Erkenntnis 53 (1-2):219-265 (2000)

Edward Zalta
Stanford University
In this paper, we describe "metaphysical reductions", in which the well-defined terms and predicates of arbitrary mathematical theories are uniquely interpreted within an axiomatic, metaphysical theory of abstract objects. Once certain (constitutive) facts about a mathematical theory T have been added to the metaphysical theory of objects, theorems of the metaphysical theory yield both an analysis of the reference of the terms and predicates of T and an analysis of the truth of the sentences of T. The well-defined terms and predicates of T are analyzed as denoting abstract objects and abstract relations, respectively, in the background metaphysics, and the sentences of T have a reading on which they are true. After the technical details are sketched, the paper concludes with some observations about the approach. One important observation concerns the fact that the proper axioms of the background theory abstract objects can be reformulated in a way that makes them sound more like logical axioms. Some philosophers have argued that we should accept (something like) them as being logical.
Keywords Philosophy   Philosophy   Epistemology   Ethics   Logic   Ontology
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Reprint years 2004
DOI 10.1023/A:1005614102033
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References found in this work BETA

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Empiricism, Semantics and Ontology.Rudolf Carnap - 1950 - Revue Internationale de Philosophie 4 (11):20-40.

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Citations of this work BETA

Truth in Fiction: Rethinking its Logic.John Woods - 2018 - Cham, Switzerland: Springer Verlag.
Essence and Modality.Edward N. Zalta - 2006 - Mind 115 (459):659-693.
Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
What is Neologicism?Bernard Linsky & Edward N. Zalta - 2006 - Bulletin of Symbolic Logic 12 (1):60-99.

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