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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

[statements held to be true because of a logic system]

24 ideas
Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge]
Logical truths are known by their extreme generality [Russell]
Logical truths are just 'by-products' of the introduction rules for logical constants [Wittgenstein, by Hacking]
A sentence is logically true if all sentences with that grammatical structure are true [Quine]
Having a valid form doesn't ensure truth, as it may be meaningless [Putnam]
Logical truths and inference are characterized either syntactically or semantically [Dummett]
Restrict 'logical truth' to formal logic, rather than including analytic and metaphysical truths [Shoemaker]
A logical truth or tautology is a logical consequence of the empty set [Enderton]
Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
A logical truth is true in virtue of the nature of the logical concepts [Fine,K]
Logic holding between indefinite sentences is the core of all language [Fine,K]
'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess]
'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
Logically true sentences are true in all structures [Zalabardo]
The semantical notion of a logical truth is validity, being true in all interpretations [Sider]
It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider]
A logical truth is the conclusion of a valid inference with no premisses [Read]
Modern logical truths are true under all interpretations of the non-logical words [Potter]
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall]
Logically valid sentences are analytic truths which are just true because of their logical words [McGee]
Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
Logical truths are just the assumption-free by-products of logical rules [Rumfitt]