"不可或缺性论证"与反实在论数学哲学

The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create in imagining abstract mathematical entities; second, the thoughts that we create in imagining infinite mathematical entities are bounded by external conditions. __________ Translated from Zhexue Yanjiu 哲学研究 (Philosophical Researches), 2006, (8): 74–83     

Troubles with Theoretical Virtues: Resisting Theoretical Utility Arguments in Metaphysics

In this paper we examine theoretical utility arguments in metaphysics. While philosophers claim a procedural continuity with science when using such arguments, we argue that examining famous instances from the history of science expose their fundamental flaws. We find that arguments from theoretical utility invoke considerations that are not truth conducive and that justifications for claims that a theory possesses theoretical virtues often assume the truth of the theory such virtues are supposed to support. We conclude that theoretical utility arguments provide no epistemic grounds for metaphysical inquiry.     

A Naturalistic Look into Maddy's Naturalistic Philosophy of Mathematics

This paper discusses Penelope Maddy's (b.1950) naturalistic philosophy of mathematics,which is one of the most influential forms of post-Quinean naturalism in the philosophy of mathematics.Two defining features of Maddy's theory,namely the methodological autonomy of mathematics and the equivalence of Thin Realism and Arealism,are analyzed,and some criticisms of them are posed from within the naturalistic line of thought itself.In the course of this analysis and criticism,the paper will also consider Maddy's objections to the Quinean Indispensability Argument,which are the starting point of her own version of naturalism.     

Last and fast? – A gender-specific analysis of effort gains in swimming relay events across Olympic Games and World Championships during the past 20 years

Elite swimmers are individual athletes competing mostly on their own. However, when competing in a relay team, they are exposed to social influences possibly leading to effort gains compared to their individual performance. This study investigated effort gains in relay team members during 4 × 100 m freestyle races of Olympic Games and World Championships across the past 20 years. We assumed increasing effort gains in swimmers competing on later serial positions within their relay team since weaknesses in their performances can increasingly less be compensated by their teammates (social indispensability). Furthermore, we assumed a stronger gain in female athletes since females have been shown to be more affected by social indispensability then males. Using linear mixed modelling analyses, we additionally examined the moderating impact of the relay team outcome (i.e. medal-winning chance) on effort gains and indispensability effects while accounting for current team rankings at change-over. Except for the first swimmer, overall effort gains in relay performances were found as compared to performances in individual races during the same championship. Furthermore, these gains were close to equally distributed among both laps of the 100 m distance. However, even though effort gains are tending to be most pronounced for the last relay team swimmer we failed to detect any significant indispensability effect in our data set. Noteworthy, female swimmers showed larger effort gains when winning a medal (based on the current team rankings) was likely. In contrast, males showed effort gains irrespective of the serial order within the relay team and medal chance. Consequently, tentative recommendations are derived on how to line up a relay team.     

Intrinsic Explanation and Field’s Dispensabilist Strategy

Abstract

Hartry Field defended the importance of his nominalist reformulation of Newtonian Gravitational Theory, as a response to the indispensability argument, on the basis of a general principle of intrinsic explanation. In this paper, I argue that this principle is not sufficiently defensible, and can not do the work for which Field uses it. I argue first that the model for Field’s reformulation, Hilbert’s axiomatization of Euclidean geometry, can be understood without appealing to the principle. Second, I argue that our desires to unify our theories and explanations undermines Field’s principle. Third, the claim that extrinsic theories seem like magic is, in this case, really just a demand for an account of the applications of mathematics in science. Finally, even if we were to accept the principle, it would not favor the fictionalism that motivates Field’s argument, since the indispensabilist’s mathematical objects are actually intrinsic to scientific theory.     

Quine's Weak and Strong Indispensability Argument

Quine's views on indispensability arguments in mathematics are scrutinised. A weak indispensability argument is distinguished from a strong indispensability thesis. The weak argument is the combination of the criterion of ontological commitment, holism and a mild naturalism. It is used to refute nominalism. Quine's strong indispensability thesis claims that one should consider all and only the mathematical entities that are really indispensable. Quine has little support for this thesis. This is even clearer if one takes into account Maddy's critique of Quine's strong indispensability thesis. Maddy's critique does not refute Quine's weak indispensability argument. We are left with a weak and almost unassailable indispensability argument. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mathematical Spandrels

The aim of this paper is to open a new front in the debate between platonism and nominalism by arguing that the degree of explanatory entanglement of mathematics in science is much more extensive than has been hitherto acknowledged. Even standard examples, such as the prime life cycles of periodical cicadas, involve a penumbra of mathematical features whose presence can only be explained using relatively sophisticated mathematics. I introduce the term ‘mathematical spandrel’ to describe these penumbral properties, and focus on the property that cicada period lengths are expressible as the sum of two perfect squares. I argue that mathematical spandrels pose a particular problem for nominalism because of the way in which they are entangled with scientific explanations.     

Mathematics and Program Explanations

Aidan Lyon has recently argued that some mathematical explanations of empirical facts can be understood as program explanations. I present three objections to his argument.     

Interethnic relations in Malaysia: Group identifications,indispensability and inclusive nationhood

This paper focuses on interethnic relations in Malaysia and examines survey data collected among Malay (n = 405), Chinese (n = 90), and Indian (n = 53) participants. In agreement with the Common In‐group Identity Model, inclusive nationhood was related to more positive out‐group attitudes. Relative in‐group indispensability was related to higher bias as predicted by the In‐group Projection Model. Furthermore, the dominant group of Malay had higher in‐group indispensability, more strongly endorsed an inclusive national representation, had stronger ethnic and national identification, and a stronger association between both identifications.