|Introduction, philosophy: the introduction of objects establishes rules for the use of linguistic expressions for the objects, not a determination or description of these objects. See also definitions, use, language, expressiveness, localization.|
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|Introduction||Brandom II 94
1. rule: licenses the transition from p to p tonk q for any q.
2. Rule: licenses the transition from p tonk q to q. Thus we have a "network map for inferences": any possible conclusion is allowed!
Conservativity/Conservative Expansion/Dummett: If a logical constant is introduced by introduction and elimination rules, we may call it a conservative extension of language.
For example, this might be true of Belnaps "tonk": the introduction rule of the disjunction and the elimination rule of the conjunction.
PriorVsBelnap/PriorVsGentzen: this is the bankruptcy of definitions in the style of Gentzens.
BelnapVsPrior: if one introduces logical vocabulary, one can restrict such definitions by the condition that the rule does not allow inferences with only old vocabulary that was not already allowed before the introduction of the logical vocabulary. (Conservative expansion).
Such a restriction is necessary and sufficient.
Brandom: the expressive analysis of the logical vocabulary provides us with a deep reason for this condition: only in this way the logical vocabulary can perform its expressive function.
The introduction of new vocabulary would allow new material inferences without the constraining condition (conservativity) and would thus change the contents correlated with the old vocabulary.
Facing the Future: Agents and Choices in Our Indeterminist World Oxford 2001
Expressive Vernunft Frankfurt 2000
Begründen und Begreifen Frankfurt 2001