帕森斯:"结构主义和形而上学"

结构主义认为,数学对象的本性是它们所属结构的基本关系通过适当的逻辑方式定义的。“消除性的”结构主义认为,可以设想通过一定的解释程序,那些我们用来指称数字和非数学对象的概念就会被数的系统中的数或集合所替代,即使那些概念指称和数完全不同的对象。而“非消除性”的结构主义认为,应该把数论和集合理论中的数、集合和其他数学对     

Structuralism and Meta-Mathematics

The debate on structuralism in the philosophy of mathematics has brought into focus a question about the status of meta-mathematics. It has been raised by Shapiro (2005), where he compares the ongoing discussion on structuralism in category theory to the Frege-Hilbert controversy on axiomatic systems. Shapiro outlines an answer according to which meta-mathematics is understood in structural terms and one according to which it is not. He finds both options viable and does not seem to prefer one over the other. The present paper reconsiders the nature of the formulae and symbols meta-mathematics is about and finds that, contrary to Charles Parsons’ influential view, meta-mathematical objects are not “quasi-concrete”. It is argued that, consequently, structuralists should extend their account of mathematics to meta-mathematics.     

Perceptual Variation and Structuralism

I use an old challenge to motivate a new view. The old challenge is due to variation in our perceptions of secondary qualities. The challenge is to say whose perceptions are accurate. The new view is about how we manage to perceive secondary qualities, and thus manage to perceive them accurately or inaccurately. I call it perceptual structuralism . I first introduce the challenge and point out drawbacks with traditional responses. I spend the rest of the paper motivating and defending a structuralist response. While I focus on color, both the challenge and the view generalize to the other secondary qualities.     

Structuralism, Model Theory and Reduction

In this paper, the (possible) role of model theory forstructuralism and structuralist definitions of ``reduction' arediscussed. Whereas it is somewhat undecisive with respect tothe first point – discussing some pro's and con's ofthe model theoretic approach when compared with a syntacticand a structuralist one – it emphasizes that severalstructuralist definitions of ``reducibility' do not providegenerally acceptable explications of ``reducibility'. This claimrests on some mathematical results proved in this paper.     

Structuralism and the Applicability of Mathematics

In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.     

葛洪与玄学

玄学是魏晋时期兴起的一种影响深远的社会思潮,两晋之际玄学在理论上发展到极至,其影响开始渗入社会生活的各个方面。葛洪早年深受儒家学说熏陶,又是官方道教理论的创立者,无论是为了维护传统的儒家思想,还是出于为官方道教建立理论的需要,葛洪在主观上都反对玄学所促发的行为方式。但客观上,葛洪却不自觉地受了玄学的影响。本文力图通过分析葛洪思想中玄学的成分,来揭示玄学对当时士人的巨大影响力。