Why Do We Believe Theorems?

被引：13
|
作者：
Pelc, Andrzej [1 ]
机构：
[1] Univ Quebec Outaouais, Dept Informat, Gatineau, PQ J8X 3X7, Canada
来源：
PHILOSOPHIA MATHEMATICA | 2009年 / 17卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
D O I：
10.1093/philmat/nkn030
中图分类号：
N09 [自然科学史]; B [哲学、宗教];
学科分类号：
01 ; 0101 ; 010108 ; 060207 ; 060305 ; 0712 ;
摘要：
The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to the confidence in mathematical theorems. Opposing this opinion, the main claim of the present paper is that such a gain of confidence obtained from any link between proofs and formal derivations is, even in principle, impossible in the present state of knowledge. Our argument is based on considerations concerning length of formal derivations.
引用
收藏
页码：84 / 94
页数：11
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