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Position:Home>Philosophy> Counterexample method?Question: Counterexample method!? I need to use the counterexample method to prove each argument is invalid!.
if carbon dioxide is present in the atmosphere, then plants have a source of carbon!. Hence, since plants have a source of carbon, carbon dioxide is present in the atmosphere!. if human rights are recognized, then civilization flourishes!. if equality prevails, then civilization flourishes!. thus, if human rights are recognized, then equality prevails!.Www@QuestionHome@Com Best Answer - Chosen by Asker: the first one is of the form: if A then B B therefore A!. That is called the fallacy of affirming the consequent!. You could come up with any argument of that form that is obviously false as a counterexample: if it is raining then I am wet I am wet therefore it is raining!. simply being wet does not necessitate that it is raining, I could have gone for a swim, so that argument form is a fallacy!. the second one (not sure of the name of the fallacy): if A then B if C then B therefore, if A then C!. counterexample (again turning the letters into sentences in which the sentences don't necessitate the conclusion): if I am hot I will go for a swim if I am next to a pool i will go for a swim therefore, if I am hot I am next to a pool!. obviously you can be hot and not next to a pool, so there it is!.Www@QuestionHome@Com "In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule, i!.e!., a specific instance of the falsity of a universal quantification (a "for all" statement)!. 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"!." http://en!.wikipedia!.org/wiki/Counterexam!.!.!. "Invalidity" has nothing to do with finding example of a contradiction!. "Validity" has to do with the major and minor premise being true and not leading to a false conclusion!. "A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false!. Otherwise, a deductive argument is said to be invalid!." http://www!.iep!.utm!.edu/v/val-snd!.htm Your examples are invalid simply because they are improperly formed syllogisms!. Carbon dioxide is present in the atmosphere!. Plants need carbon dioxide!. The conclusion is not available because there is nothing to indicate that the plants are not placed in a vacuum!. But then, that is your counterexample!. It also happens to be the fallacy of the missing term, which means you need two (at least) syllogisms to prove the thesis that plants get their carbon!. Now, work that logic on the 2nd example!.Www@QuestionHome@Com |