Truth predicates are widely believed to be capable of serving a certain logical or quasi-logical function. There is little consensus, however, on the exact nature of this function. We offer a series of formal results in support of the thesis that disquotational truth is a device to simulate higher-order resources in a first-order setting. More specifically, we show that any theory formulated in a higher-order language can be naturally and conservatively interpreted in a first-order theory with a disquotational truth or truth-of predicate. In the first part of the paper we focus on the relation between truth and full impredicative sentential quantification. The second part is devoted to the relation between truth-of and full impredicative predicate quantification.

人们普遍认为真值谓词能够服务于某种逻辑或准逻辑功能。然而，关于这个函数的确切性质几乎没有共识。我们提供了一系列正式的结果来支持这样的论点，即非引用真理是一种在一阶设置中模拟高阶资源的工具。更具体地说，我们表明，任何用高阶语言表述的理论都可以自然而保守地用一阶理论进行解释，该理论具有去引号的真值或谓词真值。在本文的第一部分，我们关注真值与完全禁言句量化之间的关系。第二部分专门讨论真值与完全谓语谓词量化之间的关系。