Logical extreme
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A logical extreme is a logical construct that is often useful in testing hypotheses. The use of a logical extreme is often the simplest way to disprove a hypothesis. Quite simply, a logical extreme is the statement of an extreme or even preposterous position that is nonetheless consistent with the hypothesis being tested. Thus, if the logical extreme position is obviously untrue, then the hypothesis is disproven, at least in its stated form.
As an example: Let us say that you have three different locations in the physical world: point A, point B and point C. Let us say that your hypothesis is that the shortest distance between points A and C is always passes through point B (i.e. the shortest distance A ----> C is always equal to A---->B----->C).
You can test this hypothesis by proposing the logical extreme where point A is in Los Angeles, point C is in San Francisco, and point B is on Uranus. Clearly the shortest distance between Los Angeles and San Francisco is not to proceed to Uranus and back. Rather the shortest distance would be to proceed directly from Los Angeles and San Francisco. Note that if you'd used a less extreme example (say, putting point B in Stockton), the violation of the requirements of the hypothesis would not have been obvious.
Having disproved your hypothesis, you can then restate it in a way that is consistent with fact. For example a new hypothesis would be: The shortest distance between point A and C passes through point B only when point B lies on the line segment AC. The logical extreme test for this hypothesis would be to put point B at each extreme end of the line segment - where you would find that the hypothesis still holds.
The general usefulness of a logical extreme is that it allows for hypothesis testing 'in your head'. In the example above, one could disprove the hypothesis by measuring the distances between Los Angeles, San Francisco and Stockton, but the use of an extreme (like making point B Uranus) is that one does not need to measure. That the distance from Los Angeles to Uranus to San Francisco is obviously longer than the distance from Los Angeles to San Francisco. Thus, the hypothesis is disproven by pure mental exercise requiring no measurement.