TY - JOUR
T1 - Frege's cardinals and neo-logicism
AU - Cook, Roy T
PY - 2016/2/1
Y1 - 2016/2/1
N2 - Gottlob Frege defined cardinal numbers in terms of value-ranges governed by the inconsistent Basic Law V. Neo-logicists have revived something like Frege's original project by introducing cardinal numbers as primitive objects, governed by Hume's Principle. A neo-logicist foundation for set theory, however, requires a consistent theory of value-ranges of some sort. Thus, it is natural to ask whether we can reconstruct the cardinal numbers by retaining Frege's definition and adopting an alternative consistent principle governing value-ranges. Given some natural assumptions regarding what an acceptable neo-logicistic theory of valueranges might look like, successfully implementing this alternative approach is impossible.
AB - Gottlob Frege defined cardinal numbers in terms of value-ranges governed by the inconsistent Basic Law V. Neo-logicists have revived something like Frege's original project by introducing cardinal numbers as primitive objects, governed by Hume's Principle. A neo-logicist foundation for set theory, however, requires a consistent theory of value-ranges of some sort. Thus, it is natural to ask whether we can reconstruct the cardinal numbers by retaining Frege's definition and adopting an alternative consistent principle governing value-ranges. Given some natural assumptions regarding what an acceptable neo-logicistic theory of valueranges might look like, successfully implementing this alternative approach is impossible.
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U2 - 10.1093/philmat/nkv029
DO - 10.1093/philmat/nkv029
M3 - Article
AN - SCOPUS:84959874593
SN - 0031-8019
VL - 24
SP - 60
EP - 90
JO - Philosophia Mathematica
JF - Philosophia Mathematica
IS - 1
M1 - nkv029
ER -