According to traditional syllogistic logic, which has its roots in Aristotle, there are four types of propositions: the A proposition ("All S are P"), the E proposition ("No S are P"), the I proposition ("Some S are P"), and the O proposition ("Some S are not P"). These propositional types represent all of the possible combinations of the dichotomies of affirmative/negative and universal/particular. Each makes a claim that a certain essent (the particular I and O propositions) or an entire class of essents (the universal A and E propositions), the subject or subject-class, relates in some way (belongs or does not belong) to a class of essents designated by the predicate of the proposition. The traditional, or Aristotelian, standpoint for evaluating the truth or falsity of these propositions assumes that each class designated by a term in the subject and predicate actually exists. This allows certain conclusions to be drawn regarding the relationship between the truth values about different types of propositions, and these relationships are symbolized visually in a diagram called the "Traditional Square of Opposition." (These relationships are designated as "contradictory," "subalternate," "contrary," and "subcontrary.") The modern, or Boolean, interpretation of Aristotle's syllogistic logic, however, makes no assumptions about the existence of the classes denoted by the subject and predicate terms of a proposition. Because of this, there are fewer conclusions that one is able to draw about the relationships between the truth-values of different propositions. (The only relationship on the modern square of opposition is the relationship denoted by the term "contradictory....
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...ways of thinking in the West -- the metaphysical-philosophical and the scientific-technical. (Steiner 28) Philosophy, as it was understood up to Heidegger's time, was the heir of these traditions. It is both the cause and the heir of the forgetting of being in the West. Syllogistic logic, as a part of philosophy, is also both heir and cause of this central concern of the twentieth century, and this "[obscuring] its everyday function as a grammatical copula" (Steiner 38) is both cause and symptom of the forgetting of being -- and all of the problems of the twentieth century.
Hurley, Patrick J. A Concise Introduction to Logic, Sixth Edition. Belmont, CA: Wadsworth, 1997.
Partridge, Eric. Origins: A Short Etymological Dictionary of Modern English. New York: Crown, 1983.
Steiner, George. Martin Heidegger. New York: Penguin, 1978.
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