It is shown that two formally consistent type-free second-order systems, due to Cocchiarella, and based on the notion of homogeneous stratification, are subject to a contingent version of Russell's paradox.

A brief review of the historicalrelation between logic and ontologyand of the opposition between the viewsof logic as language and logic as calculusis given. We argue that predication is morefundamental than membership and that differenttheories of predication are based on differenttheories of universals, the three most importantbeing nominalism, conceptualism, and realism.These theories can be formulated as formalontologies, each with its own logic, andcompared with one another in terms of theirrespective explanatory powers. After a briefsurvey of such a comparison, we argue (...) that anextended form of conceptual realism provides themost coherent formal ontology and, as such, canbe used to defend the view of logic as language. (shrink)

Castañeda’s guise theory is a peculiarly interesting Neo-Meinongian approach, in virtue of its bundle-theoretic and anti-representationalist features. But it also has some problematic aspects. It crucially relies on a series of sameness relations, such as consubstantiation or consociation, but this list is incomplete. Moreover, guise theory is hindered by its view of the sameness relations as forms of predication alternative to what may be called, following Plantinga, standard predication. This paper thus proposes a revised version of guise theory that acknowledges (...) two additional sameness relations and standard predication. (shrink)

This paper embeds a theory of proper names in a general approach to singular reference based on type‐free property theory. It is proposed that a proper name “N” is a sortal common noun whose meaning is essentially tied to the linguistic type “N”. Moreover, “N” can be singularly referring insofar as it is elliptical for a definite description of the form the “N” Following Montague, the meaning of a definite description is taken to be a property of properties. The proposed (...) theory fulfils the major desiderata stemming from Kripke's works on proper names. (shrink)

The problematic features of Quine's set theories NF and ML are a result of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-order logic of predication with nominalized predicates as abstract singular terms. We adopt a modified Fregean position called conceptual realism in which the concepts (unsaturated cognitive structures) that predicates stand for are distinguished from the extensions (or intensions) that their nominalizations denote as singular (...) terms. We argue against Quine's view that predicate quantifiers can be given a referential interpretation only if the entities predicates stand for on such an interpretation are the same as the classes (assuming extensionality) that nominalized predicates denote as singular terms. Quine's alternative of giving predicate quantifiers only a substitutional interpretation is compared with a constructive version of conceptual realism, which with a logic of nominalized predicates is compared with Quine's description of conceptualism as a ramified theory of classes. We argue against Quine's implicit assumption that conceptualism cannot account for impredicative concept-formation and compare holistic conceptual realism with Quine's class Platonism. (shrink)

2020 update of the entry "Properties".

This paper embeds a theory of proper names in a general approach to singular reference based on type‐free property theory. It is proposed that a proper name “N” is a sortal common noun whose meaning is essentially tied to the linguistic type “N”. Moreover, “N” can be singularly referring insofar as it is elliptical for a definite description of the form the “N” Following Montague, the meaning of a definite description is taken to be a property of properties. The proposed (...) theory fulfils the major desiderata stemming from Kripke's works on proper names. (shrink)

Konolige''s technical notion of belief based on deduction structures is briefly reviewed and its usefulness for the design of artificial agents with limited representational and deductive capacities is pointed out. The design of artificial agents with more sophisticated representational and deductive capacities is then taken into account. Extended representational capacities require in the first place a solution to the intensional context problems. As an alternative to Konolige''s modal first-order language, an approach based on type-free property theory is proposed. It considers (...) often neglected issues, such as the need for a more general account of thede dicto-de re distinction, and quasi-indicators. Extended deductive capacities require a subdivision of Konolige''s notion of belief into two distinct technical notions,potential anddispositional belief. The former has to do with what an artificial agent could in principle come to actively believe, given enough time and its specific logical competence; the latter with what an agent can be assumed to believe with respect to a specific goal to be fulfilled. (shrink)

We develop a set-theoretic semantics for Cocchiarella's second-order logical system . Such a semantics is a modification of the nonstandard sort of second-order semantics described, firstly, by Simms and later extended by Cocchiarella. We formulate a new second order logical system and prove its relative consistency. We call such a system and construct its set-theoretic semantics. Finally, we prove completeness theorems for proper normal extensions of the two systems with respect to certain notions of validity provided by the semantics.

Peter Geach's puzzle of intentional identity is to explain how the claim ‘Hob thinks a witch has blighted Bob's mare, and Nob wonders whether she killed Cob's sow’ is compatible with there being no such witch. I clarify the puzzle and reduce it to the familiar problem of negative existentials. That problem is a paradox of representations that seem to include denials of commitment , to carry commitment to what they deny commitment to, and to be true. The best proposed (...) solutions can be understood through this paradox; I evaluate them, and defend a new solution. (shrink)

Poetic license is an essential feature of intentionality. The mind is free to think about any objects, even objects with logically incompatible properties. Some philosophers maintain that a theory that embraces an ontology of objects of thought is indispensable to any account of the nature of intentionality. Any such theory, however, must face paradoxes whose solutions conflict with poetic license. In this paper, I propose a theory which rejects the argument from indispensability. The theory maintains that the intentionality of thought (...) is produced by the quantificational nature of the apparatus of thought. All de re ascriptions of propositional attitudes must respect simple-type stratification and quantify over concepts with a predicable nature only. There are no fictional objects. There are concepts which, in the impredicative reflections of quantificational thought, are presented as if objects of thought. (shrink)

A conceptual theory of the referential and predicable concepts used in basic speech and mental acts is described in which singular and general, complex and simple, and pronominal and nonpronominal, referential concepts are given a uniform account. The theory includes an intensional realism in which the intensional contents of predicable and referential concepts are represented through nominalized forms of the predicate and quantifier phrases that stand for those concepts. A central part of the theory distinguishes between active and deactivated referential (...) concepts, where the latter are represented by nominalized quantifier phrases that occur as parts of complex predicates. Peter Geach's arguments against theories of general reference in Reference and Generality are used as a foil to test the adequacy of the theory. Geach's arguments are shown to either beg the question of general as opposed to singular reference or to be inapplicable because of the distinction between active and deactivated referential concepts. (shrink)