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### 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

#### [general role and status of logical connectives]

29 ideas
 21586 The logical connectives are not objects, but are formal, and need a context [Russell]
 21597 Logical connectives have the highest precision, yet are infected by the vagueness of true and false [Russell, by Williamson]
 6563 'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin]
 10905 My fundamental idea is that the 'logical constants' do not represent [Wittgenstein]
 11065 The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
 11023 The logical connectives are 'defined' by their introduction rules [Gentzen]
 11213 Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
 13829 If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine]
 17896 We need to know the meaning of 'and', prior to its role in reasoning [Prior,AN, by Belnap]
 17898 Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B [Belnap on Prior,AN]
 11021 Prior rejected accounts of logical connectives by inference pattern, with 'tonk' his absurd example [Prior,AN, by Read]
 13836 Maybe introducing or defining logical connectives by rules of inference leads to absurdity [Prior,AN, by Hacking]
 14352 '¬', '&', 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]
 13357 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]
 16974 The nature of each logical concept is given by a collection of inference rules [Correia]
 14186 Logical connectives contain no information, but just record combination relations between facts [Read]
 18782 The connectives are studied either through model theory or through proof theory [Mares]
 15019 Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral [Sider]
 4704 Wittgenstein reduced Russell's five primitive logical symbols to a mere one [O'Grady]