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dc.contributor.author Cocchiarella, Nino
dc.date.accessioned 2018-08-06T16:40:18Z
dc.date.available 2018-08-06T16:40:18Z
dc.date.issued 2008-03
dc.identifier.citation Cocchiarella, N. "Infinity in Ontology and Mind," Axiomathes 18 (2008): 1-24. en
dc.identifier.uri http://hdl.handle.net/2022/22325
dc.description This is a post-peer-review, pre-copyedit version of an article published in Axiomathes. The final authenticated version is available online at: https://doi.org/10.1007/s10516-007-9028-6 en
dc.description.abstract 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. en
dc.language.iso en en
dc.publisher Axiomathes en
dc.relation.isversionof https://link.springer.com/article/10.1007%2Fs10516-007-9028-6 en
dc.subject Formal ontology en
dc.subject Ontology en
dc.subject Universals en
dc.subject Conceptual realism en
dc.subject Conceptualism en
dc.subject Nominalism en
dc.subject Logical realism en
dc.subject Natural realism en
dc.subject Plural objects en
dc.subject Infinity en
dc.subject Potential infinity en
dc.subject Quantum mechanics en
dc.subject Multiverse en
dc.subject String theory en
dc.title Infinity in Ontology and Mind en
dc.type Article en
dc.identifier.doi 10.1007/s10516-007-9028-6


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