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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)

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Geremia
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    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 09:10
  • 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
  • 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 Jul 31 '19 at 02:25

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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. All healthy bodies are good.
  2. Some medicine is healthy.
  3. Therefore, some medicine is good.

The occurrence of "healthy" in the major premise is the primary analogate, and "healthy" in the minor premise means "that which produces health" (secondary analogate). Do we have a valid syllogism here? According to Thomists, yes; according to Scotists and those who are suspicious of analogy, no.

Geremia
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  • 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. –  Jan 23 '15 at 04:20
  • Could you provide any references for further reading? thanks – Geremia Jan 23 '15 at 04:36
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    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: http://www.amazon.com/Doctrine-Analogy-According-Marquette-Philosophy/dp/0874626242 A somewhat different take can be found in: http://cuapress.cua.edu/books/viewbook.cfm?Book=MCAA –  Jan 23 '15 at 12:54
  • Those books treat the logical aspects of analogy, specifically? – Geremia Jan 24 '15 at 01:20
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    McInerny def does. Don't recall about the other haven't read them in years. –  Jan 24 '15 at 01:21
  • Actually, McInerny's [_The Logic of Analogy_](https://www.worldcat.org/title/logic-of-analogy-an-interpretation-of-st-thomas/oclc/851368344) sounds more relevant. – Geremia Jan 28 '15 at 04:39
  • You wrote a fallacy of four terms example. I don’t think this would apply to the question. – Logikal Jul 31 '19 at 01:56
  • @Logikal Yes, it seemed so. I changed the major premise. Does the syllogism still suffer from the same fallacy? – Geremia Aug 16 '19 at 21:03
  • @Geremia, I can no longer see the example used. Yes the order of premises matters in a syllogism. It has an effect on what is called mood & figure in many cases. Categorical form IS NOT MODERN ENGLISH as Shane uses in his answer. You can Google what standard categorical syllogisms are worded. They typically have a quantifier which is not in Shane's answer for instance . Quantifier, copula a subject term and a predicate term. That is standard form. Modern English is usually translated into Mathematical logic not syllogisms -- as most people will use math translation. – Logikal Aug 16 '19 at 21:26
  • @Logikal I made it clearly a [Datisi](https://philosophy.stackexchange.com/a/34341/2014)-type syllogism now. Does it still suffer from the four terms fallacy? – Geremia Aug 16 '19 at 21:34
  • @here is, please rewrite the syllogism so I can see it. Currently I do not see the syllogism a datisi only expresses the moo. You need the figure as well to determine validity. – Logikal Aug 16 '19 at 21:43
  • Subject terms as well as predicate terms ought to be concrete nouns or noun clauses. That is no adverbs or adjectives because they can be vague or ambiguous. So you can't use predicates in philosophy such as healthy, tall, beauty, fast, slow, handsome, etc. Perhaps you can pull those off in math but not with categorical syllogisms. – Logikal Aug 16 '19 at 21:53
  • @Logikal Can you come up with a better example with an analogical middle term? – Geremia Aug 17 '19 at 04:48