Handbook of the History of Logic: - Fordham University Faculty

Treatments of the Paradoxes of Self-reference 605
truth’. Here neither of the propositions refers to itself, but together they generate
aloop.
Two further sophisms deserve mention here. The eleventh sophism assumes
that I utter only the sentence ‘I utter a falsehood’ (‘a’). Buridan applies his
theory systematically. Thus, he says that ‘a’ is false and rejects the proof that it
follows that it is true. The crucial arguments are as follows:
‘a’ is false, therefore, ‘a’ exists
a, and ‘a’ exists, therefore, ‘a’ istrue
Buridan accepts both of these two arguments, but rejects that together they would
show that “a’ is true’ follows from “a’ is false’. As he explains, the conjunctive
antecedent of the latter inference is to be rejected because of the first part. Thus,
he distinguishes between ‘a’ is false’ and ‘a’ even in a case where ‘a’ means that
‘a’ is false. Indeed, he grants “a’ is false’ as true while claiming that ‘a’ is false
[Buridan, 2001, 978].
Then Buridan turns to the issue of contradictories and equivalencies. What
should you say to say the same as I say when I say ‘I utter a falsehood’? According
to Buridan, your sentence should be ‘You utter a falsehood, and ‘a’ is true’, ‘a’
referring to my sentence. Correspondingly, the contradictory of my sentence would
be the disjunction: “You do not utter a falsehood, or ‘a’ is not true.” As one can
see, in the paradoxical case the contradictory is indeed true [Buridan, 2001, 979–
980].
However, by claming that the paradox sentence in fact turns into a conjunction,
Buridan shows that he has not really got very far from the theory that the sentence
signifies its own truth and not only implies. For suppose a valid consequence
p → q
If we want to find the contradictory of ‘p’, we do not in general include ‘q’. That is,
it seems odd to say that the contradictory of ‘p’ has the disjunctive form ‘(¬p∨¬q)’
whenever something follows from p. This formulation — or the talk about mental
language that Buridan goes into in this context — both seem natural only if ‘q’ is
somehow signified by rather than simply follows from ‘p’. It seems that Buridan
was not able to say what he really meant by his theoretical idea that the insoluble
sentences imply rather than signify their own truth.
If compared to Bradwardine’s work, Buridan’s discussion of the insolubles does
not appear very ingenious and original. He wavers and leaves room for doubt,
allowing the reader to get the feeling that his solution is sketchy. The work is,
however, clearly on a very advanced logical level and the problems obviously result
from difficulties in the subject matter. Given the extremely wide circulation of
Buridan’s Summulae, it is very understandable that his solution achieved a very
high reputation and a wide influence in the coming centuries.
The seventeenth sophism in Buridan’s set is the sentence ‘You will throw me in
the water’. Buridan writes: “Let us posit the case that Plato is the master of the
bridge and that he guards it with such a powerful military support that nobody