Handbook of the History of Logic: - Fordham University Faculty

598 Mikko Yrjönsuuri
— the paradoxical ones — which have the truth value ‘false’ not on the basis of
their signification but due to their self-falsificatory character. Thus, any sentence
implying that it itself is false, falsifies itself and is false because of this falsification
regardless of the signification. Thus, it seems that Swyneshed did not buy
Bradwardine’s principle (P2), or at least he did not think that it would have any
significant application in the theory of self-referential paradoxes.
Swyneshed’s theory shares the feature of Bradwardine’s theory that the paradoxical
sentences are deemed false. This has the implication that there at least
appear to be contradictory sentences that are both false. Although Bradwardine
recognizes the problem, he tries to do away with it. Swyneshed, for his part,
accepts the oddity with straight face, buying the strange view that contradictories
are sometimes both false. Furthermore, there appear to be cases where two
tokens of exactly the same sentence type have different truth values as regards
the same time and the same situation (‘Socrates utters a falsehood’ as uttered by
Socrates or by someone else). Both Bradwardine and Swyneshed accept directly
this implication of their solution.
One further oddity concerns inferential relationships. Consider the consequence:
27
This is false, therefore, this is false,
where both demonstrative pronouns indicate the consequent (let the consequent
be ‘a’ and the antecedent ‘b’). According to both Bradwardine and Swyneshed, as
a self-referential token ‘a’ must be deemed false, but ‘b’ is to be counted as true,
because it is not self-referential but instead refers to ‘a’, which indeed is false. The
inference appears valid: the contradictory of the consequent is inconsistent with
the antecedent. If the same thing is indicated, ‘this is false’ and ‘this is not false’
are contradictories.
Swyneshed accepts the reasoning, confirms that the consequence is valid and
allows that in a valid inference there is a true antecedent with a false consequent
[Spade, 1979, 189]. This is an interesting choice, since it makes it appear that
he did not think that the main point in a consequence would be to account for
truth preservation or any of its modal varieties, as has mostly been the approach in
modern logic. Rather, this suggests that Swyneshed thought that consequence is a
relation between the meanings of the sentences, and it is more or less a coincidence
that in most cases it preserves truth.
It seems that Bradwardine would not need to accept the validity of this consequence
even if he would accept the same understanding of the consequential
relationship, since in his theory the difference between the truth values of ‘a’ and
‘b’ is based on a difference in signification. Thus, what is affirmed by the antecedent
is only a part of what is affirmed by the consequent. This may of course result
in the inference being blocked. Furthermore, Bradwardine tries to show that the
contradictory of a self-referential sentence like ‘a’ is not simply ‘this is not false’
but more like ‘either ‘a’ is not false or ‘a’ is not true’, which clearly would not
27 See [Heytesbury, 1979, 29].