A prosleptic syllogism is a class of syllogisms that use a prosleptic proposition as one of the premises. The term originated with Theophrastus of Eresus, although Aristotle did briefly mention such syllogisms by a different name in his Prior Analytics.
Prosleptic syllogisms are classified in three figures, or potential arrangements of the terms according to the figure of the prosleptic proposition used. First figure: “A is universally predicated of everything that is universally predicated of G” Second figure: “Everything predicated universally of A is predicated universally of G” Third figure: “A is universally predicated of everything of which G is universally predicated”
Consequently, a third figure prosleptic syllogism would read “A is universally affirmed of everything of which G is universally affirmed; G is universally affirmed of B; therefore, A is universally affirmed of B.” ("All G are A; all B are G; therefore, all B are A" or "Statement A is always true of everything for which statement G is always true; statement G is true of all things B; therefore, statement A is true of all things B.")
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