Handbook of the History of Logic: - Fordham University Faculty

Logic in the 14 th Century after Ockham 493
knowledge must come into play. 68
Φ is an ordered set of propositions φn. (No difference here with respect to
Burley’s theory.)
I is an ordered set of responses ιn =[φn; γ]. Responses are ordered pairs
of propositions and one of the replies 1, 0 or ?, corresponding to Respondent’s
response to proposition φn. 69 Note that the index of the response need not be (but
usually is) the same as the index of the proposition, in case the same proposition
is proposed twice, in different moments of the disputation (in which case, for
convenience, it is referred to by the index it received in the first time it was
proposed).
R(φ) is a function from propositions to the values 1, 0, and ?. This definition
is identical to the definition of R(φ) in the reconstruction of Burley’s theory, but
the function corresponding to the rules of Swyneshed’s theory is different from
the function of Burley’s theory, since the rules are different.
4.3.2 Rules of the game
Swyneshed’s procedural rules are quite simple (cf. [Spade, 1978, §72] 70 ), and
identical to the procedural rules in Burley’s theory. By contrast, the logical rules
are quite different from Burley’s.
Swyneshed’s analysis of the requirements for a proposition to be accepted as
obligatum (that is, the first proposition proposed, named positum in the specific
case of positio) is less extensive than Burley’s. Since an inconsistent positum
gives no chance of success for Respondent, Burley clearly says that the positum
mustn’t be inconsistent. Swyneshed does not follow the same line of argumentation;
rather, he requires that a proposition be contingent to be a positum (§ 73).
This excludes impossible propositions — always false — and necessary propositions
– always true –, and that is a necessary requirement in view of the ex impossibili
sequitur quodlibet rule: if Swyneshed’s rules of obligationes are indeed meant to
test Respondent’s abilities to recognize inferential relations, an impossible obligatum
would make the game trivial (any proposition would follow). 71 Moreover,
from a necessary proposition only necessary propositions follow, so if the obligatum
is a necessary proposition, then the game becomes that of recognizing necessary
68But why use states of knowledge, and not simply states of affairs? Because (both in Burley’s
and Swyneshed’s theories) proposed propositions whose truth-value is unknown to the participants
of the disputation — for example, ‘The Pope is sitting now’ — should be accordingly
doubted. We are dealing here with imperfect states of information.
69In my reconstruction of Burley’s theory, responses were not primitive constituents of the
game. But to express some of the interesting properties of Swyneshed’s theory, the notion of
responses is crucial.
70All references are to Spade’s edition of the text. For the relevant passages and translations,
see [Dutilh Novaes, 2006a].
71Notice that Swyneshed’s reason for excluding impossible propositions is different from Burley’s:
trivialization of the game versus absence of a winning strategy for Respondent. Keffer
[2001] has also remarked that impossible (and true) posita have a Trivialisierungseffekt on both
kinds of responses, but for different reasons (pp. 158-164).