Whatever physical truths were within the author's reach, took their place in the general array: the vacancies were filled up with the best suppositions admitted by the limited science of the time. [651] And it is worthy of remark that, whilst proceeding by this "high à priori road," he made some startling guesses at the truth, and anticipated some of the discoveries of the modern inductive method, which proceeds simply by the observation, comparison, and generalization of facts. Of these prophetic anticipations we may instance that of the definite proportions of chemistry, [652] the geometrical forms of crystallography, [653] the doctrine of complementary colors, [654] and that grand principle that all the highest laws of nature assume the form of a precise quantitative statement. [655]
2. It may be expected that a system of physics raised on optimistic principles will be mathematical rather than experimental. "Intended to embody conceptions of proportion and harmony, it will have recourse to that department of science which deals with the proportions in space and number. Such applications of mathematical truths, not being raised on ascertained facts, can only accidentally represent the real laws of the physical system; they will, however, vivify the student's apprehension of harmony in the same manner as a happy parable, though not founded in real history, will enliven his perceptions of moral truth." [656]
[Footnote 651: ][ (return) ] Butler's "Lectures on Ancient Philosophy," vol. ii. p. 157.
[Footnote 652: ][ (return) ] "Timæus," ch. xxxi.
[Footnote 653: ][ (return) ] Ibid., ch. xxvii.
[Footnote 654: ][ (return) ] Ibid., ch. xlii.
[Footnote 655: ][ (return) ] "It is Plato's merit to have discovered that the laws of the physical universe are resolvable into numerical relations, and therefore capable of being represented by mathematical formulæ."--Butler's "Lectures on Ancient Philosophy," vol. ii. p. 163.
[Footnote 656: ][ (return) ] Butler's "Lectures on Ancient Philosophy," vol. ii. p. 163.
3. Another peculiarity of such a system will be an impatience of every merely mechanical theory of the operations of nature.