Handbook of the History of Logic: - Fordham University Faculty

4 John Marenbon
using numbers as propositional variables (‘the first’, ‘the second’), but rather ‘this’
and ‘that’. In Cicero’s list, where there is some confusion because the example
sentences do not always match the vaguely given definitions, the first five modes
correspond roughly to the five Stoic modes, and Mode 6 is a re-formulation of Mode
3; whilst Mode 7 is (§57) ‘Not this and that; but not this; therefore that’ — that is
to say: ∼ (p&q); ∼ p; q, an obviously invalid inference. (For discussion, see [Kneale
and Kneale, 1962, 179-81; Hadot, 1971, 144-56]). This mistake suggests that,
already by Cicero’s time, Stoic propositional logic was not properly understood
(see below, p. 17).
Apuleius ([Sullivan, 1967; Londey and Johanson, 1987])
By contrast with Cicero’s Topics, Apuleius’s Peri Hermeneias (‘On Interpretation’
— but the Greek title, echoing Aristotle was deliberate and will be retained)
written roughly two centuries later, is very straightforwardly a logical treatise, an
exposition of Aristotelian syllogistic. Apuleius (c. 125 — c. 171) was a writer in
Roman North Africa, most famous for his comic novel, the Golden Ass, but responsible
too for a number of philosophical works, including an exposition of Plato’s
thought (De dogmate Platonis). Although his authorship of Peri hermeneias has
been questioned, recent specialists accept it [Sullivan, 1967, 9-14; Londey and Johanson,
1987, 11-15]. The treatise covers much of the material in Chapters 1-8 of
Aristotle’s On Interpretation and in the Prior Analytics, excluding modal syllogistics.
After treating the nature of propositions and their terms, and the square
of opposition, it goes on to explain the principles of the syllogism, giving both the
different moods and how the validity of the second and third figure syllogisms can
be demonstrated by reducing them to first-figure ones. Apuleius’s main differences
from Aristotle are that he casts syllogisms as inferences, rather than conditionals;
he gives third-figure syllogisms in a different order; and he does not use letters as
variables to stand for predicates. He also stands out in the Latin tradition by his
terminology, which is sometimes a very literal Latin version of the Greek — for
instance, a syllogism is a collectio. Not surprisingly, given his period, Apuleius
knows something of Stoic logic, but he takes the line about it common among the
Peripatetics, condemning it (Chapter 7) without understanding it. For instance,
he rejects the inference ‘If it is day, it is light; but it is day, therefore it is light’, on
the grounds that in the conclusion ‘it is light’ means that it is light now, whereas
in the premisses, ‘it is light’ has a different meaning: it is asserted merely that it
follows that if it is day, then it will be light. This criticism shows a clear failure
to distinguish between the propositional operator ‘if . . . then ...’ andthepropo sitional contents it links together: a failure, that is, to grasp the propositionality
which is central to Stoic logic.
Marius Victorinus ([Hadot, 1971])
Marius Victorinus (c. 280-365) was a philosophically-educated pagan rhetorician
who was converted to Christianity about ten years before his death and proceeded
to write on the Trinity. He had been one of the rare writers since Cicero to write