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A hypothesis is a proposed explanation for a phenomenon.

In early usage, a hypothesis was a clever idea or convenient mathematical approach that would simplify calculation but did not necessarily have any reality at all. This is the sense in which Cardinal Bellarmine used the word when he warned Galileo away from treating the motion of the Earth as a reality.

In common usage at present, a hypothesis is a provisional idea whose merit is to be evaluated. A hypothesis requires more work by the researcher in order to either confirm or disprove it. In the hypothetico-deductive method, a hypothesis should be falsifiable, meaning that it is possible that it be shown to be false, usually by observation. Note that if confirmed, the hypothesis is not necessarily proven, but remains provisional. See statistical hypothesis testing. See also: learning.

As an example, someone who enters a new country and observes only white sheep might form the hypothesis that all sheep in that country are white.

It can be considered a hypothesis, as it is falsifiable. It can be falsified by observing a single black sheep. Provided that the experimental uncertainties are small (for example that it is a sheep, instead of a goat) and that the experimenter has correctly interpreted the statement of the hypothesis (for example, does the meaning of "sheep" include rams?), the hypothesis is falsified.

See Philosophiae Naturalis Principia Mathematica for Newton's position on hypotheses, "Hypotheses non fingo" : "I feign no hypotheses" [1].