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首页> 外文期刊>Synthese: An International Journal for Epistemology, Methodology and Philosophy of Science >Hume on the social construction of mathematical knowledge
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Hume on the social construction of mathematical knowledge

机译：关于数学知识的社会建构

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Mathematics for Hume is the exemplary field of demonstrative knowledge. Ideally, this knowledge is a priori as it arises only from the comparison of ideas without any further empirical input; it is certain because demonstration consist of steps that are intuitively evident and infallible; and it is also necessary because the possibility of its falsity is inconceivable as it would imply a contradiction. But this is only the ideal, because demonstrative sciences are human enterprises and as such they are just as fallible as their human practitioners. According to the reading suggested here, Hume develops a radical sceptical challenge for mathematics, and thereby he undermines the knowledge claims associated with demonstrative reasoning. But Hume does not stop there: he also offers resources for a sceptical solution to this challenge, one that appeals crucially to social practices, and sketches the social genealogy of a community-wide mathematical certainty. While explaining this process, he relies on the conceptual resources of his faculty psychology that helps him to distinguish between the metaphysics and practices of mathematical knowledge. His account explains why we have reasons to be dubious about our reasoning capacities, and also how human nature and sociability offers some remedy from these epistemic adversities.
机译：休谟的数学是示范知识的示范领域。理想情况下，这种知识是一个先验，因为它只从没有任何进一步的经验投入的思想的比较中产生;这是因为展示由直观明显和充制的步骤组成;并且它也是必要的，因为它的虚假可能性是不可想象的，因为它意味着矛盾。但这只是理想的，因为证明科学是人类企业，因此它们与他们的人类从业者一样差不多。根据这里的阅读建议，Hume对数学产生了激进的持怀疑态度，从而破坏了与证明推理相关的知识声明。但休谟并没有停止存在：他还为这一挑战提供了持怀疑态度的解决方案，这是一个对社会实践至关重要的持怀疑态度的资源，并阐述了社会数学确定性的社会家谱。在解释这一过程的同时，他依赖于他的教师心理学的概念资源，帮助他区分数学知识的形而上学和实践。他的账户解释了为什么我们有理由对我们的推理能力负责，以及人类的性质和恐怖性如何提供这些认知逆境的一些补救措施。

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