THE LIMITATIONS OF ARISTOTELIAN SYLLOGISTIC AND THE NEED FOR NON-SYLLOGISTIC CONSEQUENCES
Medieval theories of consequences are theories of logical validity, providing tools to judge the correctness of various forms of reasoning. Although Aristotelian syllogistic was regarded as the primary tool for achieving this, the limitations of syllogistic with regard to valid non-syllogistic forms of reasoning, as well as the limitations of formal deductive systems in detecting fallacious forms of reasoning in general, naturally provided the theoretical motivation for its supplementation with theories dealing with non-syllogistic, non-deductive, as well as fallacious inferences. We can easily produce deductively valid forms of inference that are clearly not syllogistic, as in propositional logic or in relational reasoning, or even other types of sound reasoning that are not strictly deductively valid, such as enthymemes, probabilistic arguments, and inductive reasoning, while we can just as easily provide examples of inferences that appear to be legitimate instances of syllogistic forms, yet are clearly fallacious (say, because of equivocation). For Aristotle himself, this sort of supplementation of his syllogistic was provided mostly in terms of the doctrine of “immediate inferences” in his On Interpretation, various types of non-syllogistic or even non-deductive inferences in the Topics, and the doctrine of logical fallacies, in his Sophistical Refutations. Taking their cue primarily from Aristotle (but drawing on Cicero, Boethius, and others), medieval logicians worked out in systematic detail various theories of non-syllogistic inferences, sometimes as supplementations of Aristotelian syllogistic, sometimes as merely useful devices taken to be reducible to syllogistic, and sometimes as more comprehensive theories of valid inference, containing syllogistic as a special, and important, case.
A BRIEF SURVEY OF HISTORICAL SOURCES
Accordingly, the characteristically medieval theories of non-syllogistic inferences were originally inspired by Aristotle's logical works other than his Analytics. Aristotle's relevant ideas were handed down to medieval thinkers by Boethius’ translations of and commentaries on Porphyry's Isagoge and Aristotle's Categories and On Interpretation, along with Boethius’ own logical works, the most relevant to the development of consequences being his De Hypotheticis Syllogismis and De Topicis Differentiis.