Online research in philosophy

This is the only complete logic for properties, relations, and propositions (PRPS) that has been formulated to date. First, an intensional abstraction operation is adjoined to first-order quantifier logic, Then, a new algebraic semantic method is developed. The heuristic used is not that of possible worlds but rather that of PRPS taken at face value. Unlike the possible worlds approach to intensional logic, this approach yields a logic for intentional (psychological) matters, as well as modal matters. At the close of the paper, the origin of incompleteness in logic is investigated. The culprit is found to be the predication relation, a relation on properties and relations that is expressed in natural language by the copula.

In H-N. Castañeda's ontology, a fundamental Fregean distinction is drawn between unsaturated and saturated entities, the former corresponding to predicative aspects of reality, the latter to individuals, that is, to items which can be referred to by means of singular terms1. Within saturated entities, Castañeda attempts to distinguish between abstract and concrete individuals. Sets and Platonic Forms of the F-ness-type are the typical examples of the former category2. As to the latter category instead, concrete individual guises represent both the bottom layer in a hypothetical ontological hierarchy of individuals which has Platonic Forms at its top, and the first step in the psychological process of world cognition, which moves from the most concrete object to the most abstract3. Among concrete individual guises, moreover, Castañeda draws a further ontological distinction between possible and impossible guises, according to the different behavior guises display with respect to the possibility of existing4. Both kinds of guises, however, share that feature which enables to qualify them as guises, i.e. that of being bundles of properties. Every guise is indeed constituted out of (a certain set of) properties, or better predicative aspects5. The predication to a guise of one of its constitutive properties is taken by Castañeda as the primary sense of predication. He calls it Meinongian, or internal, predication (in symbols: "a(F)", where "a" stands for a guise and "F" for one of its constitutive properties)6. For Castañeda, moreover, the main linguistic tool by means of which a guise is denoted is a definite description, insofar as such a description clearly reveals the properties which a guise internally possesses7. Thus, we can say that "the F- er is F" is a typical expression of an internal predication of a property F to the guise denoted by the definite description "the F". If we take "F" as a metavariable for properties, we can say that the above formulation corresponds to what Routley has called the Characterization Postulate8. Now what we want to scrutinize in this paper is, first, whether the following four theses of Castañeda's Guise Theory are really compatible..

Egan argues against Lewis’s view that properties are sets of actual and possible individuals and in favour of the view that they are functions from worlds to extensions (sets of individuals). Egan argues that Lewis’s view implies that 2nd order properties are never possessed contingently by their (1st order) bearers, an implication to which there are numerous counter-examples. And Egan argues that his account of properties is more commensurable with the role they play as the semantic values of predicates than is Lewis’s.

Higher-order theories of properties, relations, and propositions are known to be essentially incomplete relative to their standard notions of validity. It turns out that the first-order theory of PRPs that results when first-order logic is supplemented with a generalized intensional abstraction operation is complete. The construction involves the development of an intensional algebraic semantic method that does not appeal to possible worlds, but rather takes PRPs as primitive entities. This allows for a satisfactory treatment of both the modalities and the propositional attitudes, and it suggests a general strategy for developing a comprehensive treatment of intensional logic.

Identity, existence, predication, necessity, and truth are vital concepts at the center of philosophy. Yet Colin McGinn believes that orthodox views of these topics are misguided in important ways. Philosophers and logicians have often distorted the nature of these concepts in an attempt to define them according to preconceived ideas. Logical Properties aims to respect the ordinary ways we talk and think when we employ these concepts, while at the same time showing that they are far more interesting and peculiar than some have assumed; these notions correspond to real properties--logical properties--that challenge naturalistic metaphysical views. Written with a minimum of formal terminology, this book deals with logico-linguistic issues as well as ontological ones. The focus is on trying to get to the essence of the concept concerned, not merely finding some established notation for providing formal interpretations.

Terence Parsons's informal theory of intentional objects, their properties, and modes of predication does not adequately reflect ordinary ways of speaking and thinking. Meinongian theories recognizing two modes of predication are defended against Parsons's theory of two kinds of properties. Against Parsons's theory of fictional objects, I argue that no existing entities appear in works of fiction. A formal version of Parsons's theory is presented, and a curious consequence about modes of predication is indicated.

Problems about the accidental properties of properties motivate us--force us, I think--not to identify properties with the sets of their instances. If we identify them instead with functions from worlds to extensions, we get a theory of properties that is neutral with respect to disputes over counterpart theory, and we avoid a problem for Lewis's theory of events. Similar problems about the temporary properties of properties motivate us--though this time they probably don't force us--to give up this theory as well, and to identify properties with functions from world, time pairs to extensions. Again, the replacement theory is neutral with respect to a metaphysical dispute that the old theory (arguably) forces us to take a stand on--the dispute over whether objects have temporal parts. It also allows us to give a smoother semantics for predication, to better accommodate our intuitions about which objects temporary properties are properties of, and to make temporally self-locating beliefs genuinely self -locating.

Problems about the accidental properties of properties motivate us--force us, I think--not to identify properties with the sets of their instances. If we identify them instead with functions from worlds to extensions, we get a theory of properties that is neutral with respect to disputes over counterpart theory, and we avoid a problem for Lewis's theory of events. Similar problems about the temporary properties of properties motivate us--though this time they probably don't force us--to give up this theory as well, and to identify properties with functions from world, time pairs to extensions. Again, the replacement theory is neutral with respect to a metaphysical dispute that the old theory (arguably) forces us to take a stand on--the dispute over whether objects have temporal parts. It also allows us to give a smoother semantics for predication, to better accommodate our intuitions about which objects temporary properties are properties of, and to make temporally self-locating beliefs genuinely self -locating.

In this paper I rehearse two central failings of traditional possible world semantics. I then present a much more robust framework for intensional logic and semantics based liberally on the work of George Bealer in his book Quality and Concept. Certain expressive limitations of Bealer's approach, however, lead me to extend the framework in a particularly natural and useful way. This extension, in turn, brings to light associated limitations of Bealer's account of predication. In response, I develop a more general and intuitively more adequate account of the logical form of predication.

In the paper a theory of relevant properties is developed. The theory permits us to distinguish between properties that are relevant to an object and the properties that are irrelevant to it. Predication is meaningful only if a property is relevant to an object. On the base of introducing a special negative type of predication as opposed to usual sentential negation, a new notion of generalization for properties is defined. Context-free, as weIl as context-depended relevance of properties are considered.