Counter-Example
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An Counter-Example is an example in a not instance-of relation with another concept class.
- AKA: Negative Example.
- Context:
- It can be a Premise.
- It can be an Counter-Example Argument that contradicts an Argument (Mathematical or Logical).
- It can be used to describe a Concept.
- It can be used to reject a Claim (a Counterexample Argument).
- Example(s):
- Gabor Melli is a counter-example of a cat.
- A sentence a counter-example of a document.
- If formula F() claims to produce all prime numbers, but it is shown that the formula does not produce the number 5, then $5$ is a counterexample to the argument.
- A penguin (has wings and does not fly) is a counterexample to the claims that all things with wings can fly; then the example of the.
- a Negative Example.
- …
- Counter-Example(s):
- Gabor Melli is an example of a person.
- Gabor Melli is an example of a male.
- a Positive Example.
- See: Learning Record, Proof by Contradiction, Argument Pattern, Counter Evidence.
References
2013
- http://en.wikipedia.org/wiki/Counterexample
- In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule. For example, consider the proposition "all students are lazy". Because this statement makes the claim that a certain property (laziness) holds for all students, even a single example of a diligent student will prove it false. Thus, any hard-working student is a counterexample to "all students are lazy". More precisely, a counterexample is a specific instance of the falsity of a universal quantification (a "for all" statement).
In mathematics, this term is (by a slight abuse) also sometimes used for examples illustrating the necessity of the full hypothesis of a theorem, by considering a case where a part of the hypothesis is not verified, and where one can show that the conclusion does not hold.[citation needed] A counterexample may be local or global in an argument.
- In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule. For example, consider the proposition "all students are lazy". Because this statement makes the claim that a certain property (laziness) holds for all students, even a single example of a diligent student will prove it false. Thus, any hard-working student is a counterexample to "all students are lazy". More precisely, a counterexample is a specific instance of the falsity of a universal quantification (a "for all" statement).
2009
- http://planetmath.org/encyclopedia/Counterexample.html
- A counterexample is an example which is used to prove that a statement is false.
- http://mcckc.edu/longview/ctac/glossary.htm
- "Counterexample: Definition: A counter-example to an argument (as opposed to one to an argument pattern) constitutes (broadly) a demonstration that the premises of that argument could be true under certain conditions where the conclusion would nevertheless be false. Comment: This demonstration will usually consist of adding a premise to the argument, that details a particular way in which the original premises could count as true, and under which it is at least not certain that the conclusion is true. “Little Freddie had turned a blotchy yellow-green by now, and was running a temperature of 107. A scratchy ak-ak-ak escaped from his dry and wrinkled throat." You might be tempted to draw from these premises the conclusion that Little Freddie is sick (to say the least!). But now add in the premise that Freddie is a Geezengolian from the planet Zenith. Are you so sure now what's sick and what's normal?