According to Whewell, it is a strong mark of the truth of an hypothesis when it agrees with distinct inductions concerning different classes of facts, and he calls this the ‘Consilience of Inductions,’ because they jump together in the unity of the hypothesis.  It is particularly convincing when this consilience takes place easily and naturally without necessitating the mending and tinkering of the hypothesis; and he cites the Theory of Gravitation and the Undulatory Theory of Light as the most conspicuous examples of such ever-victorious hypotheses.  Thus, gravitation explains the fall of bodies on the Earth, and the orbits of the planets and their satellites; it applies to the tides, the comets, the double stars, and gives consistency to the Nebular Hypothesis, whence flow important geological inferences; and all this without any need of amendment.  Nevertheless, Mill, with his rigorous sense of duty, points out, that an induction is merely a proposition concerning many facts, and that a consilience of inductions is merely a multiplication of the facts explained; and that, therefore, if the proof is merely Agreement in each case, there can be no more in the totality; the possibility of vicarious causes is not precluded; and the hypothesis may, after all, describe an accidental circumstance.

Whewell also laid great stress upon prediction as a mark of a true hypothesis.  Thus, Astronomers predict eclipses, occultations, transits, long beforehand with the greatest precision; and the prediction of the place of Neptune by sheer force of deduction is one of the most astonishing things in the history of science.  Yet Mill persisted in showing that a predicted fact is only another fact, and that it is really not very extraordinary that an hypothesis, that happens to agree with many known facts, should also agree with some still undiscovered.  Certainly, there seems to be some illusion in the common belief in the probative force of prediction.  Prediction surprises us, puts us off our guard, and renders persuasion easy; in this it resembles the force of an epigram in rhetoric.  But cases can be produced in which erroneous hypotheses have led to prediction; and Whewell himself produces them.  Thus, he says that the Ptolemaic theory was confirmed by its predicting eclipses and other celestial phenomena, and by leading to the construction of Tables in which the places of the heavenly bodies were given at every moment of time.  Similarly, both Newton’s theory of light and the chemical doctrine of phlogiston led to predictions which came true.

What sound method demands in the proof of an hypothesis, then, is not merely that it be shown to agree with the facts, but that every other hypothesis be excluded. This, to be sure, may be beyond our power; there may in some cases be no such negative proof except the exhaustion of human ingenuity in the course of time.  The present theory of colour has in its favour the failure of Newton’s corpuscular hypothesis and