What Lakatos Could Teach the Mathematical Physicist
What Lakatos Could Teach the Mathematical Physicist
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拉卡托斯可以教给数学物理学家什么
DOI：
10.1007/978-94-017-0769-5_10
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
Michael Stoeltzner
中科院分区：
文献类型：
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作者：
Michael Stoeltzner
著名的数学物理学家亚瑟·贾菲和弗兰克·奎因在1993年发表在《美国数学学会公报》上的文章《理论数学：迈向数学和理论物理的文化合成》中，为数学家和理论物理学家之间的互动提出了一套药方，这些药方应该通过保护数学严谨性不受控制地猜测来培养数学家对物理学思想的接受度。这一提议在《公报》上引发了激烈的辩论，并导致了《合成》杂志的一期特刊。然而，到目前为止，科学哲学家们几乎没有讨论过这场辩论，可能是因为它缺乏一个系统的框架。在这篇文章中，我从伊姆雷·拉卡托斯的数学哲学的角度描述了贾菲-奎因辩论中采取的各种立场，这种哲学似乎最适合于关于数学增长的辩论。在概述了从拉卡托斯出版的著作中吸取的教训之后，我检查了拉卡托斯的描述中的哪些修改是适当的，以使对公理化在其中发挥关键作用的现代数学物理的富有成效的评估成为可能。
In their 1993 article "'Theoretical Mathematics': Toward a Cultural Synthesis of Mathematics and Theoretical Physics" published in the Bulletin of the American Mathematical Society, the eminent mathematical physicists Arthur Jaffe and Frank Quinn proposed a set of prescriptions for the interaction between mathematicians and theoretical physicists that should foster mathematicians' receptivity of ideas from physics by safeguarding mathematical rigour against uncontrolled speculation. The proposal propelled and intensive debate in the Bulletin and lead to a special issue of the journal Synthese. So far, however, philosophers of science have hardly addressed this debate, perhaps because it lacks a systematic framework. In this contribution I portray the various stances taken in the Jaffe-Quinn debate from the perspective of Imre Lakatos philosophy of mathematics that seems most suitable for a debate concerning mathematical growth. After outlining the lessons to be drawn for it from Lakatos's published works, I examine which modifications of Lakatos's account are in place to enable a fruitful assessment of present mathematical physics in which axiomatization plays a key role.