Corroborating evidence (in "corroboration") is evidence that tends to support a proposition that is already supported by some evidence. For example, W, a witness, testifies that she saw X drive his automobile into a green car. Meanwhile Y, another witness, testifies that when he examined X's car, later that day, he noticed green paint on its fender. Or there can be corroborating evidence related to a certain source, such as what makes an author think a certain way.
For more information on this type of reasoning, see: Casuistry.
Another type of corroborating evidence comes from using the Baconian method, i.e. the method of agreement, method of difference, and method of concomitant variations.
These methods are followed in experimental design. They were codified by Francis Bacon, and developed further by John Stuart Mill and consist of controlling several variables, in turn, to establish which variables are causally connected. These principles are widely used intuitively in various kinds of proofs, demonstrations and investigations, in addition to being fundamental to experimental design.
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