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Single Idea 13236
[filed under theme 5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
]
Full Idea
If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting.
Gist of Idea
Logical truth is much more important if mathematics rests on it, as logicism claims
Source
JC Beall / G Restall (Logical Pluralism [2006], 2.2)
Book Ref
Beall,J/Restall,G: 'Logical Pluralism' [OUP 2006], p.13
A Reaction
Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic.
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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