Logic, Traditional
In logic, as in other fields, whenever there have been spectacular changes and advances, the logic that was current in the preceding period has been described as "old" or "traditional," and that embodying the new material has been called "new" or "modern." The Stoics described themselves as "moderns" and the Aristotelians as devotees of the "old" logic, in the later Middle Ages the more adventurous writers were called moderni, and since the latter part of the nineteenth century the immensely expanded logic that has developed along more or less mathematical lines ("mathematical logic," "symbolic logic," "logistics") has been contrasted with the "traditional" logic inherited from the sixteenth and seventeenth centuries. In every case the logic termed "old" or "traditional" has been essentially Aristotelian, but with a certain concentration on the central portion of the Aristotelian corpus, the theory of categorical syllogism—the logic of Aristotle himself having been rather less circumscribed than that of the "tradition," especially of the sixteenth to the nineteenth century.
The Logic of Terms
To begin with the categorical syllogism, an inference, argument, or syllogism (traditionally, all arguments are assumed to be syllogistic) is a sequence of propositions (premises followed by a conclusion), such as "All animals are mortal; all men are animals; therefore, all men are mortal." Propositions, in turn, are built up from terms—for example, "animals," "mortals," "men." The traditional order of treatment, therefore, begins with the study of terms (or, in writers with a psychological or epistemological bias, ideas) and goes on to the study of propositions (or judgments), concluding with that of syllogisms (or inferences).
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