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Connectives/Gentzen/Brandom: defined according to their inferential role. (epoch-making): Definition Introduction rules: sufficient conditions for the use of the connective - Definition elimination rules: necessary consequences of the use (of the connective) - E.g. in order to define the inferential role of "&" in Boole you indicate that everyone who is defined on p and q thus has to be regarded as defined on p&q as well - the first part without the connective specifies the circumstances, i.e. the sets of the premises.
> Dummett: transferred to sentences, singular terms and predicates - it may be that we do not overlook all connections - conservative extension: by these two rules.
Expressive Vernunft Frankfurt 2000
Begründen und Begreifen Frankfurt 2001