| 20788 | The contradictory of a contradictory is an affirmation [Stoic school, by Diog. Laertius] |
| 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. | |
| From: report of Stoic school (fragments/reports [c.200 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.69 | |
| 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'. |
| 22017 | Normativity needs the possibility of negation, in affirmation and denial [Fichte, by Pinkard] |
| Full Idea: To adopt any kind of normative stance is to commit oneself necessarily to the possibility of negation. It involves doing something correctly or incorrectly, so there must exist the possibility of denying or affirming. | |
| From: report of Johann Fichte (The Science of Knowing (Wissenschaftslehre) [1st ed] [1794]) by Terry Pinkard - German Philosophy 1760-1860 05 | |
| A reaction: This seems to be the key idea for understanding Hegel's logic. Personally I think animals have a non-verbal experience of negation - when a partner dies, for example. |
| 21777 | Negation of negation doubles back into a self-relationship [Hegel, by Houlgate] |
| Full Idea: For Hegel, the 'negation of negation' is negation that, as it were, doubles back on itself and 'relates itself to itself'. | |
| From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 6 'Space' | |
| A reaction: [ref VNP 1823 p.108] Glad we've cleared that one up. |
| 16489 | Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell] |
| Full Idea: Imagine a person who knew everything that can be stated without using the word 'not' or some equivalent; would such a person know the whole course of nature, or would he not? | |
| From: Bertrand Russell (Human Knowledge: its scope and limits [1948], 9) | |
| A reaction: Nowadays we might express Russell's thought as 'Does God need the word 'not'?'. Russell's thesis is that such words concern psychology, and not physics. God would need 'not' to describe how human minds work. |
| 18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
| Full Idea: Russell explained ¬p by saying that ¬p is true if p is false and false if p is true. But this is not an explanation of negation, for it might apply to propositions other than the negative. | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Ludwig Wittgenstein - Lectures 1930-32 (student notes) B XI.3 | |
| A reaction: Presumably he is thinking of 'the light is on' and 'the light is off'. A very astute criticism, which seems to be correct. What would Russell say? Perhaps we add that negation is an 'operation' which achieves flipping of the truth-value? |
| 18723 | We may correctly use 'not' without making the rule explicit [Wittgenstein] |
| Full Idea: Correct use does not imply the ability to make the rules explicit. Understanding 'not' is like understanding a move in chess. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B XII.1) |
| 23493 | 'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein] |
| Full Idea: If there were an object called 'not', it would follow that 'not-not-p' would say something different from what 'p' said, just because the one proposition would then be about 'not', and the other would not. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.44) | |
| A reaction: That is, the first proposition would be about not-p, and the second would be about p. Assuming we can say what such things are 'about'. A rather good argument that the connectives are not entities. P and double-negated P should be indistinguishable. |
| 23066 | Negation doesn't arise from reasoning, but from deep instincts [Cioran] |
| Full Idea: Negation never proceeds from reasoning but from something much more obscure and old. Arguments come afterward, to justify and sustain it. Every no rises out of the blood. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 02) | |
| A reaction: Music to my ears. In the Fregean era no one is allowed to talk about the origins of logical relations in the universal facts of physical existence. You can watch dogs saying no. |
| 18903 | Sommers promotes the old idea that negation basically refers to terms [Sommers, by Engelbretsen] |
| Full Idea: If there is one idea that is the keystone of the edifice that constitutes Sommers's united philosophy it is that terms are the linguistic entities subject to negation in the most basic sense. It is a very old idea, tending to be rejected in modern times. | |
| From: report of Fred Sommers (Intellectual Autobiography [2005]) by George Engelbretsen - Trees, Terms and Truth 2 | |
| A reaction: Negation in modern logic is an operator applied to sentences, typically writing '¬Fa', which denies that F is predicated of a, with Fa being an atomic sentence. Do we say 'not(Stan is happy)', or 'not-Stan is happy', or 'Stan is not-happy'? Third one? |
| 18801 | Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett] |
| 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. | |
| From: Michael Dummett (The Logical Basis of Metaphysics [1991], p.299), quoted by Ian Rumfitt - The Boundary Stones of Thought 1.1 | |
| A reaction: [compressed wording] This is Dummett explaining why he prefers intuitionistic logic, with its doubts about double negation. |
| 19052 | Natural language 'not' doesn't apply to sentences [Dummett] |
| Full Idea: Natural language does not possess a sentential negation-operator. | |
| From: Michael Dummett (Presupposition [1960], p.27) | |
| A reaction: This is a criticism of Strawson, who criticises logic for not following natural language, but does it himself with negation. In the question of how language and logic connect, this idea seems important. Term Logic aims to get closer to natural language. |
| 18476 | 'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride] |
| Full Idea: Statements of the form 'a is F' aren't invariably positive ('a is dead'), and nor are statements of the form 'a isn't F' ('a isn't blind') always negative. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.4) | |
| A reaction: The point is that the negation may be implicit in the predicate. There are many ways to affirm or deny something, other than by use of the standard syntax. |
| 18908 | Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen] |
| Full Idea: Standard logic recognises only one kind of negation: sentential negation. Consequently, negation of a general term/predicate always amounts to negation of the entire sentence. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 3) |