Difference between revisions of "Contradiction"
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| − | A '''contradiction''' is the simultaneous acceptance and denial of a proposition or statement. "It was the best of times and the worst of times" is a | + | A '''contradiction''' is the simultaneous acceptance and denial of a proposition or statement. "It was the best of times and the worst of times" is a poetic example: the contradiction is being used to enhance the poetic nature of the piece. |
| − | In a [[proof]], if two contradictory [[inference]]s can be drawn from the [[premise]], this indicates either that a premise is false or that the argument is invalid. | + | According to J.Sarfati, a contradiction is defined as the conjunction of the affirmation and denial of a premise, in the same time, place, and sense (i.e. p and not-p, or in symbolic form, p.~p).<ref>{{cite web |
| + | |title=Is God a particle-wave duality? | ||
| + | |author=Jonathan Sarfati | ||
| + | |publisher=Creation Ministries International | ||
| + | |date=4 November 2012 | ||
| + | |url=https://creation.com/god-particle-wave-duality | ||
| + | |accessdate=2012-11-04}}</ref> | ||
| + | |||
| + | In a [[proof]], if two contradictory [[Conclusion|inference]]s can be drawn from the [[premise]], this indicates either that a premise is false or that the argument is invalid. | ||
It is often held that from a contradiction anything can be inferred. This can be demonstrated: | It is often held that from a contradiction anything can be inferred. This can be demonstrated: | ||
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# Take anything that you want to prove, “P” | # Take anything that you want to prove, “P” | ||
# Now because “A and Not A” is true, “A” is true, by virtue of the simplification rule. | # Now because “A and Not A” is true, “A” is true, by virtue of the simplification rule. | ||
| − | # “A or P” is true just so long as | + | # “A or P” is true just so long as both Not A and P are false. |
# So, As “A” is true, “A or P” must be true. | # So, As “A” is true, “A or P” must be true. | ||
# If “A or P” is true, then one of “A” or “P” must be true. | # If “A or P” is true, then one of “A” or “P” must be true. | ||
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# “P”, absolutely anything you like, is true. | # “P”, absolutely anything you like, is true. | ||
| + | ==References== | ||
| + | <references/> | ||
| − | [[ | + | [[Category:Logic]] |
Latest revision as of 12:07, January 13, 2020
A contradiction is the simultaneous acceptance and denial of a proposition or statement. "It was the best of times and the worst of times" is a poetic example: the contradiction is being used to enhance the poetic nature of the piece.
According to J.Sarfati, a contradiction is defined as the conjunction of the affirmation and denial of a premise, in the same time, place, and sense (i.e. p and not-p, or in symbolic form, p.~p).[1]
In a proof, if two contradictory inferences can be drawn from the premise, this indicates either that a premise is false or that the argument is invalid.
It is often held that from a contradiction anything can be inferred. This can be demonstrated:
- Take any contradiction, “A” and “Not A”, and take it to be true.
- Take anything that you want to prove, “P”
- Now because “A and Not A” is true, “A” is true, by virtue of the simplification rule.
- “A or P” is true just so long as both Not A and P are false.
- So, As “A” is true, “A or P” must be true.
- If “A or P” is true, then one of “A” or “P” must be true.
- As “Not A” is true then “A” is false which means that the remaining term in “A or P” must be true.
- “P”, absolutely anything you like, is true.
References
- ↑ Jonathan Sarfati (4 November 2012). Is God a particle-wave duality?. Creation Ministries International. Retrieved on 2012-11-04.
