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SEVENTEENTH-CENTURY SCHOLASTIC SYLLOGISTICS. BETWEEN LOGIC AND MATHEMATICS?

Published online by Cambridge University Press:  28 January 2019

MIROSLAV HANKE
MIROSLAV HANKE*
Affiliation:
Institute of Philosophy of the Czech Academy of Sciences
*
*DEPARTMENT FOR THE STUDY OF ANCIENT AND MEDIEVAL THOUGHT INSTITUTE OF PHILOSOPHY OF THE CZECH ACADEMY OF SCIENCES JILSKÁ1, 110 00 PRAGUE 1 CZECH REPUBLIC E-mail: [email protected]
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Abstract

The seventeenth century can be viewed as an era of (closely related) innovation in the formal and natural sciences and of paradigmatic diversity in philosophy (due to the coexistence of at least the humanist, the late scholastic, and the early modern tradition). Within this environment, the present study focuses on scholastic logic and, in particular, syllogistic. In seventeenth-century scholastic logic two different approaches to logic can be identified, one represented by the Dominicans Báñez, Poinsot, and Comas del Brugar, the other represented by the Jesuits Hurtado, Arriaga, Oviedo, and Compton. These two groups of authors can be contrasted in three prominent features. First, in the role of the theory of validity, which is either a common basis for all particular theories (in this case, sentential logic and syllogistic), or a set of observations regarding a particular theory (in this case, syllogistic). Second, in the view of syllogistic, which is either an implication of a general theory of validity and a semantics of terms, or an algebra of structured objects. Third, in the role of the scholastic analysis of language in terms of suppositio, which either is a semantic underpinning of syllogistic, or it is replaced by a semantics of propositions.

Keywords

01A3501A4001A45scholastic logicmathematisationsecond scholasticismsyllogistic reasoningsubstructural logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 2 , June 2020 , pp. 219 - 248
Copyright
Copyright © Association for Symbolic Logic 2019 

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References

BIBLIOGRAPHY

Ashworth, E. J. (1974). Language and Logic in the Post-Medieval Period. Dordrecht: Reidel.CrossRefGoogle Scholar
Ashworth, E. J. (2016). The post-medieval period. In Dutilh Novaes, C. and Read, S., editors. The Cambridge Companion to Medieval Logic (first edition). Cambridge: Cambridge University Press, pp. 166–191.CrossRefGoogle Scholar
Ashworth, E. J. (2017). Buridan and his successors on “ex impossibili sequitur quodlibet”. In Grellard, C., editor. Miroir de l’amitié. Mélanges offerts à Joël Biard (first edition). Paris: Vrin, pp. 243–252.Google Scholar
Arriaga, R. de. (1639). Cursus philosophicus. Paris: Jacques Quesnel.Google Scholar
Báñez, D. (1599). Institutiones minoris dialecticae quas summulas vocant . Salamanca: Andreas Renaut.Google Scholar
Bernoulli, J. (1685). Paralellismus ratiocinii logici et algebraici . Basil: Johan Conrad a Mechel.Google Scholar
Bernoulli, J. (1744a). Centum positionum philosophicarum cento. In Bernoulli, J., editor. Opera (tom. 1). Geneva: Cramer, pp. 175–191.Google Scholar
Bernoulli, J. (1744b). Methodus ratiocinandi sive usus logicae in praeclaro aliquo phaenomeno physico enodando. In Bernoulli, J., editor. Opera (tom. 1). Geneva: Cramer, pp. 251–276.Google Scholar
Blaise of Parma. (1486). Questiones super tractatu De latitudinibus formarum. Padua: Mathaeus Cerdonis.Google Scholar
Broadie, A. (1985). The Circle of John Mair. Logic and Logicians in Pre-Reformation Scotland. Oxford: Oxford University Press.Google Scholar
Buridan, J. (1976). Tractatus de consequentiis. Louvain: Publications univertsitaires.Google Scholar
Capozzi, M. & Roncaglia, G. (2008). Logic and philosophy of logic from humanism to Kant. In Haaparanta, L., editor. The Development of Modern Logic (first edition). Oxford: Oxford University Press, pp. 78–158.Google Scholar
Comas del Brugar, M. (1661). Quaestiones minoris dialecticae. Barcelona: Antonius Lacavalleria.Google Scholar
Compton Carleton, T. (1649). Philosophia universa. Antwerpen: Jacob Meursius.Google Scholar
Dutilh Novaes, C. (2008). Logic in the 14th century after Ockham. In Gabay, D. M. and Woods, J., editors. Handbook of the History of Logic (first edition), Vol. 2, Mediaeval and Renaissance Logic. Amsterdam: Elsevier, pp. 433–504.Google Scholar
Euler, L. (1770). Lettres à une princesse d’Allemagne sur divers sujets de physique et de Philosophie (tom. 1). Mietau, Leipzig: Steidel.Google Scholar
Gentzen, G. (1935). Untersuchungen über das logische Schließen I. Mathematische Zeitschrift, 39, 176–210.CrossRefGoogle Scholar
Heider, D. (2014). Universals in Second Scholasticism. A comparative study with focus on the theories of Francisco Suárez, S. J. (1548–1617), João Poinsot, O. P. (1589–1644) and Bartolomeo Mastri da Meldola O. F. M. Conv. (1602–1673)/Bonaventura Belluto O. F. M. Conv. (1600–1676). Amsterdam: John Benjamins Publishing Company.CrossRefGoogle Scholar
Hilbert, D. (1923). Die logischen Grundlagen der Mathematik. Mathematische Annalen, 88(1–2), 151–165.CrossRefGoogle Scholar
Hurtado de Mendoza, P. (1619a). Disputationes in universam philosophiam a Summulis ad Metaphysicam pars prior. Mainz: typis et sumptibus Ioannis Albini.Google Scholar
Hurtado de Mendoza, P. (1619b). Disputationes in universam philosophiam a Summulis ad Metaphysicam pars posterior. Mainz: typis et sumptibus Ioannis Albini.Google Scholar
Hurtado de Mendoza, P. (1624). Universa philosophia. Lyon: Louis Prost.Google Scholar
Knebel, S. K. (2011). Suarezismus, Erkenntnistheoretisches aus dem Nachlass des Jesuitengenerals Tirso de Santalla, González. (1624–1705). Abhandlung und Edition. Amsterdam: B. R. Grüner.Google Scholar
Kvasz, L. (2008). Patterns of Change. Basel: Birkhäuser.CrossRefGoogle Scholar
Kvasz, L. (2013). Zrod vedy ako lingvistická udalost: Galileo, Descartes a Newton ako tvorcovia jazyka fyziky [The Scientific Revolution as a Linguistic Event. Galileo, Descartes, and Newton as Creators of the Language of Physics]. Praha: Filosofia.Google Scholar
Leibniz, G. W. (1903). De formae logicae comprobatione per linearum ductus. In Couturat, L., editor. Opuscules et fragments inédits de Leibniz. Extraits des manuscrits de la Bibliothèque royale de Hanovre (first edition). Paris: Presses Universitaires de France, pp. 292–321.Google Scholar
Leibniz, G. W. (1999). Generales inquisitiones de analysi notionum et veritatum. In Schepers, H., Schneider, M., Biller, G., Franke, U., and Kliege-Biller, H., editors. Sämtliche Schriften und Briefe. Sechste Reihe, Philosophische Schriften, Vierter Band (first edition). Berlin: Akademie Verlag, pp. 739–788.Google Scholar
Oresme, N. (2010). Questiones super Geometriam Euclidis. Stuttgart: Steiner.Google Scholar
d'Ors, A. (1998). Ex impossibili quodlibet sequitur (Domingo Báñez). Medioevo, 24, 177–217.Google Scholar
d'Ors, A. (1983). Las Summulae de Domingo de Soto. Anuario Filosófico, 16(1), 209–217.Google Scholar
Mugnai, M. (2010). Logic and mathematics in the seventeenth century. History and Philosophy of Logic, 31(4), 297–314.CrossRefGoogle Scholar
Oviedo, F. de (1640). Cursus philosophicus. Lyon: Pierre Prost.Google Scholar
Paul of Venice, , (1990). Logica Magna, Part II, Fascicule 4. Secunda Pars, Capitula de Conditionali et de Rationali. Oxford: Oxford University Press.Google Scholar
Poinsot, J.. (1638). Cursus philosophici Thomistici pars prima. Cologne: Constantini Münich Bibliopolae.Google Scholar
Read, S. (1993). Formal and material consequence, disjunctive syllogism and gamma. In Jacobi, K., editor. Argumentationstheorie: Scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgerns (first edition). Leiden: Brill, pp. 233–259.Google Scholar
Read, S. (2015). Medieval theories: Properties of terms. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy (Spring 2015 Edition). Available at: https://plato.stanford.edu/archives/spr2015/entries/medieval-terms/.Google Scholar
Risse, W. (1964/1970). Die Logik der Neuzeit, 2 vols. Stuttgart: Frommann.Google Scholar
Soto, D. De (1529). Summule. Burgis, : in officina Joannis Junte.Google Scholar
Soto, D. De. (1554). Summule. Salamanca: Andreas à Portonariis.Google Scholar
Weise, C. & Lange, J. C. (1712). Nucleus logicae Weisianae. Giessen: Henning Müller.Google Scholar