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)

  • According 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 Jan 23 '15 at 9:10
  • Good 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 Jan 23 '15 at 12:02

Think of some examples. Here's a classic Thomist "analogical" term: "healthy". Properly speaking it is only bodies that are healthy, and for a body to be healthy is for it to be in good working order. For medicine to be healthy isn't for the medicine to be in good working order, it is for the medicine to have the power to put bodies into good working order. So here we clearly have two distinct but senses of "healthy".

So let's consider an example of a syllogism.

(1) If something is healthy, it is good. (2) This medicine is healthy. (3) Therefore, this medicine is good.

Understand the occurrence of "healthy" in the first line as meaning healthy in the sense that bodies are healthy. Do we have a valid syllogism here? According to Thomists yes; according to Scotists and those who are suspicious of analogy no.

  • To give more detail about why the thomists and scotists disagree about this goes beyond what could reasonably be conveyed in a message board. it's a really deep problem. – shane Jan 23 '15 at 4:20
  • Could you provide any references for further reading? thanks – Geremia Jan 23 '15 at 4:36
  • 1
    Here's one: Klima, G. (2002) “Aquinas’ Theory of the Copula and the Analogy of Being”, Logical Analysis and History of Philosophy, 5(2002), pp. 159-176. Or, if you're more in the mood for a book, one classic text is: amazon.com/Doctrine-Analogy-According-Marquette-Philosophy/dp/… A somewhat different take can be found in: cuapress.cua.edu/books/viewbook.cfm?Book=MCAA – shane Jan 23 '15 at 12:54
  • Those books treat the logical aspects of analogy, specifically? – Geremia Jan 24 '15 at 1:20
  • 1
    McInerny def does. Don't recall about the other haven't read them in years. – shane Jan 24 '15 at 1:21

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