What are numbers?
pp. 1099-1112
Abstract
This paper argues that (cardinal) numbers are originally given to us in the context ‘Fs exist n-wise’, and accordingly, numbers are certain manners or modes of existence, by addressing two objections both of which are due to Frege. First, the so-called Caesar objection will be answered by explaining exactly what kind of manner or mode numbers are. And then what we shall call the Functionality of Cardinality objection will be answered by establishing the fact that for any numbers m and n, if there are exactly m Fs and also there are exactly n Fs, then m = n.
Publication details
Published in:
(2013) Synthese 190 (6).
Pages: 1099-1112
DOI: 10.1007/s11229-011-9883-y
Full citation:
Kim Joongol (2013) „What are numbers?“. Synthese 190 (6), 1099–1112.