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The proof-theoretic way of capturing consequence was challenged by Alfred Tarski (1936), who in fact denied that the approach would be capable of yielding an adequate account of consequence. Tarski claims that, e.g., to infer every natural number has the property E from the infinite number of statements 0 has the property E, 1 has the property E, ... is legitimate, but in principle not graspable proof-theoretically. He thus urges the necessity of a better account for consequence; the one he proposes is based on the intuitive idea that valid inferences are those which remain valid whatever concrete objects the expressions in them may be considered to refer to.

DOI: 10.1007/978-94-015-8468-5_4

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