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Article ID: CBB399393209

Peirce’s Dragon-Head Logic (R 501, 1901) (2022)

Ma, Minghui (Author)
Pietarinen, Ahti-Veikko (Author)

Archive for History of Exact Sciences
Volume: 76
Issue: 3
Pages: 261-317

URI: https://doi.org/10.1007/s00407-021-00285-0

DOI: 10.1007/s00407-021-00285-0

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Semiotics Philosophy Logic 20th century, early Peirce, Charles Sanders

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 We provide a complete reconstruction and transcription of these previously unpublished sets of manuscript sheets and analyse their main content.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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