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Research on Brouwer's Philosophy and the notion of continuum in Intuitionism

布劳威尔哲学与直觉主义连续统概念研究

基本信息

批准号：
15520026
负责人：
KANEKO Hiroshi
金额：
$ 1.28万
依托单位：
Senshu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

项目摘要

In this research project, we could establish the following results. (1) It was usual until now to investigate formal systems of intuitionistic mathematics and logic independently from Brouwer's philosophy because it was thought that his philosophy is intrinsically subjective and solipsistic. However, according to our research, it is showed that we need not interpret Brouwer's criticism of language in mathematics as a rejection of communication but we should take his claims as a requirement for undetachability of propositional content and its construction process. And according to this interpretation we can understand Brouwer's intuitionistic philosophy and his intuitionistic mathematics in the unified way. (2) Brouwer's requirement for the undetachability of content and process is based on his view on mathematics that mathematics is not a system of conceptual operations but a system of action. From this view on mathematics it turns out that Brouwer has two different notions of possibil … More ity---conceptual possibility and possibility of developing actions. Then it is showed that Brouwer uses the difference of the notions of possibility as a device in order to introduce the notion of choice sequence into his mathematics. Therefore, it turns out that the undetachability requirement provides with one of the basic devices to intuitionistic analysis. (3) But then why must Brouwer require the undetachability of content and process? Although we could not arrive at the final answer, our tentative answer is as follows. Brouwer's undetachability requirement is based on the requirement for preserving personal process through which we arrive at mathematical results. So it is dear that Brouwer takes the preservation of personal process as valuable. Our answer to the question what is the epistemic significance of preservation of personal process is that it is also a requirement of preserving mathematical perspective. Therefore, Brouwer's skepticism to linguistic communication is not necessarily interpreted as a slide to subjectivism. We can understand his dawns as a strong requirement for communication, that is, the requirement of the share of perspective Less

在这个研究项目中，我们可以建立以下结果。(1)这是通常直到现在调查正式系统的直观数学和逻辑独立于布劳威尔的哲学，因为它被认为是他的哲学本质上是主观和唯我论。然而，根据我们的研究，它表明，我们不需要解释布劳威尔的批评语言的数学作为一个拒绝的沟通，但我们应该把他的要求作为一个不可否认的命题内容及其建设过程。根据这种解释，我们可以统一地理解布劳威尔的直觉主义哲学和他的直觉主义数学。(2)布劳威尔对内容和过程不可分离性的要求是基于他的数学观，即数学不是一个概念操作系统，而是一个行动系统。从这种数学观点出发，布劳威尔对可能性有两种不同的看法。 ...更多信息概念的可能性和发展行动的可能性。然后，它表明，布劳威尔使用的差异的概念的可能性作为一种手段，以引进的概念，选择序列到他的数学。因此，不可解释性要求为直觉分析提供了一种基本手段。(3)但是，为什么布劳威尔必须要求内容和过程的不可重复性？虽然我们不能得出最后的答案，但我们的初步答案如下。布劳威尔的不可解释性要求是基于保持个人过程的要求，通过这个过程我们得到数学结果。因此，布劳威尔认为个人过程的保存是有价值的。我们对保留个人过程的认识意义的回答是，它也是保留数学观点的一个要求。因此，布劳威尔对语言交际的怀疑论并不必然被解释为滑向主观主义。我们可以把他的黎明理解为对沟通的强烈要求，也就是对视角份额的要求减