TY - JOUR
T1 - A vindication of logicism
AU - Roeper, Peter
N1 - Publisher Copyright:
© The Author [2015]. Published by Oxford University Press. All rights reserved.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - Frege regarded Hume's Principle as insufficient for a logicist account of arithmetic, as it does not identify the numbers; it does not tell us which objects the numbers are. His solution, generally regarded as a failure, was to propose certain sets as the referents of numerical terms. I suggest instead that numbers are properties of pluralities, where these properties are treated as objects. Given this identification, the truth-conditions of the statements of arithmetic can be obtained from logical principles with the help of definitions, just as the logicist thesis maintains.
AB - Frege regarded Hume's Principle as insufficient for a logicist account of arithmetic, as it does not identify the numbers; it does not tell us which objects the numbers are. His solution, generally regarded as a failure, was to propose certain sets as the referents of numerical terms. I suggest instead that numbers are properties of pluralities, where these properties are treated as objects. Given this identification, the truth-conditions of the statements of arithmetic can be obtained from logical principles with the help of definitions, just as the logicist thesis maintains.
UR - http://www.scopus.com/inward/record.url?scp=84992573779&partnerID=8YFLogxK
U2 - 10.1093/philmat/nkv026
DO - 10.1093/philmat/nkv026
M3 - Article
SN - 0031-8019
VL - 24
SP - 360
EP - 378
JO - Philosophia Mathematica
JF - Philosophia Mathematica
IS - 3
M1 - nkv026
ER -