Handbook of the History of Logic: - Fordham University Faculty

600 Mikko Yrjönsuuri
signification. Even more strongly, if the respondent is asked to assume that the
sentence signifies precisely as terms pretend, the whole assumption should be refused.
As a practical advice for a disputation, this may seem satisfactory. But as
Heytesbury recognizes, logically the solution is far from perfect.
JOHN BURIDAN
John Buridan’s massive textbook of logic Summulae de Dialectica ends with a
collection of sophisms, seemingly as a section containing exercises. The last set in
this collection deals with self-referential propositions and thus also with insolubles.
This is not the only location where Buridan discusses paradoxes of self-reference,
but it is perhaps the most accessible one. The textbook as a whole was widely
used for several centuries, but no other section in it is directly dedicated to selfreference.
28
Buridan’s way of treating these paradoxes becomes obvious through looking at
how he has put together the set dedicated to self-reference. Let us start from the
second sophism in the set [Buridan, 2001, 956–958]. The sophism is the consequence:
‘No proposition is negative; therefore, some proposition is negative.’
Buridan’s proof for this is straightforward, and for us interesting not so much because
of the self-refuting character of the antecedent but because of the connection
that the reasoning has to the Tarskian truth-scheme. For Buridan uses the claim
“no proposition is negative’ is true’ as an intermediate step. The crucial claim
that he will use in his solution of the insolubles is that all sentences imply their
own truth. This is something that he tackles already at this stage of the series.
Thus, the following chain appears to be a valid inference:
Proof.
(1) No proposition is negative
(2) ‘No proposition is negative’ is true
(3) The proposition ‘no proposition is negative’ exists
(4) A negative proposition exists
(5) Some proposition is negative
Buridan’s solution of the sophism is that it must be denied. Surprisingly, the step
at which he blocks the inference is already (2) [Buridan, 2001, 957]. Thus, he seems
to reject a principle that will turn out to be of utmost importance for his solution
of the insolubles. However, this is a move where we see a good logician at work.
28 [Buridan, 2001] has the English translation. See [Buridan, 2004] for a critical edition, and
e.g. [Pironet; 1993; 1998] and [Zupko, 2003] for an evaluation of Buridan’s different texts on
insolubles and more bibliographical information.