Neo-logicism? An ontological reduction of mathematics to metaphysics

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)
DOI 10.1023/A:1005614102033
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 15,879
External links
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.

Add more references

Citations of this work BETA
Edward N. Zalta (2002). A Common Ground and Some Surprising Connections. Southern Journal of Philosophy (Supplement) 40 (S1):1-25.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

32 ( #98,697 of 1,725,158 )

Recent downloads (6 months)

8 ( #81,204 of 1,725,158 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.