数学证明的非形式逻辑
The Informal Logic of Mathematical Proof
摘要：
非形式逻辑是一种论证分析的方法，它是形式逻辑的补充，提供了对论证特征的务实处理，这些特征不能被还原为逻辑形式。本文的中心主张是，一个更细致入微的理解数学证明和发现可以通过关注数学论证的方面，可以捕获的非正式的，而不是正式的，逻辑。两个帐户的论证被认为是：开创性的工作斯蒂芬图尔明[使用的论点，剑桥大学出版社，1958年]和最近的研究道格拉斯沃尔顿，[例如，新的辩证法：会话语境的论点，多伦多大学出版社，1998年]。这两种方法的重点在很大程度上都局限于自然语言论证。然而，沃尔顿的方法特别提供了一个富有成效的分析数学证明。他提供了一个辩论策略的上下文帐户，区分各种不同类型的对话中可能发生的论点。这种分析代表了许多不同的谬误或非法论点，因为部署了有时在不允许的情况下可以接受的战略。我认为，数学证明部署在更广泛的各种类型的对话比通常被认为。我继续表明，许多重要的哲学和教学问题的数学证明产生的失败，使明确的类型的对话中，证明介绍。
英文摘要：
Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is that a more nuanced understanding of mathematical proof and discovery may be achieved by paying attention to the aspects of mathematical argumentation which can be captured by informal, rather than formal, logic. Two accounts of argumentation are considered: the pioneering work of Stephen Toulmin [The uses of argument, Cambridge University Press, 1958] and the more recent studies of Douglas Walton, [e.g. The new dialectic: Conversational contexts of argument, University of Toronto Press, 1998]. The focus of both of these approaches has largely been restricted to natural language argumentation. However, Walton's method in particular provides a fruitful analysis of mathematical proof. He offers a contextual account of argumentational strategies, distinguishing a variety of different types of dialogue in which arguments may occur. This analysis represents many different fallacious or otherwise illicit arguments as the deployment of strategies which are sometimes admissible in contexts in which they are inadmissible. I argue that mathematical proofs are deployed in a greater variety of types of dialogue than has commonly been assumed. I proceed to show that many of the important philosophical and pedagogical problems of mathematical proof arise from a failure to make explicit the type of dialogue in which the proof is introduced.
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