William Whewell was an influential Cambridge philosopher and scientist (in fact, he coined the word scientist, in 1833) in the mid-1800s. Among his broad range of interests was the history and philosophy of science, in which he produced some of the seminal works of the fields. In his The Philosophy of the Inductive Sciences, Founded upon Their History (1840, new edition in 1847), Whewell attempted to outline not only the logic of scientific discovery and confirmation, but to anchor the philosophy in the practice of successful scientists. The section on the "construction of science" has a chapter describing several "characteristics of inductive science." In discussing confirmation of theories, a prime case was made of Newton’s reasoning. How do we know Newton’s theory of gravitational attraction to be true? One of the tests of hypotheses that convinces us Whewell described, in a new term, as “consilience” —

“We have spoken of the prediction of facts of the same kind as those from which our rule was collected. But the evidence in favour of our induction is of a much higher and more forcible character when it enables us to explain and determine cases of a kind different from those which were contemplated in the formation of our hypothesis. The instances in which this has occurred, indeed, impress us with a conviction that the truth of our hypothesis is certain. No accident could give rise to such an extraordinary coincidence. No false supposition could, after being adjusted to one class of phenomena, exactly represent a different class, when the agreement was unforeseen and uncontemplated. That rules springing from remote and unconnected quarters should thus leap to the same point, can only arise from that being the point where truth resides.

Accordingly the cases in which inductions from classes of facts altogether different have thus jumped together, belong only to the best established theories which the history of science contains. And as I shall have occasion to refer to this peculiar feature in their evidence, I will take the liberty of describing it by a particular phrase; and will term it the Consilience of Inductions.” [1840, Vol. II: 230]

His example is Newton's theory of gravitation, connected to multiple phenomena and separate hypotheses. Whewell claims that

"No example can be pointed out, in the whole history of science, so far as I am aware, in which this Consilience of Inductions has given testimony in favour of an hypothesis afterwards discovered to be false. If we take one class of facts only, knowing the law which they follow, we may construct an hypotheses, or perhaps several, which may represent them : and as new circumstances are discovered, we may often adjust the hypothesis so as to correspond to these also. But when the hypothesis, of itself and without adjustment for the purpose, gives us the rule and reason of a class of facts not contemplated in its construction, we have a criterion of its reality, which has never yet been produced in favour of falsehood. " [1840, Vol II: 233]

As the applications of a true theory progress over time,

"all the additional suppositions tend to simplicity and harmony; the new suppositions resolve themselves into the old ones, or at least require only some easy modification of the hypothesis first assumed : the system becomes more coherent as it is further extended. The elements which we require for explaining a new class of facts are already contained in our system. Different members of the theory run together, and we have thus a constant convergence to unity. In false theories, the contrary is the case. The new suppositions are something altogether additional; — not suggested by the original scheme ; perhaps difficult to reconcile with it. Every such addition adds to the complexity of the hypothetical system, which at last becomes unmanageable, and is compelled to surrender its place to some simpler explanation." [1840, Vol II: 233-34]

In his History of the Inductive Sciences, From the Earliest to the Present Time (1837), he uses this to explain the rejection of the earlier theories of heat, for failing to meet this characteristic "that the hypotheses, which were assumed in order to account for one class of facts, are found to explain another class of a different nature." In optics, the new theory of light after 1800 had to be true, because it explained such "diverse" and separate laws. This explanation "by the same general and symmetrical theory, could not result from anything but the truth of the theory." [1847, new ed., Vol II: 590, 458]

Recognizing the increasingly complex and intertwined structure of the sciences, Whewell reasoned that history and philosophy reveal a confident path to certainty for accepting theories. For progress in science, the goal is unification, and with hypothesis and the tests of observation and experiment

"we must, as far as possible, devise hypotheses which, when we thus test them, display those characters of truth of which we have already spoken; — an agreement with facts such as will stand the most patient and rigid inquiry; a provision for predicting truly the results of untried cases; a consilience of inductions from various classes of facts; and a progressive tendency of the scheme to simplicity and unity. " [Philosophy, 1840, Vol II: 270]

It is clear how he is describing the science of Newton and of the later Newtonian developments.