论文标题
维特根斯坦，皮尔斯和数学证明的悖论
Wittgenstein, Peirce, and paradoxes of mathematical proof
论文作者
论文摘要
维特根斯坦（Wittgenstein）的矛盾论文，即未经证实的命题毫无意义，构成新的概念和规则，矛盾的关注程度有限，导致了各种解释，其中大多数以遵守规则遵守规则的怀疑主义为中心。我们认为，他的直觉反映了对将意义视为固定内容的抵抗力，并且根据C.S. Peirce在化学和理论证明之间的区别，可以更好地理解。我们展示了Peirce在现代认识论逻辑和语义信息理论中证明“所有必要的推理都是图形的”的见解，有助于解释推论产生新知识和含义的矛盾能力。
Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on the rule-following skepticism. We argue that his intuitions rather reflect resistance to treating meaning as fixed content, and are better understood in the light of C.S. Peirce's distinction between corollarial and theorematic proofs. We show how Peirce's insight that "all necessary reasoning is diagrammatic", vindicated in modern epistemic logic and semantic information theory, helps explain the paradoxical ability of deduction to generate new knowledge and meaning.
