Handbook of the History of Logic: - Fordham University Faculty

Treatments of the Paradoxes of Self-reference 587
and refutations of the earlier solutions of the paradox. This part of the treatise
is useful even in a historical sense. After that he presents his own solution in
the form of “divisions, definitions, postulates and theses” In other words, he puts
forward a kind of axiomatic basis for discussions of insolubles, and derives results
that are directly applicable to different kinds of self-referential paradoxes. The
rest of the treatise applies the offered solution to a variety of examples, including
even “sophisms which seem to be insolubles but are not”. 10
The core of Bradwardine’s solution of the paradoxes of self-reference is that a
sentence that claims itself to be false signifies not only that it is false but also that
it is true. On the basis of such a signification, it is unproblematic to judge that
the sentence is false because the falsity can now be associated to the truth-claim.
The problematic point in this solution is, as is easy to see, the proof that and the
explanation how and why the insoluble sentence signifies itself to be true, since
there seems to be nothing such explicitly said in the sentence. Bradwardine deals
with the issue in terms of his second thesis, which has been put under close scrutiny
by modern scholars. 11 Instead of starting with that, let us however first see how
Bradwardine’s solution works in a real case, taking up postulates and theses as
they are needed in the argumentation.
The first example analyzed by Bradwardine after the discussions presenting the
axiomatic basis is cast in the format of an analysis of a very simple obligational
disputation. [Bradwardine, internet, 47]. It runs as follows:
Case: Socrates utters only this: (a) Socrates utters a falsehood
Proposition: (b) Socrates utters a falsehood
The idea is this. You, the respondent, will have to evaluate the proposition
‘Socrates utters a falsehood’ on the basis of an imagined case, where Socrates
only utters ‘Socrates utters a falsehood’. Bradwardine’s solution of the paradox is
that you ought grant the sentence, because what Socrates says (that is, ‘a’) would
in the imagined case be false. Therefore, the proposition put forward to you (that
is, ‘b’) is true.
The crucial practical edge of the discussion comes from the fact that as said by
your opponent, ‘Socrates utters a falsehood’ is not self-referential, and thus it can
be admitted as true, but as Socrates himself utters ‘Socrates utters a falsehood’,
the sentence is self-referential in a problematic way. Bradwardine makes a distinction
between these two propositions (‘a’ and ‘b’) and points out that in granting
‘b’ you do not grant the proposition ‘a’ uttered by Socrates, but “another like it”
(aliam sibi similem) [Bradwardine, internet, 47]. The discussion thus relies on
the standard medieval approach that truth-values are attributed to sentence tokens
and not types (in Bradwardine’s terms, to sentences as they differ secundum
numerum, rather than secundum speciem; cf. [Bradwardine, internet, 62].
10 Printed edition of the treatise can be found in [Roure, 1970]. I have used Stephen Read’s
edition and translation available on the internet [Bradwardine, internet].
11 See esp. [Read, 2002; Spade, 1981; Spade, internet].