Abstract
Self-deductibility is the Stoic version of the law of identity : if A, then A. After a discussion on its role, we suggest a natural system of axioms and rules for a logic in which this law is not valid, based on a simple model where proofs are families of strictly injective maps. Finally we develop some general theory of taxonomies (i.e. “categories without identities”) and place this particular example into a more general algebraic picture.
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Ageron, P. (2005). Logic without Self-Deductibility. In: Beziau, JY. (eds) Logica Universalis. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7304-0_5
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DOI: https://doi.org/10.1007/3-7643-7304-0_5
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7259-0
Online ISBN: 978-3-7643-7304-7
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