Handbook of the History of Logic: - Fordham University Faculty

Treatments of the Paradoxes of Self-reference 589
The issue makes a difference, as can be seen by considering whether Bradwardine
accepts a modified version of (P2), namely,
(P2)* Every proposition signifies or means as a matter of fact or absolutely
everything which follows from what it signifies
as a matter of fact or absolutely.
There are two ways to attribute (P2)* to Bradwardine. One is to claim that
Bradwardine accepted both (P2) and (P2)*, the latter through accepting that
every sentence implies what it signifies. However, this attribution has the problem
that it forces Bradwardine quite visibly to consequences that he explicitly wanted
to avoid. 15 Also, it does not accord very well with the way he puts the example.
The other way is to attribute minor textual problems to Bradwardine’s formulation
and claim that he means to state (P2)* rather than (P2). This would make the
example run smoothly.
The question concerns the exact way in which Bradwardine believed that signification
is “closed” under the consequence relation. To put it formally (using the
colon for the relation of signifying), 16 Bradwardine may mean:
a → p
(P2)
‘a’ :p
or he may rather mean:
‘a’ :p, p → q
(P2)*
‘a’ :q
The problem with (P2) is that it is somewhat counterintuitive and does not work
the way Bradwardine puts his principle to work. The problem with (P2)* is mainly
that it is not what he appears to say in the text. To some extent, thus, the question
comes down to the historian’s methodological choices.
Immediately after Bradwardine’s work, medieval scholars started to discuss the
nature of propositional significates (complexa significabilia). In this discussion,
the problem was to determine what exactly is signified by a proposition over and
above that which is signified by its terms. Indeed it is possible that Bradwardine’s
work gave a seminal motivation for such a discussion in a context where standard
semantic theories had room only for things and not for states of affairs as signified
entities.
Be that problem as it may, we can see what Bradwardine is aiming at in the
examined example. Given (2), Bradwardine points out that the subject of the
signified proposition ‘what is uttered by Socrates is false’, or ‘what is uttered by
Socrates’ has in the assumed case only one suppositum, or refers to only one thing,
which is ‘a’. Thus, ‘a’ signifies the affirmative predication of falsehood to that
15 Paul Spade has defended this kind of reading of Bradwardine. See e.g. [Spade, 1981].
Stephen Read rejects the reading. See [Read, 2002, 208–214].
16 I am using the arrow for medieval consequence, which makes it in certain cases ambiguous
between conditional and inference.