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

[defining when one idea logically follows another]

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