Difference between revisions of "Principle of explosion"

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(→‎The Principle: Spelling, grammar, and general fixes, typos fixed: ie, → i.e.,)
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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==
 
==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:Logic]]
 
[[Category:Obama Criticism]]
 
[[Category:Obama Criticism]]

Revision as of 22:08, September 24, 2018

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

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

P1: A · ~A
P2: A (1, simplification)
P3: ~A (1, simplification)
P4: A v B (2, addition)
C: B, (3, 4 disjunctive syllogism)
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