On the interpretation of intuitionistic number theory
On the interpretation of intuitionistic number theory
复制标题
论直觉数论的解释
DOI：
--
复制
发表时间：
1945
期刊：
影响因子：
--
通讯作者：
S. Kleene
中科院分区：
文献类型：
--
作者：
S. Kleene
本文的目的是介绍“递归可实现性”的概念。设P是自然数的一个性质。考虑存在命题，“存在一个具有性质P的数n”。为了解释这对建构主义者或直觉主义者的意义，它被描述为一个部分的判断，或一个更具体的陈述的不完整的沟通，这个陈述说某个给定的数n，或通过某种给定的方法可获得的数n，具有属性P。因此，存在陈述的意义在于对某些信息的引用，它意味着可以详细地陈述，尽管不愿意这样做。也许细节被抑制，以便传达对某些事实的一般看法。所参考的信息应该被认为可能包括除了n的值或获得它的方法之外的其他项目，即完成n具有属性P的通信所必需的项目。
The purpose of this article is to introduce the notion of “recursive realizability.” Let P be some property of natural numbers. Consider the existential statement, “There exists a number n having the property P.” To explain the meaning which this has for a constructivist or intuitionist, it has been described as a partial judgement, or incomplete communication of a more specific statement which says that a certain given number n, or the number n obtainable by a certain given method, has the property P. The meaning of the existential statement thus resides in a reference to certain information, which it implies could be stated in detail, though the trouble is not taken to do so. Perhaps the detail is suppressed in order to convey a general view of some fact. The information to which reference is made should be thought of as possibly comprising other items besides the value of n or method for obtaining it, namely such items as may be necessary to complete the communication that that n has the property P.