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Updated: June 6, 2025
If all this is so, Progress as an ideal of action cannot be precisely identical with Progress as a fact or object of actual or possible knowledge. We can never know what we are aiming at. But though different, the two are and must be congruent, and this may be enough to justify us in using the one name for the two.
The axiom also enables us to measure time in any time-system; but does not enable us to compare times in different time-systems. The second axiom of congruence concerns parallelograms on congruent bases and between the same parallels, which have also their other pairs of sides parallel.
Some objects can palpably alter as they move for example, an elastic thread; but a yard measure does not alter if made of the proper material. What is this but a judgment of congruence applied to the train of successive positions of the yard measure? We know that it does not alter because we judge it to be congruent to itself in various positions.
The art of teaching grew up in the schoolroom, out of inventiveness and sympathetic concrete observation. The two were congruent, but neither was subordinate. And so everywhere the teaching must agree with the psychology, but need not necessarily be the only kind of teaching that would so agree; for many diverse methods of teaching may equally well agree with psychological laws.
Therefore the termination of life for every man is no evil, because neither is it shameful, since it is both independent of the will and not opposed to the general interest, but it is good, since it is seasonable, and profitable to and congruent with the universal. For thus too he is moved by the Deity who is moved in the same manner with the Deity, and moved towards the same things in his mind.
Also rectangularity is in fact often not perceived when it can be proved to have been there for perception. Thus an object is often known merely as an abstract relation not directly posited in sense-awareness although it is there in nature. The identity of quality between congruent segments is generally of this character. In certain special cases this identity of quality can be directly perceived.
"It is a sufficient account of that Appearance we call the World, that God will teach a human mind, and so makes it the receiver of a certain number of congruent sensations, which we call sun and moon, man and woman, house and trade.
This way of putting it in my judgement intolerably misconceives and misrepresents the truth. Our ideals of action must be self-made or self-begotten, but yet they must be congruent with known fact; but the manner of such congruence is hard to see, hard to express.
It is a sufficient account of that Appearance we call the World, that God will teach a human mind, and so makes it the receiver of a certain number of congruent sensations, which we call sun and moon, man and woman, house and trade.
For we need a doctrine, a scheme of knowledge, into which all that we discover about the world and our own nature may find its place; we need principles of action which will guide us in attaining a state of society more congruent with our knowledge of the possibilities of the world and human nature, more thoroughly inspired by human love, love of man for man as a being living his span of life here and now, under conditions which call for a concentration of skill and effort to realize the best.
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