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 rule-following skepticism. We argue, with the help of C. S. Peirce's distinction between corollarial and theorematic proofs, that his intuitions are better explained by resistance to what we call conceptual omniscience, treating meaning as fixed content specified in advance. We interpret the distinction in the context of modern epistemic logic and semantic information theory, and show how removing conceptual omniscience helps resolve Wittgenstein's paradoxes and explain the puzzle of deduction, its ability to generate new knowledge and meaning.

中文翻译：

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维特根斯坦、皮尔斯和数学证明悖论

维特根斯坦关于未经证明的命题毫无意义、证明形成新概念和新规则、矛盾关注有限的悖论命题，导致了各种解释，其中大部分都集中在遵循规则的怀疑论上。我们认为，在 CS Peirce 对推论证明和理论证明之间的区别的帮助下，他的直觉可以通过对我们所谓的概念无所不知的抵抗得到更好的解释，将意义视为预先指定的固定内容。我们在现代认知逻辑和语义信息理论的背景下解释了这种区别，并展示了去除概念无所不知如何帮助解决维特根斯坦悖论并解释演绎之谜，即演绎产生新知识和意义的能力。