I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects.

中文翻译：

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数学中的客观性，没有数学对象

我确定相信数学知识的客观性的两个原因：表面客观性和科学应用。围绕算术，我从解释这两个原因的角度来分析柏拉图主义和认知本土主义。在确定这两种理论都遇到困难之后，我提出了一种替代的认识论解释，它结合了文化适应和累积文化进化的理论框架。我表明这个说明可以解释为什么算术知识看起来是客观的并且具有科学应用。最后，我会争辩说，虽然这个解释与柏拉图主义的形而上学兼容，但它不需要假设独立于心灵的数学对象。