Handbook of the History of Logic: - Fordham University Faculty

604 Mikko Yrjönsuuri
As Buridan explains, the antecedent proposition ‘c’ cannot be true unless the
implied condition is true, that is unless its subject ‘c’ and its predicate ‘true’
supposit for the same [Buridan, 2001, 969].
‘Supposite for the same’ is Buridan’s normal theory of truth, but here he claims
carefully and explicitly that this criterion is not quite sufficient. The consequential
consideration needs to be added as a condition. It can be argued that by the
condition Buridan makes the truth of a sentence dependent on itself. No sentence
can be true, unless it fills all the normal conditions and in addition is true. This
sounds circular, and thus a problem. 31 Be that as it may, the criterion does help
Buridan to evaluate the paradoxical sentences as false. Thus, when it is claimed
that the sophism ‘every proposition is false’ is true because all the propositions
that the subject supposits for are indeed supposited for by the predicate as well,
Buridan can answer that the sameness of supposition is not enough for the truth
of the proposition, since the implied consequent affirming truth to the sentence
turns out inconsistent and false. For if one looks at the content of the antecedent,
it follows that
No proposition is true, therefore, ‘c’ is not true
And if this consequence is valid together with the one that has the same antecedent
but the opposite consequent, it can only be because the antecedent is false and
even impossible.
As we noted, Buridan’s second sophism in this set shows that consequences of
the form
p, therefore, ‘p’ istrue
are not as such valid. Now we have seen on the contrary that his solution of the
insolubles requires or even is based on such consequences being valid. Buridan
notes this fact, but points out that consequences of the form
p, and ‘p’ exists, therefore, ‘p’ istrue
are valid. Buridan seems to think that this issue forces him to qualify his theory,
but then he also notes that in an insoluble case it is normally assumed that the
sentence at issue exists. For this reason, the qualification should not engender
problems [Buridan, 2001, 970].
It seems that Buridan thinks that at this point he has given a sufficient explanation
of how the core of the paradoxes of self-reference can be solved. He turns
to different versions of the paradox and considers further examples.
The series of sophisms contains thirteen more. They develop interestingly different
problems resulting from either immediate or mediated self-reference. By the
latter Buridan means situations like the one in the ninth sophism, where Plato is
supposed to say ‘Socrates utters a falsehood’ while Socrates says ‘Plato utters a
31 See [Read, 2002, 200–201].