Ideas from 'On the General Idea of Proof Theory' by Dag Prawitz [1974], by Theme Structure

[found in 'A Philosophical Companion to First-Order Logic' (ed/tr Hughes,R.I.G.) [Hackett 1993,0-87220-181-3]].

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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
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)
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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)