Handbook of the History of Logic: - Fordham University Faculty

466 Catarina Dutilh Novaes
2.2 Other important developments
2.2.1 The doctrine of proof of terms/propositions
Besides the ‘older’ semantic tradition based on the concept of supposition, another
semantic tradition became very influential in the 14 th century. 32 This tradition
was known as the doctrine of the proof of terms (probationes terminorum) or
propositions, and its most influential text was Billingham’s Speculum Puerorum.
Billingham’s text was not the first in this tradition (for example, de Rijk dates
Martin of Alnwick’s text also edited in [De Rijk, 1982] as earlier than Billigham’s),
but it seems to have been the main source for the popularity of this genre in the
second part of the 14 th century.
‘Proof’ here is not to be understood in its mathematical/logical sense, as demonstration;
in this sense, to prove a proposition is to show what its truth depends on,
in particular which simpler propositions must be true in order for a given proposition
to be true. It is essentially an analytic procedure, in which the meaning
of a ‘difficult’ proposition is decomposed in terms of simpler propositions, known
as immediate propositions, on the basis of the analysis of the term(s) causing the
proposition to be a ‘difficult’ one. Immediate propositions are those, according
to Billingham, which cannot be proved (verified) except by a direct appeal to
the senses or the understanding. These would be primarily propositions with directly
referential pronouns or adverbs such as ‘I’, ‘this’, ‘that’, ‘here’, ‘now’ etc (cf.
Billigham, Probationes Terminorum, in [De Rijk, 1982, 49]).
There are three basic techniques to ‘prove’ a proposition, according to whether
the proposition is an exponible, a resoluble or an officiable proposition. An exponible
proposition is one that corresponds to several propositions taken in conjunction,
such as ‘Socrates begins to be white’, which corresponds to ‘Socrates was
not white and Socrates is now white’. Propositions containing comparative and
superlative terms, or the verbs ‘begins’, ‘ceases’ and ‘differs from’ are analyzed
in this fashion. A resoluble proposition is one that involves the descent from a
general term to discrete terms, such as ‘A man is running’, which is proved by an
appeal to sense experience codified by the propositions ‘This is a man’ and ‘This
is running’. Finally, an officiable proposition is one containing the nominalization
of a proposition with the accusative-plus-infinitive construction, and corresponds
roughly to what is now known as ‘opaque contexts’ (modalities and verbs related
to propositional attitudes such as ‘think’, ‘believe’ etc.).
Although we dispose of several texts presenting the doctrine of the proof of
propositions/terms, it is still in fact quite understudied. Indeed, it is fair to say
that we still do not really understand the purpose and the mechanisms defining it
(see [Spade, 2000, part IV]). For this reason, it is to be hoped that scholars will
at some point take up the challenge of analyzing this doctrine systematically, as
32 This approach was sometimes used instead of supposition theories (cf. Johannes Venator’s
Logica which uses the doctrine of the proof of propositions exclusively), but at other times both
theories co-existed together, for example as distinct chapters of the same work (such as Paul of
Venice’s Logica Parva).