Aquinas Day by Day: Logic of Judgments: Logical Properties of Propositions

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Aquinas’ Topic: Logic of Judgments: Logical Properties of Propositions

Scripture: Luke 15:1-4

“Tax collectors and sinners were all drawing near to listen to Jesus, but the Pharisees and scribes began to complain, saying, ‘This man welcomes sinners and eats with them.’ So to them Jesus addressed this parable. ‘What man ;a;mong you with a hundred sheep, losing one, would not leave the ninety-nine in the wilderness and go after the missing one till he found it?”

Aquinas’ text: Expositio libri Peryermenias Bk. 1, lec. 13, n.2-3

Here Aquinas sums up the results of analyzing propositions based on their quality (affirmative or negative), quantity (universal or particular), time, and matter (necessary, impossible, or possible).  The simplified version of this doctrine developed in the middle ages was to use the Latin words affirmo and nego as mneymonic devices to distinguish four kinds of categorical propositions: universal affirmative (A), particular affirmative (I), universal negative (E), and particular negative (O).

2. Note that the Philosopher has given three divisions of the proposition. The first was based on the unity of the proposition, and according to this a proposition is one proposition absolutely or it is one by conjunction. The second was based on quality, and according to this a proposition is affirmative or negative. And the third was based on quantity, and according to this a proposition is either universal, particular, indefinite, or singular.

3] Here he treats of a fourth division of propositions, one based on time. Some propositions are about the present, others about the past, and still others are about the future. Now this division can be taken from what Aristotle has already said, namely, that every proposition must have a verb or a mode of a verb, the verb being that which signifies the present time, the modes with past or future time.

Now a fifth division of propositions can be seen, based on matter. This division is taken from the relation of predicate to subject. If the predicate is in the subject essentially [per se], the proposition it will be said to be about necessary or natural matter; for example, the propositions “A human is an animal,” and “A human is risible.” But if the predicate essentially [per se] is repugnant to the subject as excluding its meaning, the proposition will be said to be about impossible or removed matter; for example, the proposition “A human is an ass.” But if the predicate is related to the subject in a way midway between these two, neither essentially repugnant to the subject nor in it essentially, the proposition will be said to be about possible or contingent matter.

2] Circa primum considerandum est quod philosophus in praemissis triplicem divisionem enunciationum assignavit, quarum prima fuit secundum unitatem enunciationis, prout scilicet enunciatio est una simpliciter vel coniunctione una; secunda fuit secundum qualitatem, prout scilicet enunciatio est affirmativa vel negativa; tertia fuit secundum quantitatem, utpote quod enunciatio quaedam est universalis, quaedam particularis, quaedam indefinita et quaedam singularis.

3] Tangitur autem hic quarta divisio enunciationum secundum tempus. Nam quaedam est de praesenti, quaedam de praeterito, quaedam de futuro; et haec etiam divisio potest accipi ex his quae supra dicta sunt: dictum est enim supra quod necesse est omnem enunciationem esse ex verbo vel ex casu verbi; verbum autem est quod consignificat praesens tempus; casus autem verbi sunt, qui consignificant tempus praeteritum vel futurum.

Potest autem accipi quinta divisio enunciationum secundum materiam, quae quidem divisio attenditur secundum habitudinem praedicati ad subiectum: nam si praedicatum per se insit subiecto, dicetur esse enunciatio in materia necessaria vel naturali; ut cum dicitur, homo est animal, vel, homo est risibile. Si vero praedicatum per se repugnet subiecto quasi excludens rationem ipsius, dicetur enunciatio esse in materia impossibili sive remota; ut cum dicitur, homo est asinus. Si vero medio modo se habeat praedicatum ad subiectum, ut scilicet nec per se repugnet subiecto, nec per se insit, dicetur enunciatio esse in materia possibili sive contingenti.

[Introductions and translations © R.E. Houser]