Explicative Syllogisms

Some scholastic goodies for those who care to see it.  Dense stuff—but important distinctions regarding what is and what is not a syllogistic inference.  Used this to explain something in a footnote to a forthcoming translation of Fr. Garrigou-Lagrange's Le principe de finalité.

Austin Woodbury, Logic, The John N. Deely and Anthony Russell Collection, St. Vincent College, Latrobe, PA, p.239-241 (n.299-300).

"In every syllogism properly so-called, from one truth is inferred ANOTHER TRUTH.  Therefore, whenever by a syllogism there is not inferred a NEW TRUTH, this is a syllogism improperly so-called.  The syllogism improperly so-called is twofold, to wit: the expository syllogism and the explicative syllogism…  From the expository syllogism must be distinguished the explicative syllogism; whereof, this is an example: ‘Man is mortal.  But a rational animal is a man.  Therefore, a rational animal is mortal.’"

"Here, [the middle term] is universal, and therefore there is a true illation.  Nevertheless, it is not a syllogism properly so-called, because it does NOT infer in the conclusion another truth, i.e. a judgment other than in the premises.  For here, the conclusion expresses the same truth but explicates it BY OTHER CONCEPTS.  For these two propositions, ‘man is mortal,’ and, ‘rational animal is mortal,’ express the same truth, but the latter expresses it by more distinct concepts than the former.  Wherefore, to this is rightly given the name of EXPLICATIVE syllogism."

"In the explicative syllogism, the conclusion is IDENTICAL AS REGARDS ITSELF (quoad se) with the major but NOT AS REGARDS US (non quoad nos); and therefore, there is a formal illation, but not an objective illation.  [He cites here R.-M. Schultes, Introductio ad historiam dogmatum (Paris: Lethielleux, 1922).]"

"OBSERVE that the major [premise] and the conclusion of an explicative syllogism are in THE SAME MODE OF SAYING ‘PER SE’; otherwise, there would be had, not an explicative syllogism but a syllogism PROPERLY SO-CALLED.  In the example given above, both these propositions are IN THE SECOND MODE of saying ‘per se.’  But the case is otherwise with this syllogism: ‘A rational animal is capable of science.  But man is a rational animal.  Therefore man is capable of science.’  Here, the major [premise] is in the FOURTH mode of saying ‘per se’; otherwise, the syllogism would be employed to no purpose.  But the conclusion is in the SECOND manner of saying ‘per se.’  Wherefore this is a syllogism properly so-called."