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Philosophical Perspectives on Formal Theories of Predication

In Dov M. Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic. Dordrecht, Netherland: Kluwer Academic Publishers. pp. 253--326 (1983)

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  1. Logic and Ontology.Nino B. Cocchiarella - 2001 - Axiomathes 12 (1-2):117-150.
    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 (...)
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  • Reference to Abstract Objects in Discourse.Nicholas Asher - 1993 - Dordrecht, Boston, and London: Kluwer.
    This volume is about abstract objects and the ways we refer to them in natural language. Asher develops a semantical and metaphysical analysis of these entities in two stages. The first reflects the rich ontology of abstract objects necessitated by the forms of language in which we think and speak. A second level of analysis maps the ontology of natural language metaphysics onto a sparser domain--a more systematic realm of abstract objects that are fully analyzed. This second level reflects the (...)
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  • Toward a modal-structural interpretation of set theory.Geoffrey Hellman - 1990 - Synthese 84 (3):409 - 443.
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  • Some Notes on Boolos’ Semantics: Genesis, Ontological Quests and Model-Theoretic Equivalence to Standard Semantics.Francesco Maria Ferrari - 2018 - Axiomathes 28 (2):125-154.
    The main aim of this work is to evaluate whether Boolos’ semantics for second-order languages is model-theoretically equivalent to standard model-theoretic semantics. Such an equivalence result is, actually, directly proved in the “Appendix”. I argue that Boolos’ intent in developing such a semantics is not to avoid set-theoretic notions in favor of pluralities. It is, rather, to prevent that predicates, in the sense of functions, refer to classes of classes. Boolos’ formal semantics differs from a semantics of pluralities for Boolos’ (...)
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  • An argument against nominalism.Francesco Maria Ferrari - 2022 - Synthese 200 (5):1-23.
    Nominalism in formal ontology is still the thesis that the only acceptable domain of quantification is the first-order domain of particulars. Nominalists may assert that second-order well-formed formulas can be fully and completely interpreted within the first-order domain, thereby avoiding any ontological commitment to second-order entities, by means of an appropriate semantics called “substitutional”. In this paper I argue that the success of this strategy depends on the ability of Nominalists to maintain that identity, and equivalence relations more in general, (...)
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  • Quantifying over the reals.Philip Hugly & Charles Sayward - 1994 - Synthese 101 (1):53 - 64.
    Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...)
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  • Predication versus membership in the distinction between logic as language and logic as calculus.Nino Cocchiarella - 1988 - Synthese 77 (1):37 - 72.
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  • Adventures of abstraction.Ignacio Angelelli - 2004 - Poznan Studies in the Philosophy of the Sciences and the Humanities 82 (1):11-35.
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