Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 543
if something contained under the predicate term is unchangeable with
respect to something contained under the subject term, as long as this
exists. This holds when the terms are common. When the terms are
singular, it is required that what is signified by one is not changeable
with respect to what is signified by the other, as long as this exists. 130
Unchangeable features signified by common terms may be transcendental properties,
such as ‘something’, substantial forms, properties based on the species nature
of things, such as ‘mortal’, ‘living’, or other inseparable attributes. 131 Divided
affirmative necessity propositions with common or singular terms express that
things under a necessarily predicated term are in various ways the same as actual
things under a subject term, as long as both exist. 132 Campsall believes that
this reading of divided necessity propositions explains why they are regulated by
the Aristotelian rules of conversion. The strict restriction to actual things is not
separately explained since Campsall probably thought that Aristotelian necessity
premises should be treated in this way and that only actual things can have necessary
properties. Much attention is paid to the example ‘A pale Socrates is necessarily
Socrates’. This is said to be false for the reason that what the accidental
subject term signifies is not an invariable characterization of Socrates. 133 Campsall
does not deal with the traditional universal or particular counter-examples,
thinking that they can be analysed into the conjunctions or disjunctions of singular
propositions with terms standing for accidental combinations.
The equation of necessity with unchanging relations pushes Campsall’s theory
toward the temporal frequency approaches of necessity. It is also characterized by
some versions of the principles that the present is necessary and that possibility
implies actuality. Let us take a look at his proofs of the conversion of divided
necessity propositions. According to Campsall, ‘Every/some B is necessarily A’
is converted into ‘some A is necessarily B’, because the negation of the converted
proposition ‘Every A is possibly not B’ is not compatible with the proposition to
be converted. This is allegedly shown by the fact that were the negation true, a
particular being, say c, whichisB and necessarily A wouldbepossiblynotB.
This is said to be impossible, apparently because c is necessarily B qua being
unchangingly A. 134 Campsall’s proof of the convertibility of universal negative
divided necessity proposition is similar — this time he states that ‘this consequence
is necessary: c can be one of those which are now contained under B; therefore it
130 6.25 (122-3).
131 5.43-5 (112-3); 9.18 (157).
132 For the actuality condition, see 5.40 (111); divided negative propositions express that the
things under the terms are necessarily separated (5.38 (110)).
133 6.25-31 (122-5).
134 6.22 (121-2). According to Lagerlund, Campsall assumes that if c is possibly not B now, it
is not B now (2001, 68). Campsall explicitly denies this principle later (19.21 (297)) and the
argument can be understood as indicated above. Campsall maintains, however, that if c is not
B now, it is necessarily not B now (5.50 (114)). If all negative propositions about actual things
are necessary, it is clear that there are no simultaneous de re alternatives. In this sense actuality
implies necessity. It seems that Campsall was not fully aware of the problems embedded in his
formulations.