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Counting Things
Author(s) -
Eveling Stanley
Publication year - 2013
Publication title -
philosophical investigations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.172
H-Index - 14
eISSN - 1467-9205
pISSN - 0190-0536
DOI - 10.1111/phin.12008
Subject(s) - acknowledgement , numbering , appeal , transitive relation , skepticism , axiom , computer science , mathematics , epistemology , discrete mathematics , mathematical economics , philosophy , algorithm , combinatorics , computer security , law , political science , geometry
This paper argues that it is part of the concept of the positive integers that they are for the sake of numbering things (what B enacerraf calls transitive counting). Numbers are necessarily associated with standard, conventionally established counting sets constituted by the P eano axioms; they cannot be specified independently of a paradigm counting stock, any more than lengths can be part of a system of assessment without appeal to some standard object. Scepticism deriving from K ripke and Salmon is countered by acknowledgement that the paradigms themselves are among the means by which the terms of the system get applied and adjudicated.