Orthodoxy holds that there is a determinate fact of the matter about every arithmetical claim. Little argument has been supplied in favour of orthodoxy, and work of Field, Warren and Waxman, and others suggests that the presumption in its favour is unjustified. This paper supports orthodoxy by establishing the determinacy of arithmetic in a well-motivated modal plural logic (Theorem 1). Recasting this result in higher-order logic (Theorem 13) reveals that even the nominalist who thinks that there are only finitely many things should think that there is some sense in which arithmetic is true and determinate.

中文翻译：

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算术是确定的

正统派认为，每一个算术断言都有一个确定的事实。支持正统的论据很少，而菲尔德、沃伦和韦克斯曼等人的工作表明，支持正统的推定是不合理的。本文通过在动机良好的模态复数逻辑（定理 1）中建立算术的确定性来支持正统观念。在高阶逻辑（定理 13）中重铸这个结果表明，即使是认为事物只有有限的唯名论者，也应该认为在某种意义上算术是真实和确定的。