[Herbert Spencer] has discovered a great law of evolution in nature, which underlies all phenomena, & which is as important & more comprehensive than Newton’s law of gravitation.

He who has mastered the Darwinian theory, he who recognizes the slow and subtle process of evolution as the way in which God makes things come to pass, … sees that in the deadly struggle for existence that has raged throughout countless aeons of time, the whole creation has been groaning and travailing together in order to bring forth that last consummate specimen of God’s handiwork, the Human Soul

If logical training is to consist, not in repeating barbarous scholastic formulas or mechanically tacking together empty majors and minors, but in acquiring dexterity in the use of trustworthy methods of advancing from the known to the unknown, then mathematical investigation must ever remain one of its most indispensable instruments. Once inured to the habit of accurately imagining abstract relations, recognizing the true value of symbolic conceptions, and familiarized with a fixed standard of proof, the mind is equipped for the consideration of quite other objects than lines and angles. The twin treatises of Adam Smith on social science, wherein, by deducing all human phenomena first from the unchecked action of selfishness and then from the unchecked action of sympathy, he arrives at mutually-limiting conclusions of transcendent practical importance, furnish for all time a brilliant illustration of the value of mathematical methods and mathematical discipline.

Of our three principal instruments for interrogating Nature,—observation, experiment, and comparison,—the second plays in biology a quite subordinate part. But while, on the one hand, the extreme complication of causes involved in vital processes renders the application of experiment altogether precarious in its results, on the other hand, the endless variety of organic phenomena offers peculiar facilities for the successful employment of comparison and analogy.

The ability to imagine relations is one of the most indispensable conditions of all precise thinking. No subject can be named, in the investigation of which it is not imperatively needed; but it can be nowhere else so thoroughly acquired as in the study of mathematics.

The barrenness of doubt had to make itself felt before it could be supplanted by knowledge. It was not until Hume, by carrying scepticism to its uttermost extent, had shown its unsatisfactory character and vain results, that the germs of scientific method, implanted by Bacon and Descartes, could develop and bear fruit in the positive philosophy of Comte.

There is an integration of the present impressions with such past ones as they resemble, and a differentiation of them from such past ones as they do not resemble; and this comparison of present with past impressions, dependent on memory, implies classification, and is the germ of what we call Perception and Reasoning.