Double negation
Theorem
In propositional logic, the double negation of a statement states that "it is not the case that the statement is not true". In classical logic, every statement is logically equivalent to its double negation, but this is not true in intuitionistic logic; this can be expressed by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation.
Nº Q5300067 ★
Common · Knowledge
Double negation
Theorem
In propositional logic, the double negation of a statement states that "it is not the case that the statement is not true". In classical logic, every statement is logically equivalent to its double negation, but this is not true in intuitionistic logic; this can be expressed by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation.
Last price
—
Floor price
—
7-day median
—
30-day sales
0
30-day range
—
In circulation
0
Price history
median
low – high
sales
No sales in this period
Show table
| Date | median | Low | High | sales |
|---|
Sales history
- Last sale
- —
- 30-day average
- —
- 30-day low
- —
- 30-day high
- —
- Sales 7d
- 0
- Sales 30d
- 0
No sales yet.
Anonymous sales: no buyer or seller shown. Figures count player-to-player sales only.
From Wikipedia
In propositional logic, the double negation of a statement states that "it is not the case that the statement is not true". In classical logic, every statement is logically equivalent to its double negation, but this is not true in intuitionistic logic; this can be expressed by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation. Like the law of the excluded middle, this principle is considered to be a law of thought in classical logic, but it is disallowed by intuitionistic logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as: ∗ 4 ⋅ 13 . ⊢ . p ≡ ∼ ( ∼ p ) {\displaystyle \mathbf {*4\cdot 13} .\ \ \vdash .\ p\ \equiv \ \thicksim (\thicksim p)} "This is the principle of double negation, i.e. a proposition is equivalent of the falsehood of its negation."
Text: Wikipédia, CC BY-SA 4.0. ·
Related cards
-
Law of noncontradiction
Theorem of logic
Nº Q868437 ★★★
Not listed
-
Peirce's law
Axiom used in logic and philosophy
Nº Q2387196 ★
Not listed
-
d
double negative elimination
Inference rule that allows to infer a formula without the relevant negations when they immediately follows in an original formula
Nº Q737471 ★
Not listed
-
C
Contraposition
Inference that says that a conditional statement is logically equivalent to its contrapositive
Nº Q1077442 ★★
Not listed
-
Axiom
Statement of a theory that is taken to be true
Nº Q17736 ★★★★
Not listed
-
Negation
Operation that takes a proposition p to another proposition "not p", written ¬p, which is interpreted intuitively as being true when p is false, and false when p is true; unary (single-argument) logical connective
Nº Q190558 ★★
Not listed