Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 555
According to Buridan and Pseudo-Scotus, the subject terms of all divided
modals are ampliated to stand for actual and possible beings which fall under
those terms. The phrase ‘what is’ (quod est) attached to subject terms restrict
them to standing for actual beings only. 182 Divided necessity modals with restricted
subject terms are not converted simply or accidentally, and the same
holds true of the conversions of divided necessity propositions with non-restricted
subject terms, with the exception that universal negative propositions are convertible
simply. 183 Unlike Buridan and Pseudo-Scotus, Ockham did not accept any
conversions of terms of divided necessity propositions. 184 In fact he did not treat
divided necessity propositions with unrestricted subject terms at all in his modal
logic. 185
As to unrestricted divided possibility propositions, Ockham, Buridan and Pseudo-
Scotus state that affirmative modals are converted in the same way as assertoric
propositions, those with restricted subject terms not being convertible. 186 According
to Buridan and Pseudo-Scotus, an unrestricted divided proposition de
contingenti ad utrumlibet can be converted into one of the opposite quality, but
no conversions of the terms are valid. 187 They treated these propositions as ampliated
with respect to possibility. Ockham states that if the subject terms are
ampliated with respect to contingency, unrestricted universal contingency propositions
convert into particular contingency propositions. 188
In discussing the logical properties of the unrestricted divided modal propositions,
Buridan and Pseudo-Scotus made some comments on the question whether
such propositions should be treated as categorical propositions with a disjunctive
subject (what is or can be ...), as they did, or whether they should be taken as
complex propositions. 189 Pseudo-Scotus claimed that they could be read as conjunctions
or disjunctions as follows: ‘Every A is-possibly(-not) B’ is a conjunction
of ‘Everything which is A is-possibly(-not) B’ and ‘Everything which can be A,
etc.’ and ‘Some A is-possibly(-not) B’ is the disjunction: ‘Something which is A
is-possibly(-not) B’ or ‘Something which can be A, etc.’ 190
It has been suggested that one could supply a Kripke-style possible worlds
semantics for Buridan’s modal system as an axiomatic basis for it. 191 I think
182 BC II.4, 58; II.6, 61, 63; IV.1, 111; Summulae de dialectica IV.6.2, 299; PS I.26, 312-13.
183 BC II.6.6, 67; PS I.26, 312-13.
184 OSL II.24, 329-30; III-1.21, 416.
185 See also Lagerlund 2000, 112-15.
186 OSL II.25, 331-2; III-1.24, 423-4; BC II.6.5, 66-7; PS I.26, 312.
187 BC II.6.7, 68; PS I.30, 320.
188 OSL II.27, 338; III-1.27-8, 430-33.
189 BC II.4, 58-60; PS I.26, 310-11.
190 Pseudo-Scotus’s remarks on the conversion of these readings are sketchy and problematic. It
is not clear why he thinks that possibility propositions would be convertible in the same was as
assertoric propositions, the simple conversion of universal negative included. Necessity propositions
are said to be non-convertible except when they are about the necessary characteristics of a
necessary being. The author does not mention that a conversion from universal negative to particular
negative necessity propositions would be acceptable in this approach. See also Lagerlund
2000, 172-6.
191 Hughes 1989.