Handbook of the History of Logic: - Fordham University Faculty

Treatments of the Paradoxes of Self-reference 597
when two sentence tokens of the same type have different truth values at the same
time, there is a fallacy involved and what really happens is that neither of them
is true absolutely but that they we must speak of truth “in a certain respect.”
WILLIAM HEYTESBURY
Another Oxford calculator, William Heytesbury wrote in 1335 a work titled “Rules
for Solving Sophisms” (Regulae solvendi sophismata). 25 The aim of this work, as
the introduction tells us, is to advice young students in their everyday duty to deal
with sophisms. It seems that such exercises formed at the time the core of the
practical side of the study of logic and semantics, and it seems that paradoxes of
self-reference held a place of pride there. The first chapter of Heytesbury’s Rules
is dedicated to insolubles.
Right in the beginning Heytesbury tells his readers, “although the insolubles
can be solved, nevertheless they have not yet been solved.” [Heytesbury, 1979,
15]. Accordingly, his work should not be understood as offering a solution to the
paradox. Rather, he aims at telling students how to deal with the paradox in their
logic exercises. Essentially, Heytesbury’s advice is to avoid problems through not
admitting that any examined paradoxical sentence would signify exactly as the
common meaning of the terms would make it to signify. Thus, he reverts back to
the strategy we saw in the thirteenth century treatises: avoid the paradox rather
than face and solve it. But now this strategy has a Bradwardinian twist. Instead
of saying that the respondent in a disputation should simply refuse self-referential
paradoxes, Heytesbury advices the respondent to avoid admitting that one knows
what exactly a sentence like ‘I utter a falsehood’ means.
Before going into his advice in detail, Heytesbury criticizes earlier solutions. He
lists three different views that he takes to be worse than his own approach. The
second and third of these are not very interesting. They verge on the question
whether insolubles are truth-bearing sentences. The second denies their sentential
status. The third allows, in Heytesbury’s formulation, that insolubles are sentences
and thus truth-bearers, but claims that they just do not have a truth value. Quite
righteously Heytesbury wonders what it means to be a truth bearer without a
truth value.
The first view has been interpreted as Roger Swyneshed’s theory, 26 and Heytesbury’s
discussion of it is perhaps the most interesting part of the treatise. Since
Swyneshed’s approach was developed on the basis built by Bradwardine, many of
Heytesbury’s arguments tackle issues already in Bradwardine, though still not by
abandoning the approach. Rather, Heytesbury continues on the same track.
The modification Swyneshed made to Bradwardine’s theory was to shift attention
from signification to consequences. His idea was that there are sentences
25The whole work is edited in [Heytesbury, 1494]. For the chapter on insolubles, see translation
in [Heytesbury, 1979].
26See Spade’s study in [Heytesbury, 1979, esp. p. 72–79]. For a study of Swyneshed’s theory,
see Spade, 1983; for an edition of the text, see [Spade 1980].