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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not

[role of 'not' in systems of logic]

11 ideas
The contradictory of a contradictory is an affirmation [Stoic school, by Diog. Laertius]
Normativity needs the possibility of negation, in affirmation and denial [Fichte, by Pinkard]
Negation of negation doubles back into a self-relationship [Hegel, by Houlgate]
Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell]
Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell]
We may correctly use 'not' without making the rule explicit [Wittgenstein]
Sommers promotes the old idea that negation basically refers to terms [Sommers, by Engelbretsen]
Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett]
Natural language 'not' doesn't apply to sentences [Dummett]
'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride]
Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen]