Negation : Not
In logic, logical negation is a unary logical operator that reverses the truth value of its operand.The negation of the statement p is written in various ways:
- ~p;
- ¬p;
- p (which is p with a bar over it);
- NOT p;
- !p
~p is true if and only if p is false. For instance, if p denotes the statement "today is Saturday", then its negation ~p is the statement "today isn't Saturday".
In classical logic, double negation means affirmation; i.e., the statements p and ~(~p) are logically equivalent. In intuitionistic logic, however, ~~p is a weaker statement than p. Nevertheless, ~~~p and ~p are logically equivalent even intuitionistically.
Logical negation can be defined in terms of other logical operations. For example, ~p can be defined as p → F, where → is material implication and F is absolute falsehood. Conversely, one can define F as p & ~p for any proposition p, where & is logical conjunction. The idea here is that any contradiction is false. While these ideas work in both classical and intuitionistic logic, they don't work in Brazilian logic[?], where contradictions are not necessarily false. But in classical logic, we get a further identity: p → q can be defined as ~p ∨ q, where ∨ is logical disjunction.
Algebraically, logical negation corresponds to the complement in a Boolean algebra (for classical logic) or a Heyting algebra[?] (for intuitionistic logic).
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The monk, is a very respectable fighter.
Eustace:
Had he and his fellows thrown open the gate.html">gate
With thirty picked soldiers their siege we might weather,
[Enter Ursula.]
Thurston:
He was dead when we carried him in at the gate.
Thurston:
But he won't speak again, he must lie on his shelf.
Ursula:
And what then? to-morrow we, too, one and all,
I knelt down by Hugo and heard his last words:
Say a mass for my soul -- and give Rollo a mash."
Ursula:
We listened and caught every syllable clear.
Eustace:
Ere the onset, young Henry rode Rollo away;
To-morrow -- though to-morrow for us is too late.
Disembowel'd by the thrust of a freebooter's pike.
Eustace:
But we may hold the walls till to-morrow.
Thurston: Not we.
They'll storm your old building -- and take it, of course,
One-third are disabled, and two-thirds are kill'd.
Ursula:
But your water is brackish, unwholesome and rough;
Let us gaily give battle and merrily die.
Thou art safe, Lady Abbess! The convent is safe!
The vanguard of Otto is looming in sight!
Their foremost are scarce half a mile from the wall.
Thurston:
SCENE -- The Chapel of the Convent.
Earth to earth, and dust.html">dust.html">dust.html">dust to dust,
Judge not. He who judgeth just,
Earthly penitence hath fled,
Pile the sods on heart and head,
Domine! precamur te
Miserere Domine!
Pride and greed, and wrath and lust,
When the dust returns to dust?
Load the wild and worthless tree.
.
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