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William A. Wallace, O.P., in “Thomism and the Quantum Enigma,” *The Thomist* 61 (1997): 455–468, claims that

analogical middle terms are sufficient for a valid demonstration

and that this is

a teaching that is distinctive of Thomism

that other Scholastic schools do not uphold.

How would one justify that "analogical middle terms are sufficient for a valid demonstration"?

(cf. this on "mixed sciences" or *scientia media* and this answer here)

If you are a math person your definition of what a proposition is does not match with the proper definition of “proposition “ used in Philosophy. Aristotelian logic did not use MODERN LANGUAGE in this case MODERN ENGLISH. One would need to convert the propositions to standard categorical form. If you are a literal reader you will likely MISS the point that there are hidden premises in the argument in order to prove such an argument deductively valid. As written the argument may not look valid. The analogous use of terms would need to be related as premises with further propositions. – Logikal – 2019-07-31T02:25:29.133

2According to modern formal logic (but also the ancient one, from Aristotle on, see shane's answer) :

no, because the "analogical" use of the middle term invalidates the syllogism : in shane's example, "healthy" is predicated with different "meaning" in the two premises. – Mauro ALLEGRANZA – 2015-01-23T09:10:48.680Good question; I hadn't knbown that there was such a thing as a logic of analogy; it isn't normally understood that analogy is an important technique in mathematics - for example prime numbers as prime knots, or electrons as black holes. – Mozibur Ullah – 2015-01-23T12:02:24.383