1 I make some comments about the second question in Parsons, Terence ‘Supposition as Quantification or as Global Quantificational Effect?’ Topoi 16 (1997) 41–63.CrossRefGoogle Scholar

2 Spade, Paul Vincent ‘The Logic of the Categorical: The Medieval Theory of Descent and Ascent,’ in Kretzmann, Norman ed., Meaning and Inference in Medieval Philosophy (Dordrecht: Kluwer 1988), 187–224CrossRefGoogle Scholar

3 There are English translations of Peter in Dinneen, Francis P.Peter of Spain: Language in Dispute (Amsterdam/Philadelphia: John Benjamins Publishing Company 1990)CrossRefGoogle Scholar, and Mullally, Joseph P.The Summae Logicales of Peter of Spain (Notre Dame: University of Notre Dame Press 1945)Google Scholar; of Sherwood in Kretzmann, NormanWilliam of Sherwood's Introduction to Logic (Minneapolis: University of Minnesota Press 1966)Google Scholar and William of Sherwood's Treatise on Syncategorematic Words (Minneapolis: University of Minnesota Press 1968); of Lambert in Kretzmann, Norman and Stump, EleonoreThe Cambridge Translations of Medieval Philosophical Text, vol. 1 (Cambridge: Cambridge University Press 1988)Google Scholar; and of a typical anonymous writer in Barney, SteveLewis, WendyNormore, Calvin and Parsons, Terence (trans.), ‘On the Properties of Discourse,’ Topoi 16 (1997) 77–93.CrossRefGoogle Scholar

4 There are English translations of Burley in Spade, Paul Vincent ‘Walter Burley, From the Beginning of his Treatise on the Kinds of Supposition (De Suppositionibus),’ Topoi 16 (1997) 95–102CrossRefGoogle Scholar, and Walter Burley: On the Purity of the Art of Logic, the Shorter and the Longer Treatises (New Haven: Yale University Press, forthcoming), of Ockham in Alfred J. Freddoso and Schuurman (trans.), Ockham, WilliamSumma Logicae, Part II (Notre Dame: University of Notre Dame Press 1980)Google Scholar, and Loux, Michael J.Ockham's Theory of Terms: Part I of the Summa Logicae (Notre Dame: University of Notre Dame Press 1974)Google Scholar, and of Buridan in King, PeterJean Buridan's Logic: The Treatise on Supposition, The Treatise on Consequences (Dordrecht: D. Reidel 1985)Google Scholar.

5 See §§70-74 of Loux, Ockham's Theory of Terms.

6 Sometimes other adjustments are required. For example, an instance of ‘No dingo is spotted’ will be ‘this dingo is not spotted,’ not ‘this dingo is spotted.’

7 This is the claim that every dingo is this particular mammal, not the claim that every dingo is a mammal of this kind.

8 Principally, Boehner, PhilotheusMedieval Logic (Manchester: Manchester University Press 1959)Google Scholar, and Moody, ErnestThe Logic of William of Ockham (New York: Russell and Russell 1955 [reissued 1965])Google Scholar.

9 E.g. in Matthews, Gareth B. ‘Ockham's Supposition Theory and Modem Logic,’ Philosophical Review 73 (1964) 91–99CrossRefGoogle Scholar; ‘Suppositio and Quantification in Ockham,’ Noûs 7 (1973) 13-24; and ‘A Note on Ockham's Theory of the Modes of Common Personal Supposition,’ Franciscan Studies 44 (1984) 81-86.

10 ‘Dingo’ is distributed in ‘Some predator is not a dingo,’ but that proposition may not be inferred from ‘Some predator is not this dingo, and some predator is not that dingo, and …, and so on for all the dingos.’

11 The process of forming prenex normal forms is well-known; cf. Boolos, George and Jeffrey, RichardComputability and Logic (Cambridge: Cambridge University Press 1974), 112–113Google Scholar. The fact that the formation of a prenex normal form can be viewed as the movement of quantifiers to the front of the formula depends on the fact that the steps do not introduce new quantifiers or lose old ones. Such steps are available when the connectives in the formula are negation, conjunction, disjunction, and the material conditional. This is not so if the formula contains biconditional signs (see ibid, page 113); fortunately, medieval theorists did not employ unitary biconditional signs. It is clear from their practice that they would have seen a proposition of the syntactic form ‘A if and only if B’ as consisting of a conjunction of’ A if B’ and’ A only if B: neither of which contains a biconditional.

12 I have done that in work in draft form; I am relying on it here.

13 Parsons, ‘Supposition’

14 If you separate the restricted quantifier from its restriction, you can move the quantifier alone:

15 Kretzmann, William of Sherwood's Treatise on Syncategorematic Words, 35–36Google Scholar. Sherwood's sentence is ‘Every human who sees every human is running'; I have changed the first ‘human’ to ‘thing’ to avoid the complication of the same term being used twice; this is not essential to the point Sherwood is illustrating.

16 I assert this without proof; the reader is invited to try to find an equivalent normal form. The original sentence is a universal affirmative, and requires for its truth that there be a thing that sees every human; this aspect of it will be lost in most prenex forms. (If you decide to ignore this medieval doctrine about universal affirmatives and instead hold that universal affirmatives with empty subject terms are vacuously true, then the vacuous truth of the original sentence when there is no thing that sees every human is lost in most prenex forms.)

17 It might appear that this is a peculiar result, dependent on a special view about existential import of subject terms. But the same result follows if we take the modem view that universal affirmatives are vacuously true when their subject terms are empty. For on that view the original proposition is true if nothing sees every human; thus the descent condition for determinate supposition fails: the original proposition does not entail that ‘Every thing that sees this human is running’ for some particular case of ‘this human’. (Just imagine that each thing sees some human, but nothing sees every human, and nothing is running.)

18 I rely here on Read, Stephen ‘Thomas Cleves and Collective Supposition,’ Vivarium 29 (1991) 50–84CrossRefGoogle Scholar.

19 Spade, ‘The Logic of the Categorical’

20 Rijk, L.M. DeLogica Modernorum, vol. II part 2 (Assen, The Netherlands: Koninklijke Van Gorcum & Company N.V. 1967), 615Google Scholar

21 Kretzmann, William of Sherwood's Treatise on Syncategorematic Words, 35-6Google Scholar

22 King, Jean Buridan's Logic, 141Google Scholar

23 Perreiah, AlanLogica Parva: Translation of the 1472 Edition (München: Philosophia Verlag 1984), 152-53Google Scholar

24 He says, “…‘man’ is properly distributed here, since part of the sentence is ‘which is not a man.’ Even though this is not a sentence (since it is part of a sentence) it nevertheless has a likeness to a sentence with respect to the distribution and supposition of the terms; such terms supposit and appellate in an expression which is part of a sentence and which taken of itself is a sentence as they would in a sentence taken per se.” King, Jean Buridan's Logic, 138.Google Scholar

25 Geach, PeterReference and Generality (Ithaca, New York: Cornell University Press 1962)Google Scholar

26 If you want to make a conjoint something-or-other, you need to make a conjoint negative predicate in the twentieth century meaning of ‘predicate': ‘Every[ thing] not seeing this dingo and not seeing that dingo and … runs.’ But this is not the test; the test is descent to a conjoint term.

27 Read, ‘Thomas Cleves and Collective Supposition’

28 This requires a slight refinement of the theory concerning how to treat repeated terms; you have to test for supposition on the assumption that repeated terms are logically independent of one another. This fine tuning adjustment must be made both in the formal account for global quantificational effect, and in the theory couched in terms of ascent and descent.

29 This is subject to the grammatical idiosyncrasies of individual languages; sometimes in ordinary language it is not clear whether such descent is possible, or exactly how it is to be formulated.

30 King, Jean Buridan's Logic, 130Google Scholar. Buridan adds to the definition that “perhaps a sentence with a disjunctive extreme follows,” but he makes clear in other discussion that the ‘perhaps’ means that some terms with merely confused supposition satisfy this and some do not. So it is not a requirement. (See discussion below.)

31 King, Jean Buridan's Logic, 145Google Scholar

32 This descent and ascent condition means descent to and ascent from the whole conjunction of instances, not just to/from a single instance. This is the condition used by Paul of Venice; see Perreiah, AlanLogica Magna (Tractatus de Suppositionibus) (St. Bonaventure, NY: The Franciscan Institute 1971)Google Scholar.

33 In his Logica Magna, translated in Perreiah, 89-121. This account differs from that in the Logica Parva, translated in Perreiah.