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.     

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     

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 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.     

Model Theory and Validity

Synthese - Take a formula of first-order logic which is a logical consequence of some other formulae according to model theory, and in all those formulae replace schematic letters with English...     

心身理论还原重构与新潮还原论

在人类探索知识的历程中,科学家一直把理论之间的还原作为一种机会,以此来发展对我们的知识的适用范围、结构以及事物根本构成关系的深远解释。在科学领域,科学家们认为某领域建立的理论只不过是基本领域如微观物理学理论的具体的体现,因而高层次理论解释并不必要,科学的发展就是用基本的理论取而代之却又不丧失前者的解释力。科学的发展证明了理论还原的成功,如伽俐略定律还原到牛顿定律,牛顿定律还原到爱因斯坦的相对论,甚至在生物学中,DNA双螺旋结构的发现被视为理论还原最伟大的成果,以至于DNA发现者、科学家克里克(Francis Crick)…     

儿童心理理论的模块论:假设、方法与模型

模块论是儿童心理理论研究领域中主要理论取向之一。这一观点认为,儿童的心理理论能力是一种天赋的、领域特殊的心理结构,个体出生时便以模块的形式存在于神经系统,其发展是一个内部生物机能逐渐展开的过程。该文试图对儿童心理理论模块论的基本假设(天赋性和领域特殊性)、主要实验方法、重要模型(ToMM-SP模型)等进行评述,并就心理理论的天赋性与发展性、领域特殊性与领域普遍性、实验研究的方法与结果等引发争鸣的问题进行简评。     

Natures,Human Nature,Genes and Souls: Reclaiming Theological Anthropology Through Biological Structuralism

Abstract : Within the field of Theology and Science, discussions regarding the relationship between biology and theological anthropology have tended to focus on the themes of ‘human uniqueness’ and ‘human nature’. These ideas have continued among theologians and anthropologists despite the widespread agreement among neo‐Darwinian evolutionary biologists that such general or universal accounts of ‘natures’ in general, or ‘human nature’ in particular, have no proper place within the neo‐Darwinian evolutionary framework. In view of this neo‐Darwinian rejection of universal human nature and the subsequent undermining of theological anthropologies based on such, Biological Structuralism is proposed as an alternative theoretical framework through which to construct a theological anthropology in light of evolution. Within the Structuralist framework scientific resources are provided which facilitate fresh perspectives on ancient theological discussions regarding the nature of the soul and the place of nonhuman animals within theological anthropology.