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Single Idea 18955
[filed under theme 5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
]
Full Idea
I don't think all substitution-instances of a valid schema are 'true'; some are clearly meaningless, such as 'If all boojums are snarks and all snarks are egglehumphs, then all boojums are egglehumphs'.
Gist of Idea
Having a valid form doesn't ensure truth, as it may be meaningless
Source
Hilary Putnam (Philosophy of Logic [1971], Ch.3)
Book Ref
Putnam,Hilary: 'Philosophy of Logic' [Routledge 1972], p.28
A Reaction
This seems like a very good challenge to Quine's claim that it is only form which produces a logical truth. Keep deductive and semantic consequence separate, with two different types of 'logical truth'.
The
24 ideas
with the same theme
[statements held to be true because of a logic system]:
16884
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Basic truths of logic are not proved, but seen as true when they are understood
[Frege, by Burge]
|
18273
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Logical truths are known by their extreme generality
[Russell]
|
13830
|
Logical truths are just 'by-products' of the introduction rules for logical constants
[Wittgenstein, by Hacking]
|
9027
|
A sentence is logically true if all sentences with that grammatical structure are true
[Quine]
|
18955
|
Having a valid form doesn't ensure truth, as it may be meaningless
[Putnam]
|
9187
|
Logical truths and inference are characterized either syntactically or semantically
[Dummett]
|
15091
|
Restrict 'logical truth' to formal logic, rather than including analytic and metaphysical truths
[Shoemaker]
|
9721
|
A logical truth or tautology is a logical consequence of the empty set
[Enderton]
|
10049
|
Logical truths may contain non-logical notions, as in 'all men are men'
[Musgrave]
|
10050
|
A statement is logically true if it comes out true in all interpretations in all (non-empty) domains
[Musgrave]
|
11174
|
A logical truth is true in virtue of the nature of the logical concepts
[Fine,K]
|
9771
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Logic holding between indefinite sentences is the core of all language
[Fine,K]
|
15408
|
'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics
[Burgess]
|
10895
|
'Logically true' (|= φ) is true for every truth-assignment
[Zalabardo]
|
10900
|
Logically true sentences are true in all structures
[Zalabardo]
|
13684
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The semantical notion of a logical truth is validity, being true in all interpretations
[Sider]
|
13704
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It is hard to say which are the logical truths in modal logic, especially for iterated modal operators
[Sider]
|
10971
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A logical truth is the conclusion of a valid inference with no premisses
[Read]
|
22295
|
Modern logical truths are true under all interpretations of the non-logical words
[Potter]
|
10696
|
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises
[Beall/Restall]
|
13236
|
Logical truth is much more important if mathematics rests on it, as logicism claims
[Beall/Restall]
|
18754
|
Logically valid sentences are analytic truths which are just true because of their logical words
[McGee]
|
14245
|
Logical truths are true no matter what exists - but predicate calculus insists that something exists
[Oliver/Smiley]
|
18809
|
Logical truths are just the assumption-free by-products of logical rules
[Rumfitt]
|