Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 537
2.3 Modalities with Temporal Determinations
Avicenna and Abelard showed particular interest in alethic modalities with determinations.
Like Boethius, Abelard divided propositions with a dum -phrase (‘so
long as’) into two groups, depending on whether the determination was intrinsic
or extrinsic, i.e., whether it is the same as the modalized predicate or not. Both
of these can be understood in two ways. The word dum can be taken to indicate
time and to form a compound predicate. In this ‘modal’ reading the intrinsic
or extrinsic dum phrase is included as a restriction in what is predicated with a
modal qualification. Or they may be considered as complex propositions which
have as parts a modal proposition and a non-modal dum proposition and assert
that something is necessary or possible or impossible and things are as the dum
phrase says they are. 106 There were similar discussions in Avicenna. In the part
on logic of his Pointers and Reminders, Avicenna distinguishes between absolute
necessity propositions (like ‘God exists), which are always true and refer to eternal
things, and various conditional necessity propositions. These are true while the
non-eternal substances referred to by the subject terms exist (like ‘Man is necessarily
a rational body’), some descriptions are attached the substances (like ‘All
that is moving is necessarily changing’), what is predicated is actual or a definite
or indefinite time is actual. 107 Propositions which are necessary on the condition
that the subject is qualified by a description show similarities to Abelard’s de re
compound modal propositions.
Apart from the distinction between two basic readings Abelard’s remarks on
the propositions which contain a modal term and a dum phrase are not always
easily understood. If the temporal dum phrase is included in the modal proposition,
one may wonder how to understand the difference between simple modal
propositions and modal propositions with temporal determinants. Abelard states
that a determined possibility proposition implies a corresponding simple possibility
proposition, but not vice versa, and a simple necessity proposition implies a
determinate necessity proposition, but not vice versa. 108 These principles could be
derived from the standard idea that simple possibilities are temporally indefinite
and may be prevented from being actualized as temporally quanified, but Abelard
also refers to a distinction between treating the determination as pertaining to
a modal term and treating it as pertaining to the scope which is modalized. 109
106 Dialectica 206.14-37; Super Periermenias 36.22-37.23.
107 Avicenna, Pointers and Reminders, partone,Logic, trans. by S.C. Inati (under the title
Remarks and Admonitions, Toronto: Pontifical Institute of Mediaeval Studies, 1984), 92-4: see
also T. Street, ‘An Outline of Avicenna’s Syllogistic’, Archiv für Geschichte der Philosophie 84
(2002), 133-4; P. Thom, Medieval Modal Systems: Problems and Concepts, Ashgate Studies in
Medieval Philosophy (Aldershot: Ashgate, 2003), 67-8, 74-6. For temporal and modal concepts
in medieval Arabic logic, see also N. Rescher, Temporal Modalities in Arabic Logic, Foundations
of Language Supplementary Series 2 (Dordecht: Reidel, 1967).
108 Super Perihermenias 36.11-21.
109 Super Perihermenias 41.23-42.6. See also the discussion in R. Pinzani, The Logical Grammar
of Abelard, The New Synthese Historical Library 51 (Dordrecht: Kluwer Academic Publishers,
2003), 111-16.