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Full Idea
Explanations of classical negation assume that knowing what it is for the truth-condition of some statement to obtain, independently of recognising it to obtain, we thereby know what it is for it NOT to obtain; but this presupposes classical negation.
Gist of Idea
Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions
Source
Michael Dummett (The Logical Basis of Metaphysics [1991], p.299), quoted by Ian Rumfitt - The Boundary Stones of Thought 1.1
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.4
A Reaction
[compressed wording] This is Dummett explaining why he prefers intuitionistic logic, with its doubts about double negation.
Related Idea
Idea 18799 Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt]
| 20788 | The contradictory of a contradictory is an affirmation [Stoic school, by Diog. Laertius] |
| 22017 | Normativity needs the possibility of negation, in affirmation and denial [Fichte, by Pinkard] |
| 21777 | Negation of negation doubles back into a self-relationship [Hegel, by Houlgate] |
| 16489 | Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell] |
| 18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
| 18723 | We may correctly use 'not' without making the rule explicit [Wittgenstein] |
| 23493 | 'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein] |
| 23066 | Negation doesn't arise from reasoning, but from deep instincts [Cioran] |
| 18903 | Sommers promotes the old idea that negation basically refers to terms [Sommers, by Engelbretsen] |
| 18801 | Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett] |
| 19052 | Natural language 'not' doesn't apply to sentences [Dummett] |
| 18476 | 'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride] |
| 18908 | Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen] |