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Conference on Computability in Europe

CiE 2010: Programs, Proofs, Processes pp 427–437Cite as

Computing with Concepts, Computing with Numbers: Llull, Leibniz, and Boole

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6158))

Abstract

We consider two ways to understand “reasoning as computation”, one which focuses on the computation of concept symbols and the other on the computation of number symbols. We illustrate these two ways with Llull’s Ars Combinatoria and Leibniz’s attempts to arithmetize language, respectively. We then argue that Boole’s development of an algebra of reasoning was in a large part successful due to its ability to marry the two types of computation that are exemplified in Llull’s and Leibniz’s works.

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Author information

Authors and Affiliations

  1. Institute for Logic, Language, and Computation,  

    Sara L. Uckelman

Authors
  1. Sara L. Uckelman
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Editor information

Editors and Affiliations

  1. Departamento de Matemática, Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016, Lisboa, Portugal

    Fernando Ferreira

  2. Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, P.O. Box 94242, 1090, Amsterdam, GE, The Netherlands

    Benedikt Löwe

  3. Departamento de Informática e Ingeniería de Sistemas, Universidad de Zaragoza, María de Luna 1, 50018, Zaragoza, Spain

    Elvira Mayordomo

  4. Universidade dos Açores, Campus de Ponta Delgada, Apartado 1422, 9501-801, Ponta Delgada, Açores, Portugal

    Luís Mendes Gomes

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Uckelman, S.L. (2010). Computing with Concepts, Computing with Numbers: Llull, Leibniz, and Boole. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_47

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  • DOI: https://doi.org/10.1007/978-3-642-13962-8_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13961-1

  • Online ISBN: 978-3-642-13962-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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