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13827 | Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work |
Full Idea: Defining logical consequence in the way Tarski does is a rather meagre result, treating an argument as a black box, observing input and output, while disregarding inner structure. We should define logical consequence on the basis of valid arguments. | |||
From: Dag Prawitz (On the General Idea of Proof Theory [1974], §2) |
13826 | Model theory looks at valid sentences and consequence, but not how we know these things |
Full Idea: In model theory, which has dominated the last decades, one concentrates on logically valid sentences, and what follows logically from what, but one disregards questions concerning how we know these things. | |||
From: Dag Prawitz (On the General Idea of Proof Theory [1974], §1) |