@article{ART001497740},
author={Lee Jong Kwon},
title={Limit of Liberty in Mathematics},
journal={Philosophical Investigation},
issn={1598-7213},
year={2010},
volume={28},
pages={53-83},
doi={10.33156/philos.2010.28..003}
TY - JOUR
AU - Lee Jong Kwon
TI - Limit of Liberty in Mathematics
JO - Philosophical Investigation
PY - 2010
VL - 28
IS - null
PB - Institute of philosophy in Chung-Ang Univ.
SP - 53
EP - 83
SN - 1598-7213
AB - In his Logical Syntax of Language Carnap proposed “the Principle of Tolerance” to the effect that there is no limit of our freedom to choose a language as a syntactical system. Gődel criticized that whereas the rules of syntax should satisfy the requirement that it should be demonstrated beforehand that they are consistent, it cannot be met in view of his Second Incompleteness Theorem. However, some philosophers including W. Goldfarb and Yongsam Chon(전영삼) retorted in defending Carnap that the freedom allowed by the Principle of Tolerance is wide enough to permit inconsistency. It is argued that in view of Carnap’s intention to define implicitly the logico-mathematical terms by adopting the suitable rules of syntax, the requirement that the syntactical rules should be consistent is a minimum limit to our freedom in mathematics and it is not permitted by the Principle to maintain the rules of syntax which were already proved to be inconsistent.
KW - Philosophy of Mathematics;Carnap;Gődel;Principle of Tolerance;Conventionalism
DO - 10.33156/philos.2010.28..003
ER -
Lee Jong Kwon. (2010). Limit of Liberty in Mathematics. Philosophical Investigation, 28, 53-83.
Lee Jong Kwon. 2010, "Limit of Liberty in Mathematics", Philosophical Investigation, vol.28, pp.53-83. Available from: doi:10.33156/philos.2010.28..003
Lee Jong Kwon "Limit of Liberty in Mathematics" Philosophical Investigation 28 pp.53-83 (2010) : 53.
Lee Jong Kwon. Limit of Liberty in Mathematics. 2010; 28 53-83. Available from: doi:10.33156/philos.2010.28..003
Lee Jong Kwon. "Limit of Liberty in Mathematics" Philosophical Investigation 28(2010) : 53-83.doi: 10.33156/philos.2010.28..003
Lee Jong Kwon. Limit of Liberty in Mathematics. Philosophical Investigation, 28, 53-83. doi: 10.33156/philos.2010.28..003
Lee Jong Kwon. Limit of Liberty in Mathematics. Philosophical Investigation. 2010; 28 53-83. doi: 10.33156/philos.2010.28..003
Lee Jong Kwon. Limit of Liberty in Mathematics. 2010; 28 53-83. Available from: doi:10.33156/philos.2010.28..003
Lee Jong Kwon. "Limit of Liberty in Mathematics" Philosophical Investigation 28(2010) : 53-83.doi: 10.33156/philos.2010.28..003
