The development of modus ponens in antiquity: from Aristotle to the 2nd century AD. (Philosophical Abstracts).
"Aristotelian logic," as it was taught from late
antiquity until the twentieth century, commonly included a short
presentation of the argument forms modus (ponendo) ponens, modus
(tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In
late antiquity, arguments of these forms were generally classified as
"hypothetical syllogisms." However, Aristotle did not discuss
such arguments, nor did he call any arguments hypothetical syllogisms.
The Stoic indemonstrables resemble the modus ponens/tollens arguments.
But the Stoics never called them hypothetical syllogisms; nor did they
describe them as ponendo ponens, and so forth. The tradition of the four
argument forms and the classification of the arguments as hypothetical
syllogisms hence need some explaining. In this paper, the author offers
some explanations by tracing the development of certain elements of
Aristotle's logic via the early Peripatetics to the logic of later
antiquity. The author considers the questions: How did the four argument
forms arise? Why were there four of them? Why were arguments of these
forms called "hypothetical syllogisms"? On what grounds were
they considered valid? She argues that such arguments were neither part
of Aristotle's dialectic, nor simply the result of an adoption of
elements of Stoic logic, but the outcome of a long, gradual development
that begins with Aristotle's logic as preserved in his Topics and
Prior Analytics; and that, as a result, we have a Peripatetic logic of
hypothetical inferences which is a far cry both from Stoic logic and
from classical propositional logic, but which sports a number of
interesting characteristics, some of which bear a cunning resemblance to
some twentieth-century theories.