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From Magnitudes to Geometry and Back: De Zolt's Postulate. 从量级到几何，再回到量级：德佐尔特公设

IF 0.6 3区哲学 Q4 SOCIOLOGY

THEORIA

Pub Date : 2022-06-01 Epub Date: 2022-02-13 DOI: 10.1111/theo.12385

Eduardo N Giovannini, Abel Lassalle-Casanave

A crucial trend of nineteenth-century mathematics was the search for pure foundations of specific mathematical domains by avoiding the obscure concept of magnitude. In this paper, we examine this trend by considering the "fundamental theorem" of the theory of plane area: "If a polygon is decomposed into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon." This proposition, known as De Zolt's postulate, was conceived as a strictly geometrical expression of the general principle of magnitudes "the whole is greater than the part." On the one hand, we illustrate this striving for purity in the foundations of geometry by analysing David Hilbert's classical proof of De Zolt's postulate. On the other hand, we connect this geometrical problem with the first axiomatizations of the concept of magnitude by the end of the nineteenth century. In particular, we argue that a recent result in the logical analysis of the concept of magnitude casts new light on Hilbert's proof. We also outline an alternative development of a theory of magnitude that includes a proof of De Zolt's postulate in an abstract setting.

十九世纪数学的一个重要趋势是通过回避晦涩难懂的大小概念来寻求特定数学领域的纯基础。本文通过研究平面面积理论的 "基本定理 "来探讨这一趋势："如果一个多边形以任何给定的方式分解成多边形的各个部分，那么除了其中一个部分之外，所有这些部分的结合都不等同于给定的多边形"。这一命题被称为 "德佐尔特公设"，是 "整体大于部分 "这一一般大小原则在几何学上的严格表达。一方面，我们通过分析戴维-希尔伯特（David Hilbert）对德佐特公设的经典证明，来说明几何学基础对纯粹性的追求。另一方面，我们将这一几何问题与十九世纪末对大小概念的首次公理化联系起来。特别是，我们认为，最近对大小概念的逻辑分析结果为希尔伯特的证明带来了新的启示。我们还概述了量纲理论的另一种发展，其中包括在抽象环境中对 De Zolt 公设的证明。

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引用次数: 0

How to Supplement Mentalist Evidentialism: What Are the Fundamental Epistemological Principles? 如何补充心智主义证据论？认识论的基本原则是什么？

IF 0.6 3区哲学 Q4 SOCIOLOGY

THEORIA

Pub Date : 2022-06-01 Epub Date: 2022-02-09 DOI: 10.1111/theo.12394

Philipp Berghofer

Evidentialism and mentalism enjoy much popularity. In fact, mentalist evidentialism is often considered the most plausible internalist approach towards epistemic justification. However, mentalist evidentialism does not amount to a comprehensive theory of epistemic justification. In their attempt to complete their epistemological system and to answer the question of why experiences are justifiers, Conee and Feldman supplement mentalist evidentialism with explanationism. They take principles of best explanation to be the fundamental epistemic principles. In this paper, I show that explanationist mentalist evidentialism is plagued by severe shortcomings. What is more, I argue for an alternative in the spirit of Conee and Feldman's internalism that avoids the problems of explanationism, offering a straightforward commonsense account of epistemic justification. The fundamental epistemological principles are phenomenological principles.

证伪主义和心智主义广受欢迎。事实上，心智主义证据论通常被认为是认识论证成的最合理的内部主义方法。然而，心智主义证据论并不等于一个全面的认识论证成理论。为了完善他们的认识论体系，回答为什么经验是正当理由的问题，科尼和费尔德曼对心智主义证据论进行了解释论的补充。他们把最佳解释原则作为认识论的基本原则。在本文中，我证明了解释主义的心智主义证据论存在严重缺陷。此外，我还根据科尼和费尔德曼的内部主义精神，提出了一种可避免解释论问题的替代方案，为认识论的合理性提供了一种直截了当的常识性解释。认识论的基本原则是现象学原则。

引用次数: 0

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