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.     

Paleo-Compatibilism and Buddhist Reductionism

Paleo-compatibilism is the view that the freedom required for moral responsibility is not incompatible with determinism about the factors relevant to moral assessment, since the claim that we are free and the claim that the psychophysical elements are causally determined are true in distinct and incommensurable ways. This is to be accounted for by appealing to the distinction between conventional truth and ultimate truth developed by Buddhist Reductionists. Paleo-compatibilists hold that the illusion of incompatibilism only arises when we illegitimately mix two distinct vocabularies, one concerned with persons, the other concerned with the parts to which persons are reducible. I explore the view, its roots in Buddhist Reductionism, and its prospects.

Challenging Sociological Reductionism

The author analyzes Christian Smith's What Is a Person? from a Christian theological‐ethical perspective, assessing the way in which he tackles sociological theories that reflect secularized and reductionist assumptions about the human person, and offering a friendly critique of the Christian personalist, humanist, and virtue ethic that he deploys to challenge his field.     

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.     

Motivating Reductionism about Sets

The paper raises some difficulties for the typical motivations behind set reductionism, the view that sets are reducible to entities identified independently of set theory.     

论心理学中的还原论

心理学中的还原论主要指方法论意义上的“理论的还原论”,可分为心理学理论向物理学、生理学与生物学理论还原等三种还原论类型。它并不像其攻击者所误解的那样,就是本体论的还原论、必然导致决定论、与整体论截然对立或者仅仅就是还原方法。相反地,还原论是研究心理现象的重要途径,与方法论的多元主义并行不悖,符合人类进行认识的规律。只要使用者注意其适用的边界条件,还原论还是不失为心理学研究的一种不错的“没有选择的选择”。     

Reductionism in Fallacy Theory

(1) The aim of the paper is to develop a reduction of fallacy theory, i.e. to 'deduce' fallacy theory from a positive theory of argumentation which provides exact criteria for valid and adequate argumentation. Such reductionism has several advantages compared to an unsystematic action, which is quite usual in current fallacy but which at least in part is due to the poor state of positive argumentation theory itself. (2) After defining 'fallacy' (3) some principle ideas and (4) the exact criteria for (argumentatively) valid and adequate arguments of the 'practical theory of argumentation' of the author are expounded. These criteria will be used as the positive basis for the following reduction. (5) In the main part of the paper a systematization, definition and explanation of the main types and many subforms of fallacies of argumentative validity and (6) adequacy is developed, following the list of positive conditions of validity and adequacy. In addition to many new types of fallacies, this systematization contains the most important of the traditionally known and named fallacies; these are explained and the criteria for some of them are corrected or put more precisely.     

Emergence, Probability, and Reductionism

Abstract. Philosopher‐theologian Bernard J. F. Lonergan defines emergence as the process in which “otherwise coincidental manifolds of lower conjugate acts invite the higher integration effected by higher conjugate forms” (Insight, [1957] 1992, 477). The meaning and implications of Lonergan's concept of emergence are considered in the context of the problem of reductionism in the natural sciences. Examples are taken primarily from physics, chemistry, and biology.     

Reductionism as Resource-Conscious Reasoning

Reductivist programs in logicand philosophy, especially inthe philosophy of mathematics,are reviewed. The paper argues fora ``methodological realism' towardsnumbers and sets, but still givesreductionism an important place,albeit in methodology/epistemologyrather than in ontology proper.