In recent years philosophers have used results from cognitive science to formulate epistemologies of arithmetic (e.g. Giaquinto in J Philos 98(1):5–18, 2001). Such epistemologies have, however, been criticised, e.g. by Azzouni (Talking about nothing: numbers, hallucinations and fictions, Oxford University Press, 2010), for interpreting the capacities found by cognitive science in an overly numerical way. I offer an alternative framework for the way these psychological processes can be combined, forming the basis for an epistemology for arithmetic. The resulting framework avoids assigning numerical content to the Approximate Number System and Object Tracking System, two systems that have so far been the basis of epistemologies of arithmetic informed by cognitive science. The resulting account is, however, only a framework for an epistemology: in the final part of the paper I argue that it is compatible with both platonist and nominalist views of numbers by fitting it into an epistemology for ante rem structuralism and one for fictionalism. Unsurprisingly, cognitive science does not settle the debate between these positions in the philosophy of mathematics, but I it can be used to refine existing epistemologies and restrict our focus to the capacities that cognitive science has found to underly our mathematical knowledge.

近年来，哲学家们利用认知科学的成果来制定算术认识论（例如，Giaquinto in J Philos 98(1):5–18, 2001）。然而，此类认识论受到了批评，例如 Azzouni（无谈之谈：数字、幻觉和小说，牛津大学出版社，2010 年）以过度数字化的方式解释认知科学发现的能力。我为这些心理过程的组合方式提供了一个替代框架，形成了算术认识论的基础。由此产生的框架避免将数字内容分配给近似数字系统和对象跟踪系统，这两个系统迄今为止一直是认知科学提供的算术认识论的基础。然而，由此产生的解释只是一个认识论的框架：在论文的最后一部分，我认为它与柏拉图主义和唯名主义的数字观点兼容，因为它适合于对物结构主义的认识论和虚构主义的认识论。不出所料，认知科学并没有解决数学哲学中这些立场之间的争论，但它可以用来完善现有的认识论，并将我们的注意力限制在认知科学发现的作为我们数学知识基础的能力上。