Handbook of the History of Logic: - Fordham University Faculty

Treatments of the Paradoxes of Self-reference 599
be inconsistent with ‘this is false’ indicating ‘a’ from the outside [Bradwardine,
internet, 51].
For his part, Heytesbury takes it to be odd if consequences of the form
p, therefore, p
are not formally valid. Since he provides the example as a criticism of the attempted
solution, he does not offer any solution of the problem. Instead, he
continues with a whole series of examples where logical properties of sentences
misbehave if Swyneshed’s (and Bradwardine’s) solution is accepted. To pick up
another example, let ‘a’ be ‘this sentence is not necessary’, indicating itself, and
let its contradictory ‘b’ be ‘this sentence is necessary,’ indicating ‘a’. Now, there
seems to be no reason to count ‘a’ as false in the way insolubles are false, and
it seems even to signify as is the case, since it does not appear to be necessary.
Indeed, if ‘a’ was necessary, its contradictory ‘b’ would signify as is the case and
thus ‘b’ would be true. This seems unacceptable. However, it appears that ‘a’
signifies as is necessarily the case, as Heytesbury puts it, and thus it seems not
to be a contingent sentence either. Thus, ‘a’ is a true sentence that cannot be
ascribed a modal status [Heytebury, 1979, 31]. Without modifications, neither
Bradwardine’s nor Swyneshed’s theory will solve the case. And if modifications
are made, it seems that they will be necessary for all kinds of logical properties,
since corresponding examples arise in many directions.
Heytesbury’s own rules about what one should do when faced with an insoluble
draw considerably on the disputational context. One really gets the feel that he is
giving advice to a student on how to behave in a specific kind of disputation. For
example, his third rule concerns the situation where the constructed case has an
insoluble sentence and it is assumed together with it that the sentence “signifies
as its terms pretend, but not precisely” [Heytesbury, 1979, 49]. In such a case, the
insoluble sentence must be granted, but one must deny its truth:
Case: Socrates is saying only this: ’Socrates is saying what is false’,
and it so signifies, but not precisely.
Proposition 1: Socrates is saying what is false. Granted, follows
Proposition 2: ‘Socrates is saying what is false’ is true. Denied
Heytesbury seems to follow Bradwardine in judging that the actual sentence uttered
by Socrates can be deemed false. This seems to be his reason for denying
proposition 2.
The text continues with a discussion of what the meaning difference between
proposition 1 and the sentence uttered by Socrates is. In putting this question,
Heytesbury seems to be thinking of Bradwardine’s theory and the idea that when
uttered by Socrates himself ‘Socrates is saying what is false’ has a different signification
than when uttered in a disputation by other people. Heytesbury does
not, however, want to specify the difference in meaning. In particular, he does not
say anything like Bradwardine’s claim that the self-referential sentence signifies its
own truth. He advises the respondent to refuse any question concerning precise