Foundations of Logical Consequence

哲学问题经常以两难境地的形式出现：是否有可能对某个概念进行描述，既能解释其全部性质，又能表明我们如何才能了解它？一个这样的问题是由推理的概念提出的，或者使用技术术语逻辑结果。好的推理和坏的推理、合理的推理和不合理的推理之间是有区别的，任何对逻辑结果的充分描述都必须正确地得出和解释这些区别。然而，这是一个大多数人都有直觉领会的区别。即使我们不知道推理本质的理论基础，但我们都对好的和不好的论点之间的区别有一些概念，而且大部分理由都是正确的。应该给出什么样的逻辑结果才能同时解释我们的直觉推理能力？有两种主要的方法来应对这个挑战：模型论和推理主义。前者使用模型的数学概念，即大体上是对前提和结论的某种可接受的解释。它设想的逻辑结果是，在任何这种解释下，从前提到结论都保持真理。一个论点只有在前提为真的情况下才是有效的，这样解释的话，结论也必须为真。相反，推理论者声称，逻辑结果主要是根据推理规则来解释的。例如，使用‘and’的规则是，从形式‘A和B’的前提可以有效地推断出A或B作为结论。根据推理者的说法，有效的推理仅仅在于(连续)应用这些规则的基本规则。但这两项提议似乎都有可能遭到反对。日常推理者对数学模型了解多少？什么才有资格将一项规则纳入基本曲目？模型论的方法似乎与我们的直觉推理能力脱节，但如果没有解释基本规则是可以接受的，推理主义的方法似乎只是推迟了解释什么是逻辑结果的问题。我们对逻辑结果的令人满意的解释施加了进一步的限制：阐明与此相关的某些著名哲学辩论的地位。最特别的是，我们将集中讨论关于修改逻辑的辩论。传统上，逻辑被认为是不可修改和确定的。但一个多世纪以来，挑战这一点的观点在各种方面得到了有力的辩护，并将继续如此。这两种方法，无论是模型论的还是推理主义的，都能阐明这些辩论(要么支持修正主义者，要么支持保守主义者，要么揭示这场争论是错误的)？该项目将致力于这两种方法的最佳版本，并探索由此产生的账户解决这些困难的能力；根据我们的发现审查修正性辩论；最后返回到直觉推理能力带来的挑战。

A philosophical problem often arises in the form of a dilemma: is it possible to give a characterisation of some notion which both explains its full nature and shows how we can have knowledge of it? One such problem is raised by the notion of inference, or to use the technical term, logical consequence. There is a distinction between good inference and bad, between sound reasoning and unsound reasoning, which any adequate account of logical consequence must draw correctly and explain. Yet this is a distinction which most people have an intuitive grasp of. Even if ignorant of the theoretical underpinnings of the nature of inference, we all have some conception of the difference between good and bad argument, and reason for the most part correctly. What account should be given of what logical consequence consists in which at the same time can explain our intuitive inferential competence?There are two principal approaches to this challenge: model-theoretic, and inferentialist. The former uses the mathematical notion of a model, that is, roughly, a certain kind of admissible interpretation of the premises and conclusion. It conceives of logical consequence as consisting in preservation of truth from premises to conclusion under any such interpretation. An argument is valid just when, provided the premises are true, so interpreted, the conclusion must be true too. The inferentialist, in contrast, claims that logical consequence is to be explained primarily in terms of rules of inference. For example, it is the rule for the use of 'and' that from a premise of the form 'A and B' one can validly infer either A or B as conclusion. According to the inferentialist, valid inference then consists simply in the (successive) application of a basic repertoire of such rules. But both proposals seem open to objection. What do everyday reasoners know about mathematical models? And what qualifies a rule for inclusion in the basic repertoire? The model-theoretic approach seems to lose touch with our intuitive inferential competence, but without an account makes the basic rules acceptable, the inferentialist approach seems merely to have postponed the question of explaining what logical consequence consists in? We impose a further constraint on a satisfactory account of logical consequence: to shed light on the status of certain prominent philosophical debates that bear on it. Most particularly, we shall concentrate on the debates concerning the revision of logic. Traditionally, logic was conceived as unrevisable and certain. But views which challenge this have been vigorously defended for more than a century on a variety of counts and continue to be so. Can either of the approaches, model-theoretic or inferentialist, shed light on these debates (either by lending support to revisionists or conservatives, or by revealing the controversy to be misconceived)? The project will work toward best versions of the two approaches, and explore the ability of the resulting accounts to address these difficulties; review the revisionary debates in the light of our findings; then finally return to the challenges posed by intuitive inferential competence.