Handbook of the History of Logic: - Fordham University Faculty

472 Catarina Dutilh Novaes
Summulae — [Buridan, 2001]); however, many of them recognized that a true
conditional corresponds to a valid consequence/inference 42 (cf. Ockham, Summa
Logicae, Part II, chapter 31, where he says that he will not discuss conditionals
extensively since their logical properties correspond to the logical properties of
consequences). Moreover, if the historical hypothesis of the influence of theories
on the syncategoremata and on hypothetical syllogisms for the development of
theories of consequences is correct, it becomes then patent that the two notions of
conditionals and consequences were intimately related for our authors.
Nevertheless, as argued in [King, 2001], there are various reasons to conclude
that the medievals were not only aware of these distinctions, but also that they
viewed their consequentiae as primarily corresponding to arguments and inferences,
i.e. to relations between statements, and not to conditional statements.
Perhaps the most conspicuous of these reasons, taken from the structure of Ockham’s
Summa, is that consequences are treated there in Part III, dedicated to
arguments, and not in part II, dedicated to propositions. Buridan explicitly addresses
this distinction between conditionals and arguments in 7.4.5 of his SummulaedeDialectica,
and while he says that consequentia is a twofold concept
(covering conditionals and arguments), in most cases the logical properties of conditionals
are treated under the heading ‘conditionals’, and what is dealt with in
sections on consequence is predominantly logical properties of arguments. King
[2001, 123] also discusses how Burley presents rules of consequences involving conditional
propositions, explicitly contrasting ‘the conditional sentences that enter
into such reasoning with the consequences made out of them’. Hence, for the purposes
of the present analysis, medieval consequences are not to be understood as
conditional sentences but rather as inferences/arguments.
Now, as for the general definition of consequence, most authors of the 14 th
century accept at least as a necessary condition for a (valid) consequence that the
antecedent cannot be true while the consequent is false; many accept this as a
sufficient condition as well. This is, of course, the very familiar modal definition of
consequence, present in Aristotle and also widely accepted in current (philosophy
of) logic (at least as a necessary condition). Another formulation of the same
idea is that a consequence is valid if from the contradictory of the consequent
the contradictory of the antecedent follows [Ockham, 1974, 728] 43 , or similarly
that the contradictory of the consequent is incompatible with (the truth of) the
antecedent [Burley, 2000, 149]. In fact both Ockham and Burley give several
equivalent formulations of this core idea, but the key point is obvious: for our
authors, the most fundamental characteristic of a consequence is that the truth of
the antecedent is incompatible with the falsity of the consequent.
Buridan’s formulation of the fundamental criterion of what is to count as a
consequence follows the same idea, but it is more convoluted because he has to take
42 We shall see in due course that absolute consequences correspond to necessarily true conditionals,
while as-of-now consequences correspond to contingently true propositions.
43 Naturally, this should not be seen as a definition, as it is obviously circular, but rather as a
rule of thumb for the recognition of putative consequences.