ABSTRACT

In the debate over whether mathematical facts, properties, or entities explain physical events (in what philosophers call ‘extra-mathematical’ explanations), Aidan Lyon’s (2012 Lyon, Aidan. 2012. “Mathematical Explanations of Empirical Facts, and Mathematical Realism.” Australasian Journal of Philosophy 90 (3): 559–578.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) affirmative answer stands out for its employment of the program explanation (PE) methodology of Frank Jackson and Philip Pettit (1990 Jackson, Frank, and Philip Pettit. 1990. “Program Explanation: A General Perspective.” Analysis 50 (2): 107–117.[Crossref], [Web of Science ®] , [Google Scholar]). Juha Saatsi (2012 Saatsi, Juha. 2012. “Mathematics and Program Explanations.” Australasian Journal of Philosophy 90 (3): 579–584.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; 2016 Saatsi, Juha. 2016. “On the ‘Indispensable Explanatory Role’ of Mathematics.” Mind 125 (500): 1045–1070.[Crossref], [Web of Science ®] , [Google Scholar]) objects, however, that Lyon’s examples from the indispensabilist literature are (i) unsuitable for PE, (ii) nominalizable into non-mathematical terms, and (iii) mysterious about the explanatory relation alleged to obtain between the PEs’ mathematical explanantia and physical explananda. In this paper, I propose a counterexample to Saatsi’s objections. My counterexample is Frank Jackson’s (1998a Jackson, Frank. 1998a. “Colour, Disjunctions, Programming.” Analysis 58 (2): 86–88.[Crossref], [Web of Science ®] , [Google Scholar]) program explanation for color experience, which I argue needs recasting as an extra-mathematical PE due to its implicit reliance on reflectance, a property that suffers conceptual regress unless redefined with Fourier harmonics. Pace Saatsi, I argue that this recast example is an authoritative PE, non-nominalizable, and minimally esoteric. Important for the indispensability debate at large, moreover, is that my counterexample reifies Fourier harmonics without the Enhanced Indispensability Argument (an argument to which Lyon applies PE as a premise). Indispensabilists have long overlooked the conditionalization of a limited mathematical realism on property realism, and my counterexample to Saatsi exploits this conditionalization.

摘要

在关于数学事实、属性或实体是否可以解释物理事件（哲学家称之为“超数学”解释）的辩论中，Aidan Lyon（2012 年） 里昂，艾丹。 2012 年。“经验事实的数学解释和数学实在论。” 澳大利亚哲学杂志90 (3): 559 – 578。[Taylor & Francis Online]、[Web of Science®]  、[Google Scholar] ) 肯定答案因其采用 Frank Jackson 和 Philip Pettit (1990) 的程序解释 (PE) 方法而脱颖而出 杰克逊、弗兰克和菲利普佩蒂特。1990 年。“程序说明：一般观点。” 分析50 (2): 107 – 117。[Crossref]、[Web of Science®]、[  Google Scholar]）。尤哈·萨蒂 (2012) 萨齐，朱哈。 2012 年。“数学和程序说明。” 澳大利亚哲学杂志90 (3): 579 – 584。[Taylor & Francis Online]、[Web of Science®]  、[Google Scholar]；2016年 萨齐，朱哈。 2016 年。“论数学的'不可或缺的解释作用'。” 心智125 (500): 1045 – 1070。[Crossref], [Web of Science®] , [  Google Scholar] ) 反对，然而，里昂在不可或缺的文献中的例子 (i) 不适合 PE，(ii) 可名词化为非数学术语，以及 (iii) 神秘关于所谓PE的数学解释与物理解释之间的解释关系。在本文中，我针对 Saatsi 的反对意见提出了一个反例。我的反例是弗兰克杰克逊 (1998a 杰克逊，弗兰克。 1998a。“颜色，分离，编程。” 分析58 (2): 86 – 88。[Crossref], [Web of Science®] , [  Google Scholar] ) 颜色体验的程序解释，我认为需要将其重新定义为数学外的 PE，因为它隐含地依赖反射率，除非重新定义，否则该属性会遭受概念回归傅立叶谐波。步伐Saatsi，我认为这个重铸的例子是一个权威的 PE，不可命名的，并且最低限度的深奥。此外，对于整个不可或缺性辩论而言，重要的是，我的反例在没有增强的不可或缺性论证（里昂应用 PE 作为前提的论证）的情况下具体化了傅立叶谐波。不可或缺的主义者长期以来忽视了有限的数学现实主义对财产现实主义的条件化，而我对 Saatsi 的反例利用了这种条件化。