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### 5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

#### [defining when one idea logically follows another]

27 ideas
 12373 Something holds universally when it is proved of an arbitrary and primitive case [Aristotle]
 13342 Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap]
 18812 Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt]
 13681 Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider]
 13827 Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz]
 14181 Validity is where either the situation or the interpretation blocks true premises and false conclusion [Etchemendy, by Read]
 14180 Etchemendy says fix the situation and vary the interpretation, or fix interpretations with varying situations [Etchemendy, by Read]
 10260 Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro]
 17286 Logical consequence is verification by a possible world within a truth-set [Fine,K]
 10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
 14188 Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read]
 14182 If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read]
 14183 Maybe arguments are only valid when suppressed premises are all stated - but why? [Read]
 13682 Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider]
 13679 Maybe logical consequence is more a matter of provability than of truth-preservation [Sider]
 13678 The most popular account of logical consequence is the semantic or model-theoretic one [Sider]
 13680 Maybe logical consequence is a primitive notion [Sider]
 10970 A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read]
 10984 Logical consequence isn't just a matter of form; it depends on connections like round-square [Read]
 15029 Modal accounts of logical consequence are simple necessity, or essential use of logical words [Sider]
 18755 Validity is explained as truth in all models, because that relies on the logical terms [McGee]
 11061 Intensional consequence is based on the content of the concepts [Hanna]
 13288 Consequence is truth-preserving, either despite substitutions, or in all interpretations [Koslicki]
 18813 Logical consequence is a relation that can extended into further statements [Rumfitt]
 12195 Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
 12199 There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
 12201 We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]