Properties, Paradox, and Circularity. A New, Type-Free Account

性质、悖论和循环性。

• 批准号: AH/V015516/1
• 负责人: Carlo Nicolai
• 金额: $ 25.11万
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=AH%2FV015516%2F1
• 关键词: Properties; Paradox; Circularity.; New; Type

Theorizing about the world requires a theory of propositions, properties, and relations (PPRs). Propositions are the entities to which the properties of being true, believed, desired, known apply. Natural properties and relations are the features of physical entities studied by natural science. Social properties and relations shape human interactions. The development of a satisfactory theory of PPRs lies at the foundation of scientific and philosophical enquiry. However, theories of propositions, properties, and relations are constrained by logical paradoxes: intuitive principles such as "To every predicate in language, there corresponds a property" are in fact inconsistent with the standard laws of logic. This is why a solid formal foundation for theories of PPRs is required. The project aims to provide a new formal and philosophical foundation to theories of propositions, properties, relations. The most popular way of providing such a foundation arranges PPRs in hierarchies of logical types. The prominence of the typed approach is explained by some of its theoretical virtues: it is consistent with classical logic and it may achieve substantial mathematical strength. However, the typed approach misses out some important features of language and thought such as circularity and self-applicability. For instance, claims such as 'it's necessary that something is necessary' cannot be properly regimented in the typed setting. More generally, circular phenomena can be found in many theoretical contexts in philosophy (self-reference), computer science (streams, self-applicative programs), and mathematics (graphs, non-wellfounded sets). Circularity can also be found in natural language (self-predication). Such phenomena cannot be easily modelled in a typed theory of PPRs. The project will analyse in detail extant theories of PPRs and develop the logic and philosophy of the type-free approach, a promising but underdeveloped approach to PPRs and their paradoxes. The project will develop two kinds of type-free theories of PPRs. The first builds on naive principles for PPRs and on a restriction of classical logic. The second kind of theories is cast in classical logic. They will capture a much wider range of circular phenomena than current theories of PPRs, while retaining the theoretical benefits of the typed approach such as applicability in various contexts and mathematical strength. The project will analyze in detail the implications of the theories in semantics and metaphysics, two of the core domains of applications of PPRs. One key component of the project is its intrinsic interdisciplinary methodology; techniques from mathematics, theoretical computer science, linguistics, and philosophy are all essentially employed. The project will be informed by a corpus-based, systematic analysis of empirical linguistic evidence bearing on PPRs and by a comprehensive philosophical evaluation of desiderata for theories of PPRs. Techniques of theory building and analysis from mathematics and computer science will be employed to construct and test formal aspects of the new type-free theories. The project findings will impact on the foundations of formal sciences and philosophy. Major outputs of the project will be a monograph on circular intensional entities by the PI, and a short monograph by the CoI and the PI surveying the fundamental ideas of the available formal theories of intensional entities. Besides two traditional workshops, the project will organize an impact workshop in which the theories constructed in the project will be presented to non-academic stakeholders working on data modelling.

关于世界的理论化需要一个关于命题、性质和关系的理论（PPR）。命题是真实、可信、期望、已知等属性所适用的实体。自然属性和自然关系是自然科学所研究的物理实体的特征。社会属性和社会关系塑造了人类的互动。一个令人满意的PPR理论的发展是科学和哲学探究的基础。然而，命题、性质和关系的理论受到逻辑悖论的约束：直觉原则，如“语言中的每个谓词都对应一个性质”，实际上与逻辑的标准定律不一致。这就是为什么PPR理论需要一个坚实的形式基础。该项目旨在为命题，属性，关系的理论提供一个新的形式和哲学基础。提供这种基础的最流行的方法是将PPR安排在逻辑类型的层次结构中。类型化方法的重要性可以用它的一些理论优点来解释：它与经典逻辑相一致，并且可以获得很强的数学能力。然而，类型化方法忽略了语言和思维的一些重要特征，如循环性和自适用性。例如，像“有必要的东西是必要的”这样的声明不能在类型设置中得到适当的约束。更一般地说，循环现象可以在哲学（自指）、计算机科学（流、自应用程序）和数学（图、非良基集）的许多理论背景中找到。循环也可以在自然语言中找到（自我预测）。这样的现象不能轻易地在PPR的类型化理论中建模。该项目将详细分析PPR的现存理论，并发展无类型方法的逻辑和哲学，这是一种有前途但尚未开发的PPR及其悖论的方法。该项目将开发两种类型无关的PPR理论。第一个建立在PPR的朴素原则和经典逻辑的限制上。第二类理论是在经典逻辑中铸造的。它们将捕捉比当前PPR理论更广泛的循环现象，同时保留类型化方法的理论优势，例如在各种背景下的适用性和数学强度。该项目将详细分析语义学和形而上学理论的含义，这是PPR应用的两个核心领域。该项目的一个关键组成部分是其内在的跨学科方法;从数学，理论计算机科学，语言学和哲学的技术都基本上采用。该项目将通过基于语料库的，对PPR的经验语言学证据的系统分析和对PPR理论的必要性的全面哲学评估来提供信息。数学和计算机科学的理论构建和分析技术将被用来构建和测试新的无类型理论的形式方面。该项目的研究结果将对正式科学和哲学的基础产生影响。该项目的主要成果将是PI关于圆形内涵实体的专著，以及CoI和PI调查内涵实体的可用形式理论的基本思想的简短专著。除了两个传统的研讨会外，该项目还将组织一个影响研讨会，向从事数据建模工作的非学术利益攸关方介绍项目中构建的理论。

项目成果

Non-contractive logics, Paradoxes, and Multiplicative Quantifiers

非收缩逻辑、悖论和乘法量词

• 发表时间: 2023
• 作者: Carlo Nicolai

Two conceptions of absolute generality

绝对普遍性的两种概念

• DOI: 10.1007/s11098-022-01908-0
• 发表时间: 2023
• 期刊: Philosophical Studies
• 影响因子: 1.3
• 作者: Florio S

Gaps, gluts, and theoretical equivalence

缺口、过剩和理论等价

• DOI: 10.1007/s11229-022-03816-6
• 发表时间: 2022
• 期刊: Synthese
• 影响因子: 1.5
• 作者: Nicolai C

On Type Distinctions and Expressivity

论类型区别和表现力

• 发表时间: 2023
• 作者: Salvatore Florio

Implicit Commitment in a General Setting

一般环境中的隐含承诺

• 发表时间: 2023
• 作者: Mateusz Lelyk