In colligation, the mind “superinduces” upon facts some conception that can be used to generalize. For example, Whewell described astronomer Johannes Kepler as having colligated the points of the Martian orbit. Whewell argued that discovery occurs not as the result of new facts, but in applying the right conception to existing facts. Thus, according to Whewell, Kepler applied his ellipse conception to the facts of Mars’ orbit that were already collected by the Danish astronomer Tycho Brahe.

Whewell believed that choosing the right conception to colligate facts cannot be done by simple observation or guesswork, but requires a “special process in the mind” in which “we infer more than we see.” Once theories are created, theories can be extended to what cannot be observed, such as light waves, orbit shapes, and gravity. In other words, Whewell thought that we always approach experience with something in mind that helps us interpret experience and go beyond it.

Scientific theories must withstand the tests of consilience, coherence, and prediction. “Consilience” refers to new kinds of cases confirming the theory. A theory’s coherence is its ability to explain new kinds of facts. The theory’s “coherence” ought to increase over time. Predictions should turn out to be accurate. Once they have withstood such tests, theories and basic scientific principles become necessary—it is a contradiction to deny them, given an understanding of their meaning.