David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Erkenntnis 53 (1-2):219-265 (2000)
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Otávio Bueno, Christopher Menzel & Edward N. Zalta (2013). Worlds and Propositions Set Free. Erkenntnis (4):1-24.
Edward N. Zalta (2002). A Common Ground and Some Surprising Connections. Southern Journal of Philosophy 40 (S1):1-25.
Edward N. Zalta (2002). A Common Ground and Some Surprising Connections. Southern Journal of Philosophy (Supplement) 40 (S1):1-25.
Similar books and articles
Christopher Menzel (1987). Theism, Platonism, and the Metaphysics of Mathematics. Faith and Philosophy 4 (4):365-382.
John Bigelow (1988). The Reality of Numbers: A Physicalist's Philosophy of Mathematics. Oxford University Press.
G. Landini (2011). Logicism and the Problem of Infinity: The Number of Numbers. Philosophia Mathematica 19 (2):167-212.
Edward N. Zalta (2006). Deriving and Validating Kripkean Claims Using the Theory of Abstract Objects. Noûs 40 (4):591–622.
David J. Anderson & Edward N. Zalta (2004). Frege, Boolos, and Logical Objects. Journal of Philosophical Logic 33 (1):1-26.
Branden Fitelson & Edward N. Zalta (2007). Steps Toward a Computational Metaphysics. Journal of Philosophical Logic 36 (2):227-247.
Philip A. Ebert & Marcus Rossberg (2009). Ed Zalta's Version of Neo-Logicism: A Friendly Letter of Complaint. In Hannes Leitgeb & Alexander Hieke (eds.), Reduction – Abstraction – Analysis. Ontos 11--305.
Edward N. Zalta (2000). A (Leibnizian) Theory of Concepts. Logical Analysis and History of Philosophy 3:137-183.
Edward N. Zalta (1999). Natural Numbers and Natural Cardinals as Abstract Objects: A Partial Reconstruction of Frege"s Grundgesetze in Object Theory". [REVIEW] Journal of Philosophical Logic 28 (6):619-660.
Added to index2009-01-28
Total downloads42 ( #96,376 of 1,793,264 )
Recent downloads (6 months)9 ( #89,724 of 1,793,264 )
How can I increase my downloads?