Foundations of Logical Consequence

一个哲学问题常常以一种两难的形式出现：是否有可能对某个概念给出一个既能解释它的全部性质又能表明我们如何能对它有知识的特征？其中一个这样的问题是由推理的概念引起的，或者使用技术术语，逻辑后果。在好的推理和坏的推理之间，在合理的推理和不合理的推理之间，存在着一种区别，任何对逻辑结果的充分说明都必须正确地得出并解释这种区别。然而，这是一个大多数人都有直觉把握的区别。即使不知道推理本质的理论基础，我们都对好的和坏的论证之间的区别有一些概念，并且大部分推理都是正确的。应该怎样解释逻辑推论所包含的同时又能解释我们的直觉推理能力呢？有两种主要的方法来应对这一挑战：模型理论和推理。前者使用模型的数学概念，也就是说，粗略地说，前提和结论的某种可接受的解释。它设想的逻辑后果包括保存真理从前提到结论在任何这样的解释。一个论点是有效的，只要前提是真的，这样解释，结论也必须是真的。与此相反，推理主义者主张逻辑推论主要是根据推理规则来解释的。例如，使用“and”的规则是，从“A and B”形式的前提中，人们可以有效地推断出A或B作为结论。根据推理主义者的观点，有效的推理仅仅在于（连续地）应用这些规则的基本库。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？那么，什么样的规则才有资格被列入基本规则呢？模型论的方法似乎与我们的直觉推理能力失去了联系，但是，由于没有一个使基本规则可以接受的解释，推理主义的方法似乎只是推迟了解释什么是逻辑后果的问题。我们对逻辑结果的满意解释施加了进一步的限制：阐明与之相关的某些重要哲学辩论的地位，特别是，我们将集中讨论关于逻辑修正的辩论。传统上，逻辑被认为是不可修改的和确定的。但是，挑战这一点的观点在世纪以来一直以各种理由受到有力的辩护，而且这种情况仍在继续。无论是模型论的还是推理主义的方法，都能为这些争论提供启示吗（要么支持修正主义者或保守主义者，要么揭示争论是错误的）？该项目将致力于这两种方法的最佳版本，并探索由此产生的帐户，以解决这些困难的能力;根据我们的研究结果审查修正的辩论;然后最终回到直觉推理能力所带来的挑战。

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.