Handbook of the History of Logic: - Fordham University Faculty

158 Terence Parsons
Medieval authors did not develop an artificial symbolism, as is the custom
today. 1 Instead, they used Latin. But this was “regimented” Latin, which made
the language under consideration serve many of the purposes of modern logical
notation. For example, it was assumed (or perhaps stipulated) that the leftto-right
ordering of signs corresponds to their semantic scope — so that ‘Every
donkey not an animal is’ means that no donkey is an animal, and ‘Every donkey
an animal not is’ means that for every donkey, there is an animal distinct from
it. This was not how ordinary users of Latin understood their language, but it
was very useful for logical theory. Also, because of the presence of inflections,
Latin has a fairly free word order, so that the direct object can easily precede the
subject in a sentence, as in ‘Every donkey some man owns’, giving it scope over
the subject. Since English does not allow this, we need an artificial symbolism to
permit various scope structures; medieval logicians already had this in their own
Latin (properly, and artificially, understood).
Because this is a work on supposition theory, some important and interesting
parts of medieval logic will not be addressed. Chief among these are the Insolubles
(paradoxes), Obligations (rules for specialized debate), Consequences (general theory
of inferences among arbitrary propositions), and Syncategoremata (individual
studies of special words, such as ‘both’, ‘ceases’, ‘only’). These will be touched
upon only as they bear on Supposition theory. Also, important earlier work, such
as that by Abelard, will not be covered.
This essay is based entirely on Latin manuscripts that have been edited and
published, and it is based mostly on those works among them that have been
translated into English. Each reference to a medieval work is to book, volume,
chapter, section, subsection, etc, followed by a page reference to the English translation.
Unless otherwise stated, I use the English translations provided in the texts
cited.
1 CORE ELEMENTS OF MEDIEVAL LOGIC
Medieval Logic is built on a foundation of logical terminology, principles, and
methodology that was contained in the traditional liberal arts, in particular in
that part of the Trivium called Logic or Dialectic. This material is mostly from the
writings of Aristotle, including also the Stoics and Cicero, much of it as interpreted
by Boethius. 2 This section is devoted to the fundamental parts of logic that
1 However, authors were happy to use schematic letters, as Aristotle did in developing his
theory of the syllogism, with forms like “Some A belongs to every B”. Also, some post-medieval
writers experimented with the introduction of special signs whose function was to force special
scope readings. For example, ‘Every man is b animal’ has the truth conditions ‘For some animal,
every man is it’, because the sign ‘b’ gives the term following it wide scope. See [Ashworth, 1974,
IV.II.1] for a discussion of these special signs.
2 The parts of Aristotle’s symbolic logic that were well-known around the year 1000 were his
On Interpretation, Categories, and material (often second-hand) from the first several sections
of his Prior Analytics. This subject matter was later called the “Old Logic”, to distinguish it
from the “New Logic” which was based on several additional writings by Aristotle that became