Gerardus Odonis O.F.M. on the Principle of Non-Contradiction and the Proper Nature of Demonstration

GERARDUS ODONIS O.F.M. ON THE PRINCIPLE OF NON-CONTRADICTION AND THE PROPER NATURE OF DEMONSTRATION 1. INTRODUCTION One of the most original works by the Franciscan Master Gerardus Odonis (Guiralt Ot) is the third part of his Lógica, De principiis scientiarum} This treatise is not just a commentary on Aristotle's Posterior Analytics, nor is it a specialized treatment of its subject matter, which is demonstrative (or rather epistemonicla) knowledge, as is found in Ockham's Sum of Logic.2 Rather, Odonis took his treatise to be a supplement to the Aristotelian work, where the demonstrative principles proper to the different 'sciences' (principia propria) as well as those they all have in common (principia communia) are extensively discussed by Aristotle, but less attention is paid to the most common principles of the intellect (principia communissima intellectus), such as the twofold principle of noncontradiction .3 What Odonis means to do, then, is to discuss the 'For Odonis' philosophical works see L. M. de Rijk, "Works by Gerald Ot (Gerardus Odonis) on Logic, Metaphysics and Natural Philosophy rediscovered in Madrid, BtU. Nac. 4229," Archives d'histoire doctrinale et littéraire du moyen âge 60 (1993); 173-93; on the manuscripts of De principiis scientiarum see ibid., 178-179. In this paper I use ms Madrid, Bihl. Nac. 4229, ff. 45ra-69va (henceforth M), sometimes corrected after Madrid, BiU. Universitaria, cod. 105, ff. lra-14ra. The present author has finished a critical edition of Odonis' Lógica , including its Liber tertius, De principiis scientiarum, which in the colophon of ms Madrid, Univ. 105 (f. 14ra) is indicated more precisely: "Explicit tractatus de duobus communissimis scientiarum principiis editus a fratre G. Odonis de ordine fratrum minorum"). la For this label, see W. Guthrie, A History of Greek Philosophy V. (Cambridge University Press, 1981), 171. 2For Ockham's adaptation of the Posterior Analytics doctrine see L. M. de Rijk, "Ockham as the Commentator of His Aristotle: His Treatment of Posterior Analytics," in Aristotélica et Lulliana: magistro doctissimo Charles Lohr septuagesimum annum féliciter agenti dedicata, ed. F. Domínguez, R. Imbach, Th. Pindl, et P. Walter (The Hague: Nijhoff, 1995), esp. 109ff. 3"Principia quidem scientiarum et demonstrationum per genus trimode dividuntur. Ex eis namque sunt aliqua omni philosophie, omni scientie et omni demonstrationi communia, que recte dicuntur principia communissima et communissime animi conceptiones et dignitates simpliciter prime. Hec autem sunt 51 Franciscan Studies (54) 1994-1997 52L. M. DE RIJK well-known seven requirements concerning the proper and the common principles insofar as they apply to the principle of noncontradiction (henceforth PNC): Hiis autem omnibus principiis tarn propriis quam communibus quam communissimis attribuuntur indifferenter septem conditiones, ut patet primo Posteriorum. Quoniam, ut ibi traditur, quecumque principia demonstrationum dicentium [differentium M] propter quid sunt vera, sunt necessaria, sunt propria, sunt immediata, sunt priora conclusionibus, sunt notiora conclusionibus, sunt causa conclusionum. Hec autem omnia plene sunt determinata primo Posteriorum de principiis propriam per naturam diffinitionis et quod quid est, et satis de principiis communibus, licet non eque plene de principiis communissimis intellectus. Cuius ratio est quia termini eorum sunt universalissimi et ideo a sensu remotissimi et, per consequens, ad exponendum difficillimi. (M 45rb) Accordingly, the author has divided his treatise into ten chapters, the first of which deals with the subject matter of PNC and its constituents or terms.4 This chapter presents first ten basic assumptions (suppositiones), next twelve theses (con-clusiones) together with the discussion of a number of notable statements (notabilia) and corollaries, and finally the refutation of objections (dubia). duo principia contradictionem complectentia "De quolibet esse vel non-esse" et "de nullo simul esse et non-esse". (M 45ra) Odonis nearly always speaks of two principles. In fact, medieval logicians added to the famous ontological principle found in Aristotle (Metaph. W 3, 1005bl9-20: "The same attribute cannot at the same time belong and not-belong to the same subject.") logical disjunction "of anything whatsoever either it is or is-not"; see e.g. John Buridan, In Metaphysken Aristotelis Quaestiones argutissimae Magistri Joannis Buridani in ultima praelectione ab ipso recognitae ... [etc.] (Parisiis, 1518; Frankfurt a.M.: Minerva, 1964), IV, q. 13. It does not come as a surprise...