Numerical Abstraction via the Frege Quantifier

l Abstraction via the Frege Quantifier G. Aldo Antonelli Abstract This paper presents a formalization of first-order aritharacterizing the natural numbers as abstracta of the equinumerosity relation. The formalization turns on the interaction of a non-standard (but still first-order) cardinality quantifier abstraction operator assigning objects to predicates. The project draws its philosophical motivation from a non-reductionist on 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.

• Type: Journal
• Year: 2010
• Where: NDJFL
• Authors: Gian Aldo Antonelli
• Keywords: Cardinality Quantifier Abstraction, Computer Networks, Frege Quantifier G, Natural Numbers, NDJFL 2010