Regula et sententia convertuntur: on classified inferences in linguistic understanding

Abstract

It seems helpful to distinguish between norms that implicitly govern our action and determine its correctness in view of forms of (linguistic and non-linguistic) cooperations on one side, explicit rules that tell us what we may or must do under certain conditions on the other side. As a result, rules are made explicit in systems of (hypothetical) sentences (with premises) and sentences express rules. Under this view, the logical connectives and quantifiers can be seen as means to express complex admissible rules, as all versions of rule- or proof-theoretical semantics for the logical words convincingly show for all pure, i. e. ideal cases. In the non-pure or empirical case of world related words, admissibility turns into a condition of general harmony of the relation between differentiation and attached default inference of the corresponding ‘inferentially thick’ concepts. In the Tractatus, Wittgenstein does not see yet the difference between standing sentences that express paradigm inferences for prototype cases and their empirical applications. Since the treatment of exceptional cases must be externalized to good judgement in singular and particular applications, we need to see the contrast between an always monotonic “and” in standing sentences or pure theories and a non-monotonic “but”, which is not just an “and” with some colouring connotations, as Frege has said: the dialogical norms of its use cannot even be expressed by a list of rules or sentences.