Wednesday, July 28, 2010

Plural quantification and scholasticism

More discussion of plurals at the Maverick Philosopher. Very topical now, but it has been discussed before. Thomas Aquinas:

Unde videtur quod quidquid potest facere unus, possint facere multi, et non e
converso, sicut multi trahunt navem quam unus trahere non posset
- "it is clear
that whatever one can do, many can do, but not conversely. For example, many
persons drag the boat which one person could not drag". Summa Theologiae
III 67 a6 (See also Sententia Metaphysicae, lib. 5 l. 2 n. 11).

Aquinas was writing in the 1260's, but the idea is probably older than that. See e.g. Lambert of Auxerre:

Similiter est suppositio confusa sed immobilis quando signum additur
termino communi in singulari vel in plurali et tenetur collective ut cum
dicitur: 'omnis homo trahit navem', positione facta quod omnes homines trahunt
navem et nullus per se, et similiter cum dicitur: omnes apostoli sunt
"Similarly, confused but immobile supposition is when the
(quantifying) sign is applied to a common term in the singular or plural and is
understood collectively, as in 'every man drags the boat', assuming that all the
men are dragging the boat and none of them by himself. And similarly in 'all the
apostles are twelve'. (Logica, "De suppositionibus et de significationibus")

Later, William of Ockham discussed the 'Apostles' example in his Summa Logicae II. 4.

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