Franciscan Studies

WILLIAM OF OCKHAM AND SUPPOSITIO PERSONALIS Many have suggested that Ockham's theory of suppositio is in some sense an anticipation of contemporary quantification theory; usuaUy this is quaüfied by the suggestion that Ockham quantifies over terms or quaUties rather than individuals.1 There is also some discussion as to whether the theory is semantical or syntactical in character.2 Both these matters are, I think, tied together. If we must force a later distinction on Ockham: what he did was to develop roughly the same semantical theory which was later used to interpret contemporary quantification theory. He did so, however, in order to interpret the simple categoricals which have a quite different syntax. If this is right it means that Ockham developed a semantics which was not weU-reflected in the syntax of the categoricals which he wished to interpret. This is presumably why the theory withered in the renaissance save for the use of distribution as a syntactical device for formulating the syUogistic rules and why it waited upon the development of quantification theory for its independent rediscovery. So viewed the development, discard, and rediscovery, of suppositio personalis becomes an intriguing episode in the history of logic and, as we wiU see, the appearance of Ockham's third Summa, the Elementarium, was potentiaUy a pivotal point in that history. In order to give a clear account of these matters I wiU first give in contemporary materials a theory which would serve Ockham's purposes. What this amounts to is the presentation of a semantical interpretation for quantification over sorted individuals which emphasizes those features which are relevant to Ockham's account.3 I will then present a rough outUne of Ockham's theory as it appears in the first Summa 1 Cf., e.g., Philotheus Boehner, Medieval Logic, Manchester, 1952, and Gareth Mathews, "Ockham's suppositio theory and modern logic," Phil. Rev. 73 (1964), 91—99· 2 Cf., e.g., Ernest A. Moody, Truth and consequences in mediaeval logic, Amsterdam, 1953, and Manley Thompson, "Logic, philosophy, and history," Rev. Meta. 8 (i954~55), 9i—973 The relevance of such a system to Aristotelian logics was established by Timothy Smiley in "Syllogism and quantification," J.S.L 27 (1962), 58—72. 132ROBERT PRICE in order to stress the paraUels between it and the previously presented theory. I wiU then turn to a discussion of historical developments along the lines already indicated. I Suppose that we possess a semantics and epistemology which we deem adequate to the task of specifying the truth conditions of simple identities and of negations of identities (hereafter "negentities") such as 's = p' and 's F ?' where 's' and '?' denote individuals. Suppose further that we suspect that treatments of the traditional simple categoricals involving 'aU' and 'some' which take classes or properties or quaüties as fundamental are at best obscure. We might then attempt to treat the simple categoricals in such a way that their truth conditions wiU be dependent upon the truth conditions of certain identities and negentities. I take this to be Ockham's situation ; and his problem, then, to be one of reducing statements about the truth conditions of simple categoricals to statements about the truth conditions of identities and negentities. The key to his solution is of course the recognition that classes are (at least sometimes) classes of individuals. To present it we, therefore, require Usts of individual terms corresponding to such class terms as may be of interest. Accordingly if 'S' is an (apparent) class term, 's', 's1', 's2', . . . are individual terms denoting members of that class; if 'P' is a class term, 'p', 'p1', 'p2', . . . are individual terms denoting members of that class, and so forth as needed. Note that: i) no individual terms fail to denote an individual and so no classes are empty; 2) individual terms drawn from the same or different Usts may denote the same individual; 3) no individual term is to appear on more than one list; where 'M' stands for the class of men and 'M8' for the class of men excepting Sortes different individual terms wiU be used; 4) all Usts are to be long enough; I will in fact assume...