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Logic/Brandom: do not only restrict to formally valid inferences. - BrandomVsFormalism: one should assume silent premises and implicit logic rules with everyone - Dummett: one should not define logical consequences in concepts of logical truth.
Achilles and the tortoise/Carroll: however, some inferential definitions must be implied. - There must be rules, not only truths.
Tells us something about the conceptual contents task: not proving something - the formal accuracies are derived from the material accuracies, which contain much more non-logical vocabulary.
Logic/Frege/Brandom: The task is an expressive one: not to prove something, but to say it - even in science concepts are formed arbitrarily - Goal: not a certain kind of truth but of inferences.
Conceptual contents are considered to be identified through their inferential role - which requires that one can speak meaningfully about consequences, even before a specific logical vocabulary is introduced.
Logic/Brandom: the use of identity and quantifiers requires the use of singular terms and predicates. Terms (symmetric) must be interchangeable (identity) - predicates (asymmetric) must provide the frame for expressing incompatibilities - BrandomVsFormalism: Accuracies of inference are not always the same as logical correctness.
Logic/tradition: bottom-up: from the analysis of the meanings of the singular terms to the judgments.
Brandom, New: top-down: Pragmatism: first, the use of terms - ((s) always in complete sentences.)
Expressive Vernunft Frankfurt 2000
Begründen und Begreifen Frankfurt 2001