The move from one to two quantifiers

Wilfrid Hodges

pp. 221-240

in: Arnold Koslow, Arthur Buchsbaum (eds), The road to universal logic I, Basel, Birkhäuser, 2015

Abstract

Ibn Sīnā (Persian, 980–1037) made a dramatic extension to Aristotle's syllogistic by adding quantifiers over times or situations, thus introducing multiple and mixed quantification. The extension is unlike anything in the Latin Scholastic logic, but related extensions to syllogistic appear later in work of Leibniz and of Peirce's student Mitchell. Ibn Sīnā's version was the most integrated and systematic of these three, but at the same time it was the furthest from modern perspectives. We examine from a modern point of view the limitations, proof-theoretic and otherwise, which Ibn Sīnā's highly original introduction of multiple quantification failed to overcome.

Cited authors

Leibniz Gottfried Wilhelm

Aristoteles

Peirce Charles Sanders