Handbook of the History of Logic: - Fordham University Faculty

Treatments of the Paradoxes of Self-reference 601
The equivalence between a sentence and its truth had been put under scrutiny by
Bradwardine and others after him, and thus Buridan could by no means take it
for granted and just use for his solution of the paradox. He had to first achieve a
firm grip of what exactly is the logical relation between a sentence and its truth.
Consider the consequence
A man exists, therefore, ‘a man exists’ is true.
Buridan rejects this with the consideration that it might be the case that there
are men but no propositions. He thinks that a proposition needs to exist in order
to be true: he too is committed to token-based semantics. In the first sophism
of the series, Buridan has accepted ‘every proposition is affirmative, therefore,
no proposition is negative’ as valid inference despite the fact that the consequent
is self-refuting and thus cannot be true [Buridan, 2001, 953]. He wants to say
that inference is fundamentally a modal relation, and a proposition is not called
possible on the basis of whether it can be true, but rather on the basis of whether
the case can be as it signifies. Thus, a proposition can be possible without being
possibly-true. 29 In the same vein, consequences do not hold on the basis of a
connection between truth values, but on the basis of whether things can be as is
signified by the antecedent and consequent. In a valid consequence, the case is as
is signified by the consequent if it is as is signified by the antecedent. Existence
of the propositions will not affect inferential validity in the ordinary way, though
it will affect truth. As Buridan notes concerning the example, ‘every proposition
is affirmative, therefore, no proposition is negative’: “something true can entail
something false.” But as he explains, “when this is concluded, the former is no
longer true, but false.” [Buridan, 2001, 955].
In the case analyzed in the second sophism, existence of the proposition matters,
since the consequent in the consequence ‘a man exists, therefore, ‘a man exists’ is
true’ is about truth value, not about humans. Buridan notes that the following is
a valid inference
A man exists
‘A man exists’ exists
Therefore, ‘a man exists’ is true
Thus the above discussed inference ‘a man exists, therefore, ‘a man exists’ is true’
would be a valid enthymeme with reference to a true premise “a man exists’ exists’,
although as it stands it is not valid. A reader familiar with Richard Kilvington’s
work will at this point wonder why Buridan skips any worry about signification. As
we saw above, Kilvington — and Heytesbury — would have here made reservations
about what ‘a man exists’ means. But not Buridan.
However, as Buridan notes, in order to be valid or true, a consequence needs to
exist: not only truth but even asserted validity appears to be carried by tokens of
29 Cf. [Prior, 1969]. The corresponding problem with inferences has been discussed in, e.g.,
[King, 2001, pp. 129] and [Dutilh Novaes, 2005].