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2. De Morgan and Logic

  • Anna-Sophie Heinemann (author)
Chapter of: Augustus De Morgan, Polymath: New Perspectives on his Life and Legacy(pp. 30–54)

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Metadata
Title2. De Morgan and Logic
ContributorAnna-Sophie Heinemann (author)
DOIhttps://doi.org/10.11647/obp.0408.02
Landing pagehttps://www.openbookpublishers.com/books/10.11647/obp.0408/chapters/10.11647/obp.0408.02
Licensehttps://creativecommons.org/licenses/by-nc/4.0/
CopyrightAnna-Sophie Heinemann
PublisherOpen Book Publishers
Published on2024-09-04
Long abstractFrom 1847 onwards, Augustus De Morgan propounded an extension of classical syllogistic logic by the introduction of ‘contraries’. These are negative terms in the sense that, for example, x means non-x within a given ‘universe’. In this chapter, we will focus on De Morgan’s early research on logic between 1847 and 1850, and address De Morgan’s revisions of traditional syllogistic logic in his ‘system of contraries’ and his ‘numerically definite system’. We will discuss his approach to determining portions of ‘universes’, which is based on determining extensions by numbers of instances of terms. The main point will be that De Morgan conceived of logical quantities as scopes and of conjunctive or disjunctive enumeration as quantifications over given domains—which is one of the systematic reasons behind his being involved in a long-lasting debate over the ‘quantification of the predicate’. It will be argued that, despite its relative lack of influence on later developments, De Morgan’s work still represented a notable departure from traditional syllogistic methods and anticipated the modern understanding of quantification in logic.
Page rangepp. 30–54
Print length25 pages
LanguageEnglish (Original)
Contributors

Anna-Sophie Heinemann

(author)

Anna-Sophie Heinemann graduated in philosophy at the University of Jena, Germany, in 2007. In 2014, she received her Ph.D. from the University of Paderborn, Germany. From 2009 to 2020, she was affiliated with the University of Paderborn as a research and teaching assistant associated with the Chair of Philosophy of Science and Technology. Since 2020 she has been in charge of humanities at the head office of the Academic Advisory Commission of Lower Saxony (Wissenschaftliche Kommission Niedersachsen, www.wk.niedersachsen.de) located in Hanover, Germany.

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