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Daniel COHNITZ ;THEORIA. Revista de Teoría, Historia y Fundamentos de la Ciencia 2009, 24 2

Author: Marcus ROSSBERG

Source: http://www.redalyc.org/articulo.oa?id=339730809003


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THEORIA.
Revista de Teoría, Historia y Fundamentos de la Ciencia ISSN: 0495-4548 theoria@ehu.es Universidad del País Vasco-Euskal Herriko Unibertsitatea España ROSSBERG, Marcus; COHNITZ, Daniel Logical Consequence for Nominalists THEORIA.
Revista de Teoría, Historia y Fundamentos de la Ciencia, vol.
24, núm.
2, 2009, pp.
147168 Universidad del País Vasco-Euskal Herriko Unibertsitatea Donostia-San Sebastián, España Available in: http:--www.redalyc.org-articulo.oa?id=339730809003 How to cite Complete issue More information about this article Journals homepage in redalyc.org Scientific Information System Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Non-profit academic project, developed under the open access initiative Logical Consequence for Nominalists Marcus ROSSBERG and Daniel COHNITZ BIBLID [0495-4548 (2009) 24: 65; pp.
147-168] ABSTRACT: It has repeatedly been argued that nominalistic programmes in the philosophy of mathematics fail, since they will at some point or other involve the notion of logical consequence which is unavailable to the nominalist.
In this paper we will argue that this is not the case.
Using an idea of Nelson Goodman and W.V.
Quines which they developed in Goodman and Quine (1947) and supplementing it with means that should be nominalistically acceptable, we present a way to explicate logical consequence in a nominalistically acceptable way. Keywords: Philosophy of mathematics, nominalism, logical consequence, inferentialism, Nelson Goodman, W.V.
Quine. 1. The Argument from Logical Consequence We do not have any strong convictions concerning the question of the existence or nonexistence of abstract objects.
We do, however, believe that ontological fastidiousness is prima facie a good attitude to adopt.
More precisely, ontological parsimony provides a pro tanto reason for theory choice.
Nelson Goodman added to this fairly obvious principle the methodological observation that a more par...





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