2007 | OriginalPaper | Buchkapitel
Logic without Self-Deductibility
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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.