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Principle of explosion (view source)

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The '''principle of explosion''' is a logical principle which states that if we accept that a certain statement is true at the same time it is not true, then any other statement, no matter ~~how false~~, can be proven. In other words, from a ~~false premise~~, any imaginable conclusion can be reached~~. It is used to illustrate the importance of having a set of [[axiom]]s which are self-consistent~~.

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The '''principle of explosion''' is a logical principle which states that if we accept that a certain statement is true at the same time it is not true, then any other statement, no matter the truth value, can be proven. In other words, from a contradiction, any imaginable conclusion can be reached.

==The Principle==

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The principle comes from an argument containing a proposition and its negation. By way of simplification and addition, anything can be proved deductively.

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~~Suppose we accept both of the statements "red is a color" and "red is not a color" as true.~~

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:'''P1:''' A · ~A

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:'''P2:''' A (1, simplification)

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:'''P3:''' ~A (1, simplification)

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:'''P4:''' A v B (2, addition)

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:'''C:''' B, (3, 4 disjunctive syllogism)

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Since "red is a color" is true, at least one of the two statements "red is a color" and "Obama is a competent president" is true, and so the single statement "red is a color, or Obama is a competent president, or both" is true. Since we know "red is not a color" is true, the only clause in "red is a color, or Obama is a competent president" which can be true it the latter, i.e., "Obama is a competent president."

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~~From the false assumption "red both is and isn't a color," we have reached a false conclusion.~~

[[Category:Logic]]

[[Category:Obama Criticism]]

Logician

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