On Ockham's Supposition Theory and Karger's Rule of Inference

ON OCKHAM'S SUPPOSITION THEORY AND KARGER'S RULE OF INFERENCE I. INTRODUCTION Since 1952, there has been a considerable amount of discussion of William of Ockham's theory of the modes of common personal supposition (hereafter, following Elizabeth Karger, "TM"). The main interpretative question regarding TM has been the question, What is Ockham up to in presenting TM? Until fairly recently, an expanding body of literature on the subject has been closing in on one particular way of answering this question.1 The answer that has been gaining acceptance is this: Ockham's purpose in presenting TM is to provide a theory of quantification. The main claims of this (until recently) widely accepted interpretation of Ockham (which interpretation I will call "The Quantification Theory Interpretation of TM," or "QTI") are the following. 1 See, for example, Marilyn McCord Adams, "What Does Ockham Mean by 'Supposition'?" Notre Dame Journal of Symbolic Logic 17 (1976): 375-91; Philotheus Boehner, Medieval Logic (Manchester: University of Manchester Press, 1952); Michael J. Fitzgerald, "Ockham's Implicit Priority of Analysis Rule?" Franciscan Studies 38 (1973): 213-19; Alfred J. Freddoso, "Ockham's Theory of Truth Conditions," essay contained in William Ockham, Summa logicae, Part II, trans. Alfred Freddoso and Henry Schuurman (Notre Dame: University of Notre Dame Press, 1980) (hereafter, "Ockham, SL II"); Michael J. Loux, "Ockham on Generality," essay contained in William Ockham, Summa logicae, Part I, trans. Michael J. Loux (Notre Dame: University of Notre Dame Press, 1974) (hereafter , "Ockham, SL I"); Gareth B. Matthews, "Ockham's Supposition Theory and Modern Logic," Philosophical Review 73 (1964): 91-9; Ernest A. Moody, Truth and Consequence in Medieval Logic (Amsterdam: North-Holland Publishing Co., 1980); Graham Priest and Stephen Read, "The Formalization of Ockham's Theory of Supposition," Mind 86 (1977): 109-13; Graham Priest and Stephen Read, "Merely Confused Supposition," Franciscan Studies 40 (1980) : 265-97; Paul Vincent Spade, "Priority of Analysis and the Predicates of ?'-form Sentences ," Franciscan Studies 36 (1976): 263-70; and Robert G. Turnbull, "Ockham's Nominalistic Logic: Some Twentieth Century Reflections," The New Scholasticism 36 (1962): 313-29. Ockham's Supposition Theory and Karger's Rule41 QTI: TM is meant to be a general analysis of quantified statements that provides, for each quantified statement, q, a "descent to particulars," i.e., a materially equivalent expansion to a statement , p, about individual things such that (i) ? contains no general terms, and (ii) ? has the same truth—conditions as q. Thus, for example, Ockham tells us that we can descend from the quantified statement 'Some man is an animal' to the following statement about individual things: 'This man is an animal, or that man is an animal, or...'. Similarly, he suggests that we can descend from the quantified statement 'Every man is an animal' to the conjunctive statement 'This man is an animal and that man is an animal and...'. There are, however, some problems facing QTI. These have been recognized and developed in the last fifteen years by several commentators.2 The difficulties are summarized by Gareth Matthews in roughly the following way:3 (1)When he discusses various descents to particulars from statements with general terms, Ockham never explicity claims that the statements about individual things to which he descends are equivalent to the statements from which they are derived.4 (2)Not all of the descents Ockham offers are in fact to equivalent statements; his descents under classic O-form statements are to particular statements that are clearly weaker than the general statements from which they are derived.5 (3)In Part II of his Summa logicae Ockham explicitly does provide truth-conditions for general statements—i.e., he gives a theory of quantification—and he does so without reference to TM; but he never there mentions that he is repeating a job that the has already taken care of, in a different manner, in an earlier work.6 2 Marilyn McCord Adams, William Ockham, vol. I (Notre Dame: University of Notre Dame Press, 1987); Elizabeth Karger, "Modes of Personal Supposition: The Purpose and Usefulness of the Doctrine Within Ockham's Logic," Franciscan Studies 44 (1984): 87-106; Gareth B. Matthews, "Supposttio and Quantification in Ockham," Nous 7...