Handbook of the History of Logic: - Fordham University Faculty

Logic in the 14 th Century after Ockham 469
would be at the origin of theories of consequences, as these are essentially theories
about the relations between propositions that go beyond the patterns recognized
by syllogistic. Moreover, some earlier investigations on the notion of consequence
were made explicitly within the context of an analysis of the Topics; Abelard, in
the 12 th century, developed a sophisticated theory of the logical relations between
propositions precisely in the part of his Dialectica [Abelard, 1956] dedicated to
the topics.
However, this hypothesis did not receive the historical confirmation that one
could have expected. It has been argued [Green-Pedersen, 1984, 270] that the late
13 th century literature on the Topics, that is, the period immediately preceding
the emergence of treatises on consequences, gives absolutely no clue of what was
to come; that is, there is no significant similarity between the contents of these
13 th century treatises on the topics and 14 th century treatises on consequences.
Therefore, it has been concluded that the Topics could not have been the main
source for 14 th century theories of consequences. 34
Although our current state of knowledge on the matter still does not allow for a
conclusive account of these developments, the picture that at this point seems more
plausible is that different strands of traditional Aristotelian logic converged in order
to give rise to the 14 th century theories of consequences. It seems that at least
three other traditions contributed to the development of theories of consequence:
treatises on syncategoremata, especially in connection with the syncategorema ‘si’
(corresponding to the ‘if . . . then’ structure in English); the analysis of hypothetical
syllogisms, a concept absent from Aristotle’s logic and introduced by Boethius
in the 6 th century AD (his treatise De hypotheticis syllogismis is referred to 6
times in Burley’s De puritate artis logicae — cf. [Green-Pedersen, 1984]); and
commentaries on the Prior Analytics — indeed, it is in the Prior Analytics that
Aristotle explicitly states a formulation of the notion of ‘following’ that is arguably
the (remote) source for the most fundamental definition of consequence in the 14 th
century. 35
Be that as it may, the importance of the Topics for the development of 14 th
century theories of consequences should not be altogether dismissed. It is worth
noticing that two of the first authors having written explicitly on consequence,
Ockham and Burley, are both in some way or another influenced by the Topics.
Burley explicitly says that all valid consequences are based on dialectical Topics
[Burley, 2000, 158]. By contrast, the relation of Ockham’s theory of consequence
to the Topics is more convoluted; Green-Pedersen argued convincingly that Bird’s
reconstruction of Ockham’s theory within the framework of the Topics [Bird, 1961]
is not satisfactory [Green-Pedersen, 1984, 268], but he also confirms that Ockham’s
‘intrinsic’ and ‘extrinsic’ middles, crucial concepts for his theory of consequence,
are concepts essentially taken (albeit heavily modified) from the topical framework.
34 Chapter E of [Green-Pedersen, 1984], on topics and the theory of consequence, is the most
comprehensive survey of these developments that I am aware of.
35 “A deduction is a discourse in which, certain things being stated, something other than what
is stated follows of necessity from their being so.” Prior Analytics 24 b 19-20.