Are analogical middle terms sufficient for a valid demonstration?



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)


Posted 2015-01-23T03:56:43.033

Reputation: 6 907

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 – 2015-01-23T09:10:48.680

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 – 2015-01-23T12:02:24.383



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.


Posted 2015-01-23T03:56:43.033


You wrote a fallacy of four terms example. I don’t think this would apply to the question. – Logikal – 2019-07-31T01:56:16.670

@Logikal Yes, it seemed so. I changed the major premise. Does the syllogism still suffer from the same fallacy? – Geremia – 2019-08-16T21:03:36.803

@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 – 2019-08-16T21:26:08.050

@Logikal I made it clearly a Datisi-type syllogism now. Does it still suffer from the four terms fallacy?

– Geremia – 2019-08-16T21:34:41.943

@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 – 2019-08-16T21:43:33.193

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 – 2019-08-16T21:53:02.957

@Logikal Can you come up with a better example with an analogical middle term? – Geremia – 2019-08-17T04:48:38.880

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. – None – 2015-01-23T04:20:03.940

Could you provide any references for further reading? thanks – Geremia – 2015-01-23T04:36:24.600


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: A somewhat different take can be found in:

– None – 2015-01-23T12:54:06.497

Those books treat the logical aspects of analogy, specifically? – Geremia – 2015-01-24T01:20:31.453

1McInerny def does. Don't recall about the other haven't read them in years. – None – 2015-01-24T01:21:58.023

Actually, McInerny's The Logic of Analogy sounds more relevant.

– Geremia – 2015-01-28T04:39:42.777