/nɒn ˈsɛk wɪ tər, -ˌtʊər;
non sequitur (literally, does not follow) is a logical fallacy. Reasoning is said to be non sequitur if the conclusion does not follow from the premises or if a given reason for taking an action is completely irrelevant to taking that action.
For example, the police chief’s reasoning was a non sequitur when he defended consulting a psychic “to help investigators crack the case” based on the premise that “we tried everything else and haven’t solved the case.” The fact that the case hadn’t been solved using traditional police methods is irrelevant to whether consulting a psychic is a method that should be used.
Another example of non sequitur reasoning comes from those who try to justify seeing a homeopath or some other “alternative” therapist because scientific medicine hasn’t cured what ails them. Again, to justify using homeopathy or acupuncture, one needs direct evidence that those treatments are effective, not that some other method isn’t effective.