Ideas from 'The Logical Syntax of Language' by Rudolph Carnap [1934], by Theme Structure

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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
Each person is free to build their own logic, just by specifying a syntax