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Whewell’s authority to have accorded as accurately with the Cartesian hypothesis, in its finally improved state, as with Newton’s. But it is not, I conceive, a valid reason for accepting any given hypothesis, that we are unable to imagine any other which will account for the facts.
It would be inconsistent with the scale of this work, and not necessary to its design, to carry the analysis of the truths and processes of algebra any further; which is also the less needful, as the task has been, to a very great extent, performed by other writers. Peacock’s Algebra, and Dr. Whewell’s Doctrine of Limits, are full of instruction on the subject.
Whewell’s own statement of the fundamental principle of classification, namely, that “general assertions shall be possible.” If the class did not possess any characters in common, what general assertions would be possible respecting it? Except that they all resemble each other more than they resemble any thing else, nothing whatever could be predicated of the class.
Whewell’s phraseology, connect them by means of a new conception; if the conception does but serve to connect the observations, we have all we want.
Whewell’s celebrated observation, that Bentham’s moral theory is low because it includes justice and mercy to brutes. But, for a reflection of Young’s moral personality on a colossal scale, we must turn to those passages where his rhetoric is at its utmost stretch of inflation—where he addresses the Deity, discourses of the Divine operations, or describes the last judgment.
Whewell’s theory of the logic of science would be very perfect if it did not pass over altogether the question of Proof. But in my apprehension there is such a thing as proof, and inductions differ altogether from descriptions in their relation to that element.
Dr. Whewell’s remark, therefore, is philosophically correct. Successive expressions for the colligation of observed facts, or, in other words, successive descriptions of a phenomenon as a whole, which has been observed only in parts, may, though conflicting, be all correct as far as they go. But it would surely be absurd to assert this of conflicting inductions.
Whewell’s abilities and attainments should have written an elaborate treatise on the philosophy of induction, in which he recognizes absolutely no mode of induction except that of trying hypothesis after hypothesis until one is found which fits the phenomena; which one, when found, is to be assumed as true, with no other reservation than that if, on re-examination, it should appear to assume more than is needful for explaining the phenomena, the superfluous part of the assumption should be cut off.
Whewell’s phraseology, connect them by means of a new conception; if the conception does serve to connect the observations, we have all we want.
Whewell’s conditions, that conceptions must be appropriate. The second is, that they shall be “clear:” and let us consider what this implies. Unless the conception corresponds to a real agreement, it has a worse defect than that of not being clear: it is not applicable to the case at all.
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