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Coffa’s Kant and the evolution of accounts of mathematical necessity

机译：科法的康德与数学必要性解释的演变

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According to Alberto Coffa in The Semantic Tradition from Kant to Carnap, Kant’s account of mathematical judgment is built on a ‘semantic swamp’. Kant’s primitive semantics led him to appeal to pure intuition in an attempt to explain mathematical necessity. The appeal to pure intuition was, on Coffa’s line, a blunder from which philosophy was forced to spend the next 150 years trying to recover. This dismal assessment of Kant’s contributions to the evolution of accounts of mathematical necessity is fundamentally backward-looking. Coffa’s account of how semantic theories of the a priori evolved out of Kant’s doctrine of pure intuition rightly emphasizes those developments, both scientific and philosophical, that collectively served to undermine the plausibility of Kant’s account. What is missing from Coffa’s story, apart from any recognition of Kant’s semantic innovations, is an attempt to appreciate Kant’s philosophical context and the distinctive perspective from which Kant viewed issues in the philosophy of mathematics. When Kant’s perspective and context are brought out, he can not only be seen to have made a genuinely progressive contribution to the development of accounts of mathematical necessity, but also to be relevant to contemporary issues in the philosophy of mathematics in underappreciated ways. Keywords Kant - Alberto Coffa - Intuition - Necessity - Mathematics
机译：根据《从康德到卡尔纳普的语义传统》中的阿尔贝托·科法（Alberto Coffa）的说法，康德关于数学判断的论述建立在“语义沼泽”的基础上。康德的原始语义学使他诉诸于纯粹的直觉，试图解释数学的必要性。在科法看来，纯粹的直觉是一种错误，哲学被迫在接下来的150年中试图从中恢复。从根本上看，这种对康德对数学必要性帐户演变的贡献的惨淡评估是后向的。科法对先验的语义理论如何从康德的纯粹直觉学说中演变而来的论述正确地强调了科学和哲学的发展，这些发展共同破坏了康德的叙述的合理性。除了对康德的语义创新的任何认识之外，科法故事中缺少的是试图欣赏康德的哲学背景和康德从数学哲学角度看待问题的独特视角。康德提出自己的观点和背景时，不仅可以被视为对数学必要性说明的发展做出了真正的渐进贡献，而且还以未被充分认识的方式与当代数学哲学有关。康德-阿尔贝托·科法-直觉-必然性-数学

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