Futurorum. Ed. C.J.F. Williams. Oxford UP for the British Academy, 1991. 
  34.   Perreiah, A.R. ‘Insolubilia in the Logica Parva of Paul of Venice.’ Medioevo 4 (1978), 145-71.
  35.   Perreiah, A.R. Paul of Venice: a Bibliographical Guide. Philosophy Documentation Center 1986.
  36.   Peter of Ailly. Concepts and Insolubles: An Annotated Translation. Tr. Paul Vincent Spade. “Synthese Historical Library” vol. 19. Dordrecht: Reidel 1980.
  37.   Peter of Mantua. Logica. Padua 1477.
  38.   Pironet, Fabienne, 1993. ‘John Buridan on the Liar paradox: study of an opinion and chronology of the texts’, in Argumentationstheorie, ed. K. Jacobi (Brill), 293-300.
  39.   Pironet, Fabienne. ‘William Heytesbury and the treatment of Insolubilia in 14th-century England.’ In Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox. Ed. Shahid Rahman et al. Berlin: Springer-Verlag 2008, 255-333.
  40.   Pozzi, Lorenzo. Il Mentitore e il Medioevio. Edizioni Zara 1987. 
  41.   Read, Stephen. ‘The Liar paradox from John Buridan back to Thomas Bradwardine.’ Vivarium 40 (2002), 189-218.
  42.   Read, Stephen, 2014. ‘Concepts and meaning in medieval philosophy’, in Intentionality, edited by Gyula Klima, Fordham University Press, 9-28.
  43.   Read, Stephen and Thakkar, Mark, 2016. ‘Robert Fland, or Elandus Dialecticus?’, Mediaeval Studies 78, 167-80.
  44.   Roure, M.-L., 1970. ‘La problématique des propositions insolubles au XIIIe siècle et au début du XIVe, suivie de l’édition des traités de W.Shyreswood, W. Burleigh et Th. Bradwardine’, Archives d'histoire doctrinale et littéraire du moyen âge 36-37, 205-326.  
  45.   Spade, Paul Vincent, 1971. ‘An anonymous tract on Insolubilia from Ms Vat.Lat.674. An edition and analysis of the text’, Vivarium 9, 1-18.
  46.   Spade, Paul Vincent. The Medieval Liar. Toronto: Pontifical Institute of Medieval Studies 1975.
  47.   Spade, Paul Vincent, 1978. ‘Robert Fland’s Insolubilia: an edition, with comments on the dating of Fland’s works’, Mediaeval Studies 40, 56–80.
  48.   Spade, Paul Vincent. ‘Roger Swyneshed's Insolubilia: Edition and Comments.’ Archives d'histoire doctrinale et littéraire du moyen âge, 46 (1979), 177-220.
  49.   Spade, Paul Vincent, 1983. ‘Roger Swyneshed’s theory of insolubilia: a study of some of his preliminary semantic notions’, in History of Semiotics, ed. A. Eschbach and J. Trabant (John Benjamins), 105-13.
  50.   Spade, Paul Vincent. ‘The manuscripts of William Heytesbury’s Regulae solvendi sophismata: conclusions, notes and descriptions’, Medioevo 15 (1989), 271-314.
  51.   Spade, Paul Vincent and Read, Stephen. ‘Insolubles’, The Stanford Encyclopedia of Philosophy. Ed. E. N. Zalta. (Fall 2018 Edition).
  52.   Strobino, Riccardo. ‘Truth and Paradox in Late XIVth Century Logic: Peter of Mantua's Treatise on Insoluble Propositions.’ Documenti e studi sulla tradizione filosofica medievale, 23 (2012), 475-519.
  53.   Swyneshed, Roger, 1979. Insolubilia, in Spade (1979).
  54.   Swyneshed, Roger, 1987. Insolubilia, in Il Mentitore e il Medioevo, ed. L.Pozzi (Edizioni Zara), 173-99. 
  55.   Zupko, Jack, 2018. ‘John Buridan’, The Stanford Encyclopedia of Philosophy Edward N. Zalta (ed.). (Fall 2018 Edition).

Steering Committee

[Updated 17 January 2023]