权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Philosophical Appraisal of the Representative Standpoints in the Foundations of Logic and Mathematics: Realism, Constructivism and Physicalism

逻辑和数学基础中代表性观点的哲学评价：实在论、建构主义和物理主义

基本信息

批准号：
13410002
负责人：
OKAMOTO Kengo
金额：
$ 5.5万
依托单位：
Tokyo Metropolitan University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

项目摘要

Today, Realism(Platonism), Constructivis and Physicalistic Nominalism are three representative standpoints in the philosophical foundations of logic and mathematics. While they have their own merits and insights, they all suffer from certain philosophical difficulties peculiar to each of them. One would have to concede that those difficulties are urging us to reconsider the familiar fundamental questions in this field seriously: How should we identify the basic principles of logic and mathematics, and how should we give them adequate explanations and conceptual justifications. We seem to be simply at a loss as to how to answer these questions.On the other hand, strongly influenced by the rapid growth of theoretical computer sciences, studies in logic and foundations of mathematics have gone through remarkable reformations and innovations for recent decades. Among the most notable developments are (i)systems of Typed Lambda Calculus, (ii)Category theory and (ii) sub-structural logics. T … More hese theories throw various new lights on the questions of the fundamental principles, thereby more or less invalidating the opposition between the three standpoints mentioned above, at the same time requiring renewal of interpretations of those historical figures such as Frege, Cantor, Hilbert and Brower.Unfortunately, philosophers have been, and stall seem to be, very slow to understand and appreciate those innovative, far-reaching insights and proposals provided by the new developments in logic and foundations of mathematics. We attempt to build basic conceptual frameworks in which one could develop extensive philosophical analysis and critical examinations of those insights and proposals. Results of our present research could be summarize by the following two theses: First, we need to establish adequate principles for constructing those formalized languages (syntax) that are sensitive to dynamics of uses of language (egg making judgments, executing computations, etc). Second, in accordance with these syntactical principles, we need to find out relevant principles for constructing those mathematical structures that are flexible enough to admit of various kinds of indeterminacy and patiality. Less

今天，实在论（柏拉图主义）、建构论和物理唯名论是逻辑和数学哲学基础上的三种代表性观点。虽然他们都有自己的优点和见解，但他们都面临着各自特有的某些哲学难题。人们不得不承认，这些困难正在促使我们认真地重新考虑这一领域中熟悉的基本问题：我们应该如何识别逻辑和数学的基本原理，以及我们应该如何给予它们充分的解释和概念论证。我们似乎完全不知道如何回答这些问题。另一方面，受理论计算机科学快速发展的强烈影响，逻辑和数学基础研究近几十年来经历了显着的改革和创新。其中最显着的发展是 (i) 类型 Lambda 演算系统、(ii) 范畴论和 (ii) 子结构逻辑。这些理论对基本原理的问题提出了各种新的见解，从而或多或少地使上述三种观点之间的对立无效，同时要求对弗雷格、康托、希尔伯特和布劳尔等历史人物的解释进行更新。逻辑学和数学基础的新发展。我们试图建立基本的概念框架，在其中人们可以对这些见解和建议进行广泛的哲学分析和批判性审查。我们目前的研究结果可以概括为以下两个主题：首先，我们需要建立适当的原则来构建对语言使用动态（鸡蛋做出判断、执行计算等）敏感的形式化语言（语法）。其次，根据这些句法原则，我们需要找出相关原则来构造那些足够灵活以允许各种不确定性和宽容性的数学结构。较少的