Logical consequence and paradoxical reasoning

塔尔斯基对逻辑推论关系的传统分析是从真的角度来解释推论的。达格·普拉维茨（Dag Prawitz）最近提出了一个与之相对立的观点，目的是用证明的概念取代真理的概念。这两种方法的共同之处是将结果描述为“传递”：B是A的逻辑结果，当且仅当真理（分别为：可证明性）从A传递到B。该项目发展了一种替代的后果概念，它拒绝了"传递观点“。这是通过将推论建立在推理规则的局部特征上而不是建立在演绎的全局性质上来实现的。推论的局部特征提供了在所有步骤都是局部正确的证明中区分那些全局有效的和那些全局无效的证明的可能性。局部正确性和整体有效性之间的差距提供了一个原创性的解释，说明在一个悖论论证中的每一步都可能是合理的，而整个论证的结论是不可接受的。

The traditional analysis of the relation of logical consequence due to Alfred Tarski explains consequence in terms of truth. A more recent rival view developed by Dag Prawitz aims at replacing the notion of truth with the one of proof. What is common to both approaches is the characterization of consequence as `transmission': B is a logical consequence of A if and only if truth (resp. provability) is transmitted from A to B.The project develops an alternative conception of consequence, which rejects the ``transmission view''. This is achieved by grounding consequence on local features of inference rules, rather than on global properties of deduction.The local character of consequence offers the possibility to distinguish, among the proofs whose steps are all locally correct, those that are also globally valid from those that are not. The gap between local correctness and global validity provides an original account of how each step in a paradoxical argument may be sound, without the conclusion of the whole argument being acceptable.