Handbook of the History of Logic: - Fordham University Faculty

1.7 Essentialist Assumptions
Medieval Modal Theories and Modal Logic 529
In his treatise On Hypothetical Syllogisms Boethius speaks about two kinds of
conditionals which express a necessary consequence between the antecedent and
the consequent. The consequence is accidentally necessary when the antecedent
and consequent are immutably true but have no internal link between them, for
example ‘If fire is hot, the heavens are spherical’. In a non-accidental consequence,
which Boethius calls natural, there is a conceptual connection between the parts;
for example, ‘If something is human, it is an animal’. Abelard also teaches that
a genuine conditional expresses a necessary consequence in which the antecedent
of itself requires the consequent. These were taken to express immutable laws of
nature derivable from the nature of things. 81 A related distinction between per se
and per accidens necessary propositions was employed in mid-thirteenth century
discussions of modal conversion and modal syllogistic. Robert Kilwardby states
that some necessary connections between terms are merely accidentally necessary
in the sense that the things signified are inseparable. These necessities are not
dealt with in modal syllogistic the necessity propositions of which express per se
necessities explained in Posterior Analytics I.4. The first type is said to occur
when the definition of the subject includes the predicate and the second type
when the definition of the predicate includes the subject. Typical per se necessary
propositions were those expressing the properties determined by the substantial
form of a subject or, as in the second class, other features based on the genusspecies
structure. Terms themselves were necessary if they stood necessarily for
what they signified, for example ‘horse’. Other terms were accidental, for example
‘white’ or ‘walking’. (See also 2.4 below.)
Necessary propositions which were not per se necessary were often exemplified
by propositions about inseparable accidents. In the Isagoge, Porphyry defines the
inseparable accident as something which cannot actually be removed from its subject
though the subject can be conceived of without it (3.5-6). The idea of the
degrees of necessity and impossibility was also developed in late ancient discussions
of indirect proofs and impossible hypotheses. In order to defend Aristotle’s
indirect proofs with impossible premises, Alexander of Aphrodisias argued that
Aristotle had in mind impossibilities which were not nonsensical. 82 Some late
ancient authors were interested in impossible hypotheses as tools for conceptual
which does not imply that future contingent statements are true or false. This was an exceptional
view. See C. Schabel, Theology at Paris, 1316-1345: Peter Auriol and the Problem of Divine
Foreknowledge and Future Contingents (Aldershot: Ashgate, 2001).
81 Boethius, De hypotheticis syllogismis, I.3.7; Abelard, Dialectica, 253.28-30; 279.12-14;
280,12-18; 283.37-284.17; see also Garland the Computist, Dialectica, 141.7-22. Some later
twelfth-century masters regarded the principle that the antecedent is not true without the consequent
as a sufficient condition for the truth of a conditional and accepted the so-called paradoxes
of implication. See C.J. Martin, ‘Logic’ in J. E. Brower and K. Guilfoy (eds.), The Cambridge
Companion to Abelard (Cambridge: Cambridge University Press, 2004), 164-5, 179-81.
82 See the report in Simplicius, In Aristotelis Physicorum libros quattuor posteriores commentaria,
ed. H. Diels, Commentaria in Aristotelem Graeca 10 (Berlin: Reimer, 1895), 1039.13-14,
26-7; translated by C. Hagen in Simplicius, On Aristotle’s Physics 7 (London: Duckworth, 1994),
105.