The mediaeval logic of Aristotelian privation, represented by Ockham's expositionof All A is non-P as All S is of a type T that is naturally P and no S is P, iscritically evaluated as an account of privative negation. It is argued that there aretwo senses of privative negation: (1) an intensifier (as in subhuman), the dualof Neoplatonic hypernegation (superhuman), which is studied in linguistics asan operator on scalar adjectives, and (2) a (often lexicalized) Boolean complementrelative to the extension of (...) a privative negation in sense (1) (e.g., Brute). Thissecond sense, which is the privative negation discussed in modern linguistics, isshown to be Aristotle's. It is argued that Ockham's exposition fails to capture muchof the logic of Aristotelian privation due to limitations in the expressive power of thesyllogistic. (shrink)

Though acknowledged by scholars, Plato’s identification of the Beautiful and the Good has generated little interest, even in aesthetics where the moral concepts are a current topic. The view is suspect because, e.g., it is easy to find examples of ugly saints and beautiful sinners. In this paper the thesis is defended using ideas from Plato’s ancient commentators, the Neoplatonists. Most interesting is Proclus, who applied to value theory a battery of linguistic tools with fixed semantic properties—comparative adjectives, associated gradable (...) adjectives, mass nouns, and predicate negations—all with a semantics that demand a privative scale of value. It is shown how it is perfectly possible to interpret value terms Platonically over privative Boolean algebras so that beautifuland good diverge while at higher levels other value terms are coextensional. Considerations are offered that this structure conforms to actual usage. (shrink)

This paper explores the modal interpretation of ?ukasiewicz's n -truth-values, his conditional and the puzzles they generate by exploring his suggestion that by ?necessity? he intends the concept used in traditional philosophy. Scalar adjectives form families with nested extensions over the left and right fields of an ordering relation described by an associated comparative adjective. Associated is a privative negation that reverses the ?rank? of a predicate within the field. If the scalar semantics is interpreted over a totally ordered domain (...) of cardinality n and metric ?, an n-valued Lukasiewicz algebra is definable. Privation is analysed in terms of non-scalar adjectives. Any Boolean algebra of 2 n ?properties? determines an n + 1 valued Lukasiewicz algebra. The Neoplatonic ?hierarchy of Being? is essentially the order presupposed by natural language modal scalars. ?ukasiewicz's ≈ is privative negation, and ? proves to stand for the extensional (antitonic) dual if ? then for scalar adjectives, especially modals. Relations to product logics and frequency interpretations of probability are sketched. (shrink)

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. (shrink)

This paper argues that Malebranche’s semantics sheds light on his metaphysics and epistemology, and is of interest in its own right. By recasting issues linguistically, it shows that Malebranche assumes a Neoplatonic semantic structure within Descartes’ dualism and Augustine’s theory of illumination, and employs linguistic devices from the Neoplatonic tradition. Viewed semantically, mental states of illumination stand to God and his ideas as predicates stand in Neoplatonic semantics to ideas ordered by a privative relation on “being.” The framework sheds light (...) on interpretive puzzles in Malebranche studies such as the way ideas reside in God’s mind, the notion of resemblance by which bodies imitate their exemplar causes, and the issue of direct vs. indirect perception through a mechanism by which agents can see bodies by “seeing” ideas. Malebranche’s semantics is of interest in its own right because it gives a full account of the mediating relations that determine indirect reference; lays out a correspondence theory of truth for necessary judgments; defines contingent truth as based on an indirect reference relation that is both descriptive and causal but that does not appeal to body-mind causation; and within his theory of perception, works out an account of singular reference in which singular terms carry existential import, refer indirectly via causal relations, but describe their referents only in a general way. (shrink)