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.     

Structuralism and Metaphysics

I consider different versions of a structuralist view of mathematical objects, according to which characteristic mathematical objects have no more of a 'nature' than is given by the basic relations of a structure in which they reside. My own version of such a view is non-eliminative in the sense that it does not lead to a programme for eliminating reference to mathematical objects. I reply to criticisms of non-eliminative structuralism recently advanced by Keränen and Hellman. In replying to the former, I rely on a distinction between 'basic' and 'constructed' structures. A conclusion is that ideas from the metaphysical tradition can be misleading when applied to the objects of modern mathematics.     

Perceptual Variation,Color Language,and Reference Fixing. An Objectivist Account

I offer a new objectivist theory of the contents of color language and color experience, intended especially as an account of what normal intersubjective variation in color perception and classification shows about those contents. First I explain an abstract account of the contents of (utterances of) color and other gradable adjectives; on the account, these contents are certain objective properties constituted in part by contextually intended standards of application, which are in turn values in the dimensions of variation associated with the adjectives. Then I propose an explanation of normal variations in linguistic color classification; these are postulated to be effects of differences in intended standards for the color adjectives appearing in the classifying predicates. Next, I consider a potential objection to this explanation, based on the suggestion that contextual content should be more accessible than the explanation predicts. In reply, I point out that contextual content is occasionally opaque to unsophisticated reflection. Finally, I present a companion account of the contents of color experiences on which these represent an object as lying on certain salient intervals in the chromatic dimensions, and I show how the account accommodates intersubjective variation in color perception.     

知觉经验与知觉内容

知觉(perception)是指我们通过视觉、听觉、触觉、嗅觉、味觉等感觉器官而获得的对事物以及外部世界的意识感知.知觉经验(perceptual experience)的一个显著的特点是它具有某种现象特征,即知觉者会体验到一种"那究竟像什么(what it is like)"的感觉.例如,一个人会从红色视觉经验中体验到"红色究竟像什么"的意识感受性(qualia).知觉内容(perceptual content)粗略地讲是指通过知觉经验向知觉者所传递的信息.关于知觉问题在哲学上的重要性,我们可以从以下几点来看:在形而上学方面,知觉是我们了解外部物理世界究竟存在什么的主要手段;在认识论方面,研究知觉是研究我们如何达到关于外部物理世界的知识的主要手段;在语言哲学方面,知觉内容是我们的心灵与外部物理世界的关联及互动在语言实践上的体现;在心灵哲学方面,知觉经验中的现象特征与意识及意向性之间存在着深层的内在联系.     

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.     

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     

Dedekind's Structuralism: An Interpretation and Partial Defense

Synthese - Various contributors to recent philosophy of mathematics havetaken Richard Dedekind to be the founder of structuralismin mathematics. In this paper I examine whether Dedekind did, in...     

Structuralism and experimental aesthetics: Bridging some gaps

Structuralism in psychology has much to do with what Berlyne called his rival tradition in aesthetics, the speculative and interpretative approach. Berlyne's concern with motivation can be retained while structuralism's emphasis on understanding is accepted.This paper was originally presented at the Berlyne Symposium, American Psychological Association Meeting, San Francisco, August 1977. Support from the Connaught Development Grant to Scarborough College is acknowledged.     

Ontic Structuralism and the Symmetries of Particle Physics

According to structural realism, in mature science there is structural continuity along theoretical change. A major counterexample to this thesis is the transition from the Eightfold Way to the Standard Model in particle physics. Nevertheless, the notion of structure is significantly important in comprehending the theoretical picture of particle physics, where particles change and undergo transmutations, while the only thing which remains unchanged is the basic structure, i.e. the symmetry group which controls the transmutations. This kind of view agrees with the paradigmatic case where the structure is an internal symmetry and the instantiations are the elementary particles. The metaphysical view which reflects this situation is a version of ontic structuralism.