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Single Idea 10696
[filed under theme 5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
]
Full Idea
If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'.
Gist of Idea
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises
Source
JC Beall / G Restall (Logical Consequence [2005], 4)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.8
A Reaction
These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules.
The
24 ideas
with the same theme
[statements held to be true because of a logic system]:
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16884
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Basic truths of logic are not proved, but seen as true when they are understood
[Frege, by Burge]
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18273
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Logical truths are known by their extreme generality
[Russell]
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13830
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Logical truths are just 'by-products' of the introduction rules for logical constants
[Wittgenstein, by Hacking]
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9027
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A sentence is logically true if all sentences with that grammatical structure are true
[Quine]
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18955
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Having a valid form doesn't ensure truth, as it may be meaningless
[Putnam]
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9187
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Logical truths and inference are characterized either syntactically or semantically
[Dummett]
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15091
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Restrict 'logical truth' to formal logic, rather than including analytic and metaphysical truths
[Shoemaker]
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9721
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A logical truth or tautology is a logical consequence of the empty set
[Enderton]
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10049
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Logical truths may contain non-logical notions, as in 'all men are men'
[Musgrave]
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10050
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A statement is logically true if it comes out true in all interpretations in all (non-empty) domains
[Musgrave]
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11174
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A logical truth is true in virtue of the nature of the logical concepts
[Fine,K]
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9771
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Logic holding between indefinite sentences is the core of all language
[Fine,K]
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15408
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'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics
[Burgess]
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10895
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'Logically true' (|= φ) is true for every truth-assignment
[Zalabardo]
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10900
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Logically true sentences are true in all structures
[Zalabardo]
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13684
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The semantical notion of a logical truth is validity, being true in all interpretations
[Sider]
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13704
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It is hard to say which are the logical truths in modal logic, especially for iterated modal operators
[Sider]
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10971
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A logical truth is the conclusion of a valid inference with no premisses
[Read]
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22295
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Modern logical truths are true under all interpretations of the non-logical words
[Potter]
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10696
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A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises
[Beall/Restall]
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13236
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Logical truth is much more important if mathematics rests on it, as logicism claims
[Beall/Restall]
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18754
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Logically valid sentences are analytic truths which are just true because of their logical words
[McGee]
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14245
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Logical truths are true no matter what exists - but predicate calculus insists that something exists
[Oliver/Smiley]
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18809
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Logical truths are just the assumption-free by-products of logical rules
[Rumfitt]
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