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chaptEr 7 Four dEGrEEs oF abstraction i The doctrine of three degrees of abstraction is a venerable Scholastic commonplace . Related to Aristotle’s division of theoretical sciences,1 briefly it states that physics, mathematics, and metaphysics are distinguished one from another on the basis of the abstraction of their objects from matter. Physics has as its object mobile being, which abstracts from individual matter. The object of mathematics is quantified being, which abstracts from common sensible matter but not from intelligible matter. And metaphysics has as its object common being, or being insofar as it is being, which abstracts from all matter.2 Mutatis mutandis, many modern Scholastic authors have adopted the three degrees of abstraction doctrine.3 Especially known was Jacques Maritain who called * This essay was originally published as “Silvester Mauro, S.J. (1619-1687) on Four Degrees of Abstraction,” International Philosophical Quarterly 36 (1996): 461-74. 1 For this, see esp. Metaphysics 6.1.1025b18-1026a23 and 11.7.1064a15-b3. 2 For a summary of the three degrees doctrine, see C. Giacon, “Astrazione: Distinzioni scolastiche,” Enciclopedia filosofica (Firenze: G.C. Sansoni, 1967), vol. 1, col. 545; and Ludger Oeing-Hanhoff, “Abstraktionsgrade,” Historisches Wörterbuch der Philosophie (Basel-Stuttgart: Schwabe, 1971), vol. 1, col. 65. 3 Cf. for examples: John Joseph Urráburu, S.J., Institutiones philosophicae, vol. I Logica (Vallisoleti: Typis Viduae et Filiorum a Cuesta, 1890), 1016-19; Thomas Maria Cardinal Zigliara, Summa philosophica (Lugduni: Delhomme et Briguet, 1894), I (Logica et Ontologia ), 298 and 302; Sebastian Reinstadler, Elementa philosophiae scholasticae (Friburgi Brisgoviae: Sumptibus Herder, 1901), I, 14-15; J.S. Hickey, O. Cist., Summula philosophiae scholasticae, I, Logica et Ontologia, ed. sexta (Dublini: Apud M.H. Gill et Filium, 1923), 134-35; Pedro Descoqs, S.J., Institutiones metaphysicae generalis: Éléments d’ontologie, I (Paris: Beauchesne, 1925), 23-24; J. Maréchal, S.J., Le Point de départ de la métaphysique (Louvain-Paris: Charles Beyaert-Librairie Félix Alcan, 1926), cahier 5, 185-201; Carolus Boyer, S.J., Cursus philosophiae, ed. altera (Buenos Aires: Desclée de Brouwer, 1939), I, 27879 ; R.P. Phillips, Modern Thomistic Philosophy, 3rd impression (London: Burns Oates & Washbourne, 1941), II, 140-41; Joseph Gredt, O.S.B., Elementa philosophiae aristotelicothomisticae , ed. nona (Barcelona: Editorial Herder, 1951), I, 187-89; Ioannes di Napoli, Manuale philosophiae ad usum seminariorum (Italiae [Taurini]: Marietti, 1955) I, 32-33, n. 19; II, 352-53, n. 286; Régis Jolivet, Traité de philosophie: III Métaphysique, 5e édition (Lyon-Paris: Emmanuel Vitte, 1955), 20-21; Maurice De Wulf, An Introduction to Scholastic Philosophy, Medieval and Modern [Scholasticism Old and New], tr. P. Coffey (NY: Dover Publications, 1956), 82-83, and Jacobus M. Ramirez, O.P., De ipsa philosophia in universum (Madrid: Instituto de Filosofía “Luis Vives,” 1970), I, esp. 169-73. * 168 ChAptEr 7 it “the guiding thread” for his most important work.4 As sources for the doctrine, in addition to St. Thomas Aquinas,5 Maritain relied upon Cajetan and John of St. Thomas. Cajetan (Thomas del Vio [1469-1534]), first distinguished total from formal abstraction.6 Total abstraction, by which we pass from singulars to the universal intelligibilities they instance, was common to all sciences.7 In contrast, Cajetan enumerated three different degrees of formal abstraction from matter, based on which the theoretical sciences of physics, mathematics, and metaphysics were divided one from another.8 John of St. Thomas (John Poinsot [1589-1644]), has essentially the same doctrine as Cajetan.9 Although on its surface the common doctrine of Cajetan and John differs from that of St. Thomas, in Maritain’s opinion this was a difference of expression rather than of substance.10 Maritain made it clear that though he accepted the three degrees of abstraction theory, he did not regard these degrees as simply involving wider extension up the same line.11 This thought is prominent among other Thomists, who have 4 Distinguish to Unite or The Degrees of Knowledge, tr. from 4th French edition, G.B. Phelan (New York: Charles Scriber’s Sons, 1959), 35; cf. Distinguer pour unir ou les degrés du savoir, 5ème édition (Paris: Desclée de Brouwer, 1948), 71. For other places where the doctrine appears in Maritain’s work, see, e.g., An Introduction to Philosophy, tr. E.I. Watkin (NY: Sheed and Ward, 1937), 152 and 164, n. 1; A Preface to Metaphysics: Seven Lectures on Being (NY: New American Library [Mentor Omega], 1962), 79-85; Existence and the Existent...

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