Godel's Impact on the Philosophy of Mathematics

被引：0
作者：
Agatstsi, Evandro [1 ]
机构：
[1] Univ Genoa, Fac Philosophy, Genoa, Italy
来源：
EPISTEMOLOGY & PHILOSOPHY OF SCIENCE-EPISTEMOLOGIYA I FILOSOFIYA NAUKI | 2010年 / 25卷 / 03期
关键词：
Godel's incompleteness theorem; Hilbert's programme; realism; idealism; model theory; proof theory;
D O I：
暂无
中图分类号：
B [哲学、宗教];
学科分类号：
01 ; 0101 ;
摘要：
The author considers the consequences of K. Godel's famous theorem on semantic incompleteness of formalized arithmetic that are of general importance to the philosophy of mathematics. The author mainly explores the impact of the theorem on the so-called Hilbert's formalist program. Turning to a general criticism of formalism in mathematics, the author states that its realization may turn mathematics into a meaningless intellectual game. He then singles out two possible strategies to overcome this negative effect of formalism: the realistic strategy and the idealistic one. These strategies are evaluated against the background of Godel's incompleteness theorem as well as against some other basic results obtained within the standard model and proof theory after Godel's result.
引用
收藏
页码：16 / +
页数：27
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