Frege's Platonism and Platonism in Mathematics Today

弗雷格的柏拉图主义和当今数学中的柏拉图主义

• 批准号: AH/J00233X/1
• 负责人: Philip Ebert
• 金额: $ 4.91万
• 依托单位: University of Stirling
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2012
• 资助国家: 英国
• 起止时间: 2012 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=AH%2FJ00233X%2F1
• 关键词: Frege; Platonism; Mathematics; Today

In the 1970's Michael Dummett portrayed the 'linguistic turn' in philosophy, which he identified with the moment in Frege's discussion of arithmetic at which an epistemological and metaphysical question, that is the question of our knowledge and of the nature of numbers, is transformed into one requiring a semantic analysis of numerical expressions purporting to refer to these objects, as the essential step in giving a more tractable shape to metaphysical and epistemological issues and so making possible systematic progress towards their resolution. This 'Copernican Revolution' has lead to a very fruitful research project in the philosophy of arithmetic, namely Frege's Logicism, which, in turn inspired the so-called Neo-Fregean project. More recently there has been a shift away from a broadly Fregean methodology inspired by the linguistic turn, and a resurgence of what may be called 'constructive metaphysics'. However, it is the conviction of this applicant that, first, when dealing with the fundamental questions of our knowledge of arithmetic and our knowledge of the underlying mathematical objects, a Frege-inspired methodology still offers one of the most promising approaches to resolving the fundamental questions about our knowledge of and about the nature of numbers; but secondly, that this approach needs to draw fresh inspiration and direction from a re-evaluation of crucial but neglected details of Frege's actual approach to the introduction and justification of a mathematical ontology.The central aim of this research project is to further investigate Frege's methodology and views as adopted in his main work, 'Die Grundlagen der Arithmetik' and 'Die Grundgesetze der Arithmetik' on core themes in the philosophy of mathematics. These insights will then be used to raise new challenges for a Fregean philosophy of mathematics and to further the current debate in the philosophy of arithmetic and meta-ontology.The research project is divided into three stages. The first stage focuses on Frege's own conception of logical objects. This research is pursuit in collaboration with Professor Marcus Rossberg (UConn); the second stage develops a paradox in Frege's identification of numbers with logical objects, that is, with extensions. This research is pursuit in collaboration with Professor Roy T Cook (Minnesota); and the last and third stage aims to overcome a stalemate reached on the debate of the 'thickness' of mathematical objects within the Neo-Fregean tradition in the philosophy of arithmetic today. The core aims of the project is to produce three new and original research articles and one edited collection on Frege.

在20世纪70年代，Michael Dummett描述了哲学的“语言学转向”他认为这与弗雷格讨论算术的时刻是一致的，在这个时刻，一个认识论和形而上学的问题，即我们的知识和数字的本质的问题，被转化为一个需要对数字表达式进行语义分析的问题，这些数字表达式旨在指代这些对象，作为给形而上学和认识论问题一个更容易处理的形状的必要步骤，从而使它们的解决有可能有系统的进展。这种“哥白尼式革命”导致了一个在算术哲学方面非常富有成果的研究项目，即弗雷格的逻辑主义，这反过来又激发了所谓的新弗雷格计划。最近，在语言学转向的启发下，一种广泛的弗雷格方法论出现了转变，一种可能被称为“建设性形而上学”的复兴。然而，申请人坚信，首先，在处理我们的算术知识和我们对基础数学对象的知识的基本问题时，受弗雷格启发的方法仍然是解决关于我们对数字的知识和本质的基本问题的最有希望的方法之一；其次，这种方法需要从重新评估弗雷格对数学本体论的介绍和论证的实际方法中至关重要但被忽视的细节中汲取新的灵感和方向。本研究项目的中心目标是进一步研究弗雷格在其主要著作《数学哲学的基础》和《数学哲学的基础》中所采用的方法和观点，探讨数学哲学的核心主题。这些见解将被用来为弗雷格数学哲学提出新的挑战，并进一步推动当前在算术哲学和元本体论方面的辩论。研究项目分为三个阶段。第一阶段着重于弗雷格自己的逻辑对象概念。这项研究是与Marcus rosberg教授（UConn）合作进行的；第二阶段发展了弗雷格对数字与逻辑对象，即与扩展的认同的悖论。这项研究是与Roy T Cook教授（明尼苏达）合作进行的；最后一个也是第三个阶段的目的是克服在数学哲学的新fregean传统中关于数学对象的“厚度”的辩论所达到的僵局。该项目的核心目标是产生三篇新的原创研究文章和一篇关于弗雷格的编辑集。

项目成果

Alpenvereinsjahrbuch BERG 2014,

阿尔卑斯山年鉴 BERG 2014，

• 发表时间: 2013
• 作者: Ebert, P.A.;Robertson, S
• 通讯作者: Robertson, S

Frege's Recipe

弗雷格的食谱

• 发表时间: 2016
• 期刊: The Journal of Philosophy
• 作者: Cook, R.T.

Abstractionism - Essays in Philosophy of Mathematics

抽象主义 - 数学哲学论文集

• DOI: 10.1093/acprof:oso/9780199645268.003.0007
• 发表时间: 2016
• 作者: Ebert P

Essays on Frege's Grundgesetze

弗雷格基本原理论文集

• 发表时间: 2017
• 作者: Ebert, P.A.;Rossberg, M
• 通讯作者: Rossberg, M

Dummett's Criticism of the Context Principle

达米特对语境原则的批评

• DOI: 10.1163/9789004310841_003
• 发表时间: 2015
• 期刊: Grazer Philosophische Studien
• 作者: Ebert P