Handbook of the History of Logic: - Fordham University Faculty

616 E. Jennifer Ashworth
first published in 1582; but in addition he produced single works on a variety of
related themes, from necessary propositions to the species of demonstration. 39 He
discussed the two main types of scientific method, the compositive, which is a
priori and moves from cause to effect, and the resolutive, which is of secondary
importance, and moves from effect to cause. In his work De regressu he described
how the two methods could be united, thus allowing the scientist a method which
would enable him to discover new causal relations at the same time as proving his
conclusions apodictically. Zabarella’s Opera logica were read throughout Europe
well into the seventeenth century; and were particularly important in Germany.
Just as the Coimbra commentary represents the new Aristotelian commentary, so
Zabarella represents the new Aristotelian philosopher of logic.
Another development in Aristotelian logic that calls for some comment is the
discussion of the fourth figure of the syllogism. To understand the problem, we
need to consider the relation of the terms in the premisses to the terms in the
conclusion. In standard examples, the subject of the conclusion appears in the
second premise, and is called the minor term, and the predicate of the conclusion
appears in the first premise, and is called the major term. Whether there can be
non-standard examples depends on how one defines the major and minor terms.
John Philoponus (ca. 490–ca. 570), in a definition that became popular by the
seventeenth century, defined the major term as the predicate of the conclusion.
Given this definition, one can easily differentiate syllogisms in which the middle
term stands as subject to the major term but stands as predicate to the minor
term (first figure), from syllogisms in which the middle term stands as predicate to
the major term and stands as subject to the minor term (fourth figure). Moreover,
there can be no conclusion which is indirect in the sense that the major term is
subject and the minor term is predicate. However, during the medieval period, logicians
tended to define the major term as that which appeared in the first premise
and the minor term as that which appeared in the second premise. This definition
allows indirect conclusions, and many logicians from Theophrastus onward added
five indirect modes to the first figure, giving a standard listing of nineteen valid
syllogisms (or twenty-four, if one adds the subalternate modes). 40 It also leaves
open the possibility of acknowledging the fourth figure, but there are two ways
of introducing such a figure. One can take the first figure direct syllogisms, and
transpose their premisses, thereby changing the relationship of the middle term to
the major and minor terms, and obtaining the indirect modes of the fourth figure.
Alternatively, one can take the first figure indirect syllogisms and transpose their
For more information and bibliography, see William A. Wallace, “Circularity and the Paduan
Regressus: From Pietro d’Abano to Galileo Galilei,” Vivarium 33 (1995), 76–97.
39For Zabarella’s works, see Jacobi Zabarellae Opera Logica (Cologne, 1597; repr. Hildesheim:
Georg Olms, 1966).
40We need to remember that whereas modern logicians treat universal propositions about nonexistent
objects as true and particular propositions as false, so that there are only fifteen valid
categorical syllogisms when these are symbolized in classical first-order quantificational logic,
late medieval logicians treated affirmative propositions, whether universal or particular, about
non-existent objects as false and negative propositions as true.