Logic without Self-Deductibility

Pierre Ageron ()
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Pierre Ageron: Université de Caen, Département de mathématiques et mécanique

A chapter in Logica Universalis, 2005, pp 89-95 from Springer

Abstract: 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.

Keywords: law of identity; self-deductibility; taxonomy (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7304-7_5

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DOI: 10.1007/3-7643-7304-0_5

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