[1503]. There are few things which we know, which are not capable of being reduc’d to a Mathematical Reasoning, and when they cannot, it’s a sign our knowledge of them is very small and confus’d; and where a mathematical reasoning can be had, it’s as great folly to make use of any other, as to grope for a thing in the dark, when you have a candle standing by you.—Arbuthnot.
Quoted in [Todhunter’s] History of the Theory of Probability (Cambridge and London, 1865), p. 51.
[1504]. Mathematical Analysis is ... the true rational basis of the whole system of our positive knowledge.—Comte, A.
Positive Philosophy [Martineau], Bk. 1, chap. 1.
[1505]. It is only through Mathematics that we can thoroughly understand what true science is. Here alone we can find in the highest degree simplicity and severity of scientific law, and such abstraction as the human mind can attain. Any scientific education setting forth from any other point, is faulty in its basis.—Comte, A.
Positive Philosophy [Martineau], Bk. 1, chap. 1.
[1506]. In the present state of our knowledge we must regard Mathematics less as a constituent part of natural philosophy than as having been, since the time of Descartes and Newton, the true basis of the whole of natural philosophy; though it is, exactly speaking, both the one and the other. To us it is of less use for the knowledge of which it consists, substantial and valuable as that knowledge is, than as being the most powerful instrument that the human mind can employ in the investigation of the laws of natural phenomena.—Comte, A.
Positive Philosophy [Martineau], Introduction, chap. 2.
[1507]. The concept of mathematics is the concept of science in general.—Novalis.