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Single Idea 21586
[filed under theme 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
]
Full Idea
Such words as 'or' and 'not' are not names of definite objects, but are words that require a context in order to have a meaning. All of them are formal.
Gist of Idea
The logical connectives are not objects, but are formal, and need a context
Source
Bertrand Russell (Our Knowledge of the External World [1914], 7)
Book Ref
Russell,Bertrand: 'Our Knowledge of the External World' [Routledge 1993], p.212
A Reaction
[He cites Wittgenstein's 1922 Tractatus in a footnote - presumably in a later edition than 1914] This is the most famous idea which Russell acquired from Wittgenstein. It was yet another step in his scaling down of ontology.
The
31 ideas
with the same theme
[general role and status of logical connectives]:
21586
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The logical connectives are not objects, but are formal, and need a context
[Russell]
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23476
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Logical constants seem to be entities in propositions, but are actually pure form
[Russell]
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23477
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We use logical notions, so they must be objects - but I don't know what they really are
[Russell]
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21597
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Logical connectives have the highest precision, yet are infected by the vagueness of true and false
[Russell, by Williamson]
|
6563
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'And' and 'not' are non-referring terms, which do not represent anything
[Wittgenstein, by Fogelin]
|
10905
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My fundamental idea is that the 'logical constants' do not represent
[Wittgenstein]
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11065
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The inferential role of a logical constant constitutes its meaning
[Gentzen, by Hanna]
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11023
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The logical connectives are 'defined' by their introduction rules
[Gentzen]
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11213
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Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule
[Gentzen]
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13829
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If logical truths essentially depend on logical constants, we had better define the latter
[Hacking on Quine]
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17896
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We need to know the meaning of 'and', prior to its role in reasoning
[Prior,AN, by Belnap]
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17898
|
Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B
[Belnap on Prior,AN]
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11021
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Prior rejected accounts of logical connectives by inference pattern, with 'tonk' his absurd example
[Prior,AN, by Read]
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13836
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Maybe introducing or defining logical connectives by rules of inference leads to absurdity
[Prior,AN, by Hacking]
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14352
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'¬', '&', and 'v' are truth functions: the truth of the compound is fixed by the truth of the components
[Jackson]
|
13837
|
With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically
[Hacking]
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13357
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Truth-functors are usually held to be defined by their truth-tables
[Bostock]
|
13825
|
Natural deduction introduction rules may represent 'definitions' of logical connectives
[Prawitz]
|
11175
|
Logical concepts rest on certain inferences, not on facts about implications
[Fine,K]
|
10212
|
Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and'
[Shapiro]
|
15407
|
Formalising arguments favours lots of connectives; proving things favours having very few
[Burgess]
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16974
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The nature of each logical concept is given by a collection of inference rules
[Correia]
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14186
|
Logical connectives contain no information, but just record combination relations between facts
[Read]
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18782
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The connectives are studied either through model theory or through proof theory
[Mares]
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15019
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Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral
[Sider]
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4704
|
Wittgenstein reduced Russell's five primitive logical symbols to a mere one
[O'Grady]
|
18489
|
Connectives link sentences without linking their meanings
[MacBride]
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18751
|
Natural language includes connectives like 'because' which are not truth-functional
[McGee]
|
11210
|
Standardly 'and' and 'but' are held to have the same sense by having the same truth table
[Rumfitt]
|
11212
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The sense of a connective comes from primitively obvious rules of inference
[Rumfitt]
|
18802
|
In specifying a logical constant, use of that constant is quite unavoidable
[Rumfitt]
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