Authors account for the semantic behavior of the various modes of personal supposition in different ways, in particular with a clear cleavage between thirteenth and fourteenth century approaches. In the thirteenth century, with Peter of Spain, William of Sherwood, and Lambert of Auxerre, there was a tendency toward defining the modes of personal supposition in terms of the verification of the proposition or the supposition of its terms:
• Supposition is determinate when the locution can be expounded by means ofsome single thing, which is the case when the word supposits for some single thing. (Sherwood, Introduction to Logic, §5.2.)
• Supposition is distributive when [the word] supposits for many in such a way as to supposit for any. (Sherwood, Introduction to Logic, §5.2.)
• A term has merely confused supposition in a categorical proposition when it can be taken there for several of its supposita, not necessarily for all. (For want of a satisfactory formulation of merely confused personal supposition in our authors, this is Parsons’ (1997:45) ‘‘generic’’version.)
By contrast, in the fourteenth century with Walter Burley, William of Ockham, and John Buridan, it became customary to define the modes of personal supposition in terms of ‘‘ascent and descent,’’ that is, in terms of the inferential relations that do or do not obtain between a proposition and the singular propositions falling under it, of the form ‘‘This a is b’’ (see Priest and Read 1977; Spade 1996:chap. 9).
Let (S) and (Q) stand for any syncategorematic terms, and the general form of a proposition P be ‘‘(Q) a is (S) b.’’ The generic definitions of the modes of personal supposition in terms of ascent and descent can be formulated as (see Ockham Summa logicae I, chap. 70; Buridan, Summulae de suppositionibus, chaps. 4.3.5 and 4.3.6.):
• A term a has determinate supposition in P ) A disjunction of propositions of the form ‘‘This a is (S) h” can be inferred from P but a conjunction of propositions of the form ‘‘This a is (S) h’’ cannot be inferred from P.
• A term a has confused and distributive supposition in P ) A conjunction of propositions of the form ‘‘This a is (S) h’’ can be inferred from P.
• A term a has merely confused supposition in P ) A proposition with a disjunctive term of the form ‘‘This a, or that a etc... is (S) h’’ can be inferred from P, but neither a disjunction nor a conjunction of propositions of the form ‘‘This a is (S) h’’ can be inferred from P.
The same applies mutatis mutandis to the predicate term. Notice that among the (A), (E), (I), and (O) propositional forms, merely confused supposition occurs only in predicate position (in (A) propositions). But more generally, it can also occur in subject position, such as in exceptive propositions of the form ‘‘Only a is b.’’
By applying the two groups of rules successively (first the syntactical rules and then the semantic rules), one obtains the desired result, that is, an account of the quantity of individuals involved in a given assertion, and thus of the semantics of quantifier expressions. For example, in ‘‘Every man is an animal,’’ ‘‘man’’ has confused and distributive supposition and ‘‘animal’’ has merely confused supposition, according to the syntactical rules for ‘‘every.’’ According to the semantic rules, this proposition asserts that ‘‘man’’ supposits for all of the individuals falling under it (men) and that ‘‘animal’’ supposits for several individuals, but not (necessarily) for all of those falling under it.
Terrence Parsons (1997) has made the compelling suggestion that the differences between the thirteenth and fourteenth century approaches can also be explained on the basis of the distinction between the study of the semantics of quantifier expressions taken individually versus the study of global quantificational effect in wider propositional contexts. Indeed, fourteenth century authors had a keen interest in the effect of nested quantifier expressions, such as the effect of a negation over an affirmative universal quantifier. Take ‘‘Not every man is an animal’’: according to the thirteenth century authors, ‘‘man’’ would have distributive and confused supposition, since it is preceded by ‘‘every.’’ But for fourteenth century authors, the negation preceding ‘‘every’’ would have the effect of suppressing its distributive effect, so that ‘‘man’’ would no longer have distributive and confused supposition but rather determinate supposition (see Karger 1993; Dutilh Novaes 2008). In sum, ‘‘[w]hat distinguishes the earlier theory from the later one is whether the mode of supposition of a term in a proposition is something that that term retains when its proposition is embedded in further contexts’’ (Parsons 1997:43).
World History
