Paradoxes and Failures of Cut
Paradoxes and Failures of Cut
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剪切的悖论和失败
DOI：
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发表时间：
2013
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影响因子：
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通讯作者：
David Ripley
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作者：
David Ripley
本文提出并推动了一种新的哲学和逻辑方法来研究真理和语义悖论。它从一种推理主义，特别是双边主义的意义理论开始--一种认为意义由可断言和可否认条件构成的理论--并展示了经典逻辑通常的多结论顺序演算如何被赋予推理主义动机，使经典模型理论只具有派生重要性。然后，本文使用这一意义理论来呈现和激发一个逻辑系统-ST-它用一个完全透明的真值谓词保守地扩展了经典逻辑。这个系统被证明允许在完整的(涉及真理的)词汇上进行经典推理，但是非传递性的。概述了传递性确实成立的一些特殊情况。ST还给出了一种常见的非经典逻辑模型：强Kleene估值方案上的克里普克不动点。最后，为了给出一个悖论句子的理论，区分了两种断言和两种否认。一方面，自相矛盾的句子既不能断言，也不能否认；另一方面，它们必须既断言又否认。将目标理论与更熟悉的相关系统进行了比较，并对一些反对意见进行了考虑和回应。
This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning—one which takes meaning to be constituted by assertibility and deniability conditions—and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system—ST—that conservatively extends classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered and responded to.