Numerical Abstraction via the Frege Quantifier
Antonelli, G. Aldo
Notre Dame J. Formal Logic, Tome 51 (2010) no. 1, p. 161-179 / Harvested from Project Euclid
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This paper presents a formalization of first-order arithmetic characterizing the natural numbers as abstracta of the equinumerosity relation. The formalization turns on the interaction of a nonstandard (but still first-order) cardinality quantifier with an abstraction operator assigning objects to predicates. The project draws its philosophical motivation from a nonreductionist conception of logicism, a deflationary view of abstraction, and an approach to formal arithmetic that emphasizes the cardinal properties of the natural numbers over the structural ones.
Publié le : 2010-04-15
Classification:  cardinality quantifiers,  abstraction principles,  arithmetic,  03C99,  03C80 
@article{1276284780,
     author = {Antonelli, G. Aldo},
     title = {Numerical Abstraction via the Frege Quantifier},
     journal = {Notre Dame J. Formal Logic},
     volume = {51},
     number = {1},
     year = {2010},
     pages = { 161-179},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1276284780}
}

Antonelli, G. Aldo. Numerical Abstraction via the Frege Quantifier. Notre Dame J. Formal Logic, Tome 51 (2010) no. 1, pp.  161-179. http://gdmltest.u-ga.fr/item/1276284780/