I have not (yet) studied Ancient Greek. This comment introduced me to the pertinence of Aristotle's Prior Analytics, but the translation and commentary below do not answer question entitled above.

Source: Aristotle's Prior Analytics: Book I, Translated with an introduction and commentary (2009) by Gisela Striker

[page 5, Chapter 4, 26a, Lines 22-23]
(I call 'major' the extreme that contains the middle and 'minor' the one that is under the middle.)

[page 97] 26a21-23 '"major" . . . "minor"'. The labels 'major' and 'minor' presumably derive from a syllogism in Barbara with true premis ses, though this time Aristotle says that the minor is 'under' the middle because the second premiss is particular, so that the minor term need not be included in the middle (for similar uses of 'under' , cf. 9, 30a40; I I , 3 P30, b 1 7) . According to the tradition, the major and the minor are the predicate and the subject term of the conclusion. However, this holds only so long as one considers only conclusions with a specific order of terms. Since Aristotle defined the figures only by reference to their premisses , he determines the major and the minor in the second and third figure by their position in the standard formulation of the premisses (see [page] 5, 26b37-8; [page] 6, 28a13-14). Used in this way, the labels have no longer anything to do with the extensions of the respective terms.

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    24b27-24b30 : "That one term should be in another as in a whole is the same as for the other to be predicated of all of the first." 25b32-26a2 : "If A is predicated of every B, and B of every C, A must be predicated of every C: we have already explained what we mean by ‘predicated of every’." Thus, "A is predicated of every B" can be read as "B should be in A as in a whole". – Mauro ALLEGRANZA Jun 4 '16 at 17:32
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    Doesn't what you quote answer your question? – Geremia Jun 4 '16 at 19:44

The terminology of 'major' and 'minor' terms is not Aristolelian. It is Latin and mediaeval. What we call the major term was called by Aristotle to meizon, to proton. His to elatton, to eschaton translate across to our minor term.

In the syllogism :

  1. All living things are mortal

  2. All humans are living things

  3. All humans are mortal

the major term is 'mortal' and the minor term 'humans'. As noted in your quote, the minor term is the subject of the conclusion and the major term the predicate. So : 'Humans (subject - minor term) are mortal (predicate - major term).

Why 'major' and 'minor' ? The major term denotes a wider, more extended class; the minor a more restricted, less extended class. Thus the class of humans (minor) is a smaller, more restricted class than the class of mortals (wider). 'Major' and 'minor' have a certain plausibility for expressing this distinction.

A refinement: 'the minor term is the subject of the conclusion and the major term the predicate'. However, this holds only so long as one considers only conclusions with a specific order of terms, as you quote. That's right. It holds good for the kind of syllogism above but Aristotle by analogy tends to refer to the subject of the conclusion of any syllogism as the 'minor' term (or his Greek equivalents), and to the predicate as the 'major' (or his Greek equivalents again) - even when considerations of extension do not apply.

For the Greek terminology see Prior Analytics, IV.

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