Handbook of the History of Logic: - Fordham University Faculty

18 John Marenbon
inherited, trying to think about the meaning of these Stoic-derived formulas, but
within the context of his own term-logic.
The strange character of Boethius’s hypothetical syllogistic comes out even more
clearly when he treats the negation of a conditional in On Hypothetical Syllogisms.
Not realizing that his discussions should be construed as term logic, earlier commentators
[Dürr, 1951; Kneale and Kneale, 1975, 191; Barnes, 1981, 83; cf. Martin,
1991, 295-6] argued that Boethius thought the contradictory negation of ‘If p, then
q’ is‘Ifp, then not-q’, rather than ‘Not (If p, then q)’ as in classical propositional
calculus. Therefore, they concluded, he had a strange propositional system. But,
as Martin puts it [1991, 279]: ‘The problem is not . . . that Boethius’ logic is not
classical propositional calculus but rather it is not propositional at all.’ Boethius
is in fact both much less strange in his underlying conception than he has been seen
to be, and yet at the same time more distant from contemporary logical models.
Boethius’s account of the state of affairs that must be the case for a conditional to
be ‘negated’ or ‘destroyed’ is exactly the same as the contemporary logician’s account
of what obtains when a whole conditional is negated, but Boethius can only
offer his explanation, however tortuously, using term logic. For the conditional ‘If
A is, B is’ to be destroyed, we must show ‘not that A is not or B is not, but that,
when A is posited, it does not immediately follow that B is, but that A can be
even if the term B is not’ (I.9.7). And even in his extended discussion of the valid
forms of hypothetical syllogisms, Boethius seems, whilst always working in term
logic, to be mimicking the results which would obtain in a propositional calculus,
often employing various extra premisses that allow him to reach the results which,
by means of examples, he has identified as the correct ones (cf. [Marenbon, 2003,
53-55, 191]).
Boethius and Topical Argument ([Green-Pedersen, 1984, 37-81])
The remaining logical monograph by Boethius, On Topical differentiae (De topicis
differentiis) (TD) [Boethius, 1990, 1-92; trsl. Boethius, 1978; Boethius, 1891,
1173-1216] was written near the end of his life (c. 522-3), at a time when topical
argument became a central concern for him. Shortly before, he had written a
commentary on Cicero’s Topics (TC) [Boethius, 1833; transl. Boethius, 1988]
that is closely related to it, translated Aristotle’s Topics into Latin, and probably
written a commentary on it, now lost.
Much as in the case of hypothetical syllogistic, Boethius’ work is the only substantial
survival from the late ancient tradition of topical argument as it had
developed after the time of Cicero. One of its principle exponents had been the
fourth-century Peripatetic philosopher, Themistius. He and Cicero are Boethius’s
special authorities, and one of the main aims of TD is to compare the apparently
different lists of topical differentiae given by these two philosophers, showing that
they really coincide.
In the way it is structured around a list of topical differentiae, the topical theory
Boethius presents clearly descends from Cicero, though Cicero had just called them
‘topics’. Discussion of the topics is no longer, however, the mixture of law and