Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 553
that the notion of possibility proper (Mp = -L-p) must be added to modal syllogistics
as the basic notion. Furthermore, it was considered imperative to distinguish
between modal premises in the compound (de dicto) and the divided (de re) senses
and to divide de re modals into two groups depending on whether the subject terms
refer to actual things or possible things. Aristotle’s modal syllogistics was regarded
as a fragmentary theory in which the distinctions between different types of fine
structure were not explicated.
The truth conditions of categorical propositions in the traditional square of opposition
were given in terms of supposition theory as follows: provided that no
semantic paradoxes are involved in the propositions, a universal affirmative proposition
is true iff the predicate term stands for everything for which the subject
term actually stands. A particular affirmative proposition is true iff the predicate
terms stands for some of those for which the subject term actually stands.
Negative propositions did not have existential import, and negatives with empty
subject-terms were considered true. Aristotelian assertoric conversion rules, viz.,
the simple conversions between universal negative propositions and affirmative
particular propositions and the so-called accidental conversion from affirmative
universal proposition to particular affirmative proposition are valid in this interpretation.
174 These rules were in agreement with the identity theory of predication
which was also employed by Campsall. 175
As far as these authors treated propositions as tensed, the above remarks were
taken to pertain to propositions the copulas of which were understood as present
tense verbs. Since the twelfth century, there had been various attempts to define
the truth conditions of past and future tense propositions. This discussion continues
in early fourteenth-century logic. According to Buridan, the supposition of
the subject term of the past tense proposition ‘A was B’ is ampliated so that it
stands for past and present As while the predicate term stands for past Bs; ‘A
was B’ isreadas‘WhatwasorisA was B’. Similarly, in ‘A will be B’ the supposition
of the subject term is ampliated so that it stands for present and future
As. It is read as ‘What is or will be A will be B’. The restrictive phrase ‘which is’
(quod est) prevented ampliation when it was added to the subject term. 176 Some
early thirteenth-century logicians applied the theory of ampliation to possibility
propositions so that their subject terms associated with the verb ‘can’ were taken
to stand for actual and merely possible beings, which is how the subjects in divided
possibility propositions without the restriction (quod est) were understood
by Ockham, Buridan and Pseudo-Scotus. 177 Following the traditional doctrine
of the matter of propositions, fourteenth-century logicians stated that assertoric
174OSL II.2-4, 249-66; II.21, 318-21; BC I.5, 25-6; I.8, 44-5; PS I.12-15, 290-96.
175See Lagerlund 2000, 86.
176See BC I.6, 26-30; I.8.14, 45-7; Summulae de Dialectica IV.6.2, 299-300; cf. OSL II.7, 269-
72; II.22, 321-5; PS I.17, 297-9. In question 11 of his treatise on the Prior Analytics, Campsall
discussed syllogisms with tensed premises, and this syllogistic tense logic was developed further
in Ockham’s Summa logicae III-1.17-19, 406-11.
177OSL I.72, 216; II.25, 331-2; BC I.6, 27; PS I.3, 277; I.26, 311. See also Lagerlund 2000,
108-12, 138-40, 171-6.