Infinity in ontology and mind

Axiomathes 18 (1):1-24 (2008)
Two fundamental categories of any ontology are the category of objects and the category of universals. We discuss the question whether either of these categories can be infinite or not. In the category of objects, the subcategory of physical objects is examined within the context of different cosmological theories regarding the different kinds of fundamental objects in the universe. Abstract objects are discussed in terms of sets and the intensional objects of conceptual realism. The category of universals is discussed in terms of the three major theories of universals: nominalism, realism, and conceptualism. The finitude of mind pertains only to conceptualism. We consider the question of whether or not this finitude precludes impredicative concept formation. An explication of potential infinity, especially as applied to concepts and expressions, is given. We also briefly discuss a logic of plural objects, or groups of single objects (individuals), which is based on Bertrand Russell’s (1903, The principles of mathematics, 2nd edn. (1938). Norton & Co, NY) notion of a class as many. The universal class as many does not exist in this logic if there are two or more single objects; but the issue is undecided if there is just one individual. We note that adding plural objects (groups) to an ontology with a countable infinity of individuals (single objects) does not generate an uncountable infinity of classes as many.
Keywords Formal ontology  Ontology  Universals  Conceptual realism  Conceptualism  Nominalism  Logical realism  Natural realism  Plural objects  Infinity  Potential infinity
Categories (categorize this paper)
DOI 10.1007/s10516-007-9028-6
 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
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 28,824
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
From a Logical Point of View.W. V. Quine - 1953 - Harvard University Press.
A Model of the Universe.Storrs McCall - 1994 - Clarendon Press.
The Metaphysic of Abstract Particulars.Keith Campbell - 1981 - Midwest Studies in Philosophy 6 (1):477-488.

View all 7 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

59 ( #90,100 of 2,178,151 )

Recent downloads (6 months)

1 ( #316,504 of 2,178,151 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums