Proclus and the neoplatonic syllogistic

Journal of Philosophical Logic 30 (3):187-240 (2001)
Abstract
An investigation of Proclus' logic of the syllogistic and of negations in the Elements of Theology, On the Parmenides, and Platonic Theology. It is shown that Proclus employs interpretations over a linear semantic structure with operators for scalar negations (hypemegationlalpha-intensivum and privative negation). A natural deduction system for scalar negations and the classical syllogistic (as reconstructed by Corcoran and Smiley) is shown to be sound and complete for the non-Boolean linear structures. It is explained how Proclus' syllogistic presupposes converting the tree of genera and species from Plato's diairesis into the Neoplatonic linear hierarchy of Being by use of scalar hyper and privative negations
Keywords Proclus  syllogistic  negation  scalar adjective  hypernegation  privative negation  Neoplatonism   via negativa  negative theology
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John N. Martin (2011). Existential Import in Cartesian Semantics. History and Philosophy of Logic 32 (3):211-239.
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