Peirce’s Dragon-Head Logic (R 501, 1901)

IF 0.7 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Archive for History of Exact Sciences Pub Date : 2022-02-24 DOI:10.1007/s00407-021-00285-0
Minghui Ma, Ahti-Veikko Pietarinen
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Abstract

Peirce wrote in late 1901 a text on formal logic using a special Dragon-Head and Dragon-Tail notation in order to express the relation of logical consequence and its properties. These texts have not been referred to in the literature before. We provide a complete reconstruction and transcription of these previously unpublished sets of manuscript sheets and analyse their main content. In the reconstructed text, Peirce is seen to outline both a general theory of deduction and a general theory of consequence relation. The two are the cornerstones of modern logic and have played a crucial role in its development. From the wider perspective, Peirce is led to these theories by three important generalizations: propositions to all signs, truth to scriptibility, and derivation to transformability. We provide an exposition of such proposed semiotic foundation for logical constants and point out a couple of further innovations in this rare text, including the sheet of assertion, correction as a dual of deduction and the nature of conditionals as variably strict conditionals.

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皮尔斯龙头逻辑(r501, 1901)
皮尔斯在1901年底写了一篇关于形式逻辑的文章,用一种特殊的龙头和龙尾符号来表达逻辑结果与其性质的关系。这些文本以前从未在文献中提及。我们对这些以前未发表的手稿进行了完整的重建和转录,并分析了它们的主要内容。在重建后的文本中,皮尔斯既概括了一般的演绎理论,又概括了一般性的结果关系理论。二者是现代逻辑的基石,对现代逻辑的发展起着至关重要的作用。从更广泛的角度来看,皮尔斯通过三个重要的概括得出了这些理论:命题到所有符号,真理到可写性,以及推导到可转换性。我们对逻辑常数的符号学基础进行了阐述,并在这篇罕见的文章中指出了一些进一步的创新,包括断言表、作为演绎对偶的更正以及条件句作为可变严格条件句的性质。
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来源期刊
Archive for History of Exact Sciences
Archive for History of Exact Sciences 管理科学-科学史与科学哲学
CiteScore
1.30
自引率
20.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.
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