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Three Versions of Ockham's Reductionist Program1 ? Perhaps the best known feature of William of Ockham's philosophy is his denial of real universal entities in his ontology.2 But a second, equally important feature of it is his claim that there is no philosophical reason to postulate real entities at all in all ten of Aristotle's categories, but only in two, namely substance and quality.3 Although these claims are sometimes not clearly distinguished, they are in fact totally independent of one another. One might well reject real universal entities, for example, but hold that individual entities are needed in more categories than the ones Ockham allowed.4 Or, conversely, one might hold that some of the 1An earlier version of this paper was read as part of a symposium on Ockham 's ontological reductionism, held at the Twenty-Sixth International Congress on Medieval Studies, Kalamazoo, Michigan, in 1991. I am grateful to the participants in that symposium for their spirited comments and discussion. 2Ockham maintained this view throughout his entire career, and expressed it in many places in his writings. Perhaps the most exhaustive discussion is found in his Scriptum in librum primum Sententiarum: Ordinatio, d. 2, qq. 4-8, (Opera theologica, vol. 2; St. Bonaventure, N. Y.: The Franciscan Institute, 1970) 99-292, translated in Paul Vincent Spade, trans., Five Texts on the Mediaeval Problem of Universals: Porphyry, Boethius, Abelard, Duns Scotus, Ockham, (Indianapolis, Ind.: Hackett, 1994) 114-231. For a thorough discussion of this aspect of his doctrine, see Marilyn McCord Adams, William Ockham, 2 vols., (Notre Dame, Ind.: University of Notre Dame Press, 1987), Chs. 1-4, 3-141. Combined with the previous claim, this view has the consequence that the only entities philosophy demands are individual substances and their individual qualities. Ockham also grants that entities in the category of relation are sometimes required in certain contexts in the theology of the Trinity. But the need for such relational entities is purely a consequence of theological doctrine; unaided natural reason finds no such need. For a discussion of this second strand of Ockham's thought, see Adams, William Ockham, Chs. 5-9, 143-313. Throughout this paper, I shall tacitly omit these theological "special cases" for the sake of simplicity. Thus I shall speak of Ockham 's reduction of me categories to substance and quality alone — with the unexpressed understanding that certain dieological relations are also real. Ockham certainly did believe in and accept these "special cases." But their inclusion in my discussion would only complicate the presentation without affecting any substantive point I want to make. 4As, for example, John Buridan did. See Calvin G. Normore, "Buridan's Ontology," in James Bogen and James E. McGuire, ed., How Things Are: Studies in 347 Franciscan Studies, Vol. 56 (1998) 348Paul V. Spade Aristotelian categories can be eliminated in roughly the way Ockham indicated, but also maintain that universal entities, not just individual ones, are needed in some or all of the remaining, "real" categories.5 It is the second of these two features of Ockham's ontology, his rejection of real entities for most of Aristotle's list of ten categories, that is the focus of the present paper. For convenience, I shall refer to it as Ockham's "reductionist program." There is general agreement that Ockham did in fact have some such program, but there is much less agreement about how successful it was, or indeed about what exactly he was and was not claiming.6 II The ultimate success or failure of Ockham's reductionist program depends of course not only on what he actually said, but Predication and the History of Philosophy and Science, (Philosophical Studies Series in Philosophy; Dordrecht: D. Reidel, 1985) 189-203. Buridan admitted magnitude (in the category of quantity) as a real entity, whereas Ockham did not. For that matter, he also admitted the reality of motion, even though motion in not an Aristotelian category; Ockham did not allow its reality. 'Something like this was done by those realists who held that the three "absolute" categories (substance, quality, quantity) are real, whereas the other seven are not, or at least not in the same sense. As...


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