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Single Idea 20788

[filed under theme 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not ]

Full Idea

A double contradictory is the contradictory of a contradictory, for example, 'It s not the case that it is not day'. It posits that it is day.

Gist of Idea

The contradictory of a contradictory is an affirmation

Source

report of Stoic school (fragments/reports [c.200 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.69

Book Ref

'The Stoics Reader', ed/tr. Inwood,B/Gerson,L.P. [Hackett 2008], p.18


A Reaction

Seems like common sense to the stoics, but verifying the double negative may be a different procedure to verifying the affirmative. 'Are you happy?' 'Well ….I'm not unhappy'. 'Is it day yet?' 'Well, it's not night'.


The 13 ideas with the same theme [role of 'not' in systems of logic]:

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]
'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein]
Negation doesn't arise from reasoning, but from deep instincts [Cioran]
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]