Some thinkers claim, however, that this seemingly immediate knowledge of ours is the result of the experience of our ancestors. Thus our assumption that every effect must have a cause, is said to be based on the universal experience of the race in the past. This reasoning is, however, based on a misconception of the nature of our a priori or self-evident knowledge. It is not that we simply naturally assume a certain proposition to be true; it is more: we cannot conceive anything different to be true, and we see directly that the proposition must be true. Besides, in many cases, experience cannot possibly teach these truths.

Take the axiom last referred to: Every effect must have a cause. This cannot be verified by experiment without using the most refined scientific instruments and methods. Experience seems in fact to teach just the opposite. Trees shoot up from the ground, as if by magic, and no visible or tangible cause can be found. The wind bloweth whither it listeth and we know not whence it cometh. In fact, we can never in ordinary experience trace the chain of cause and effect more than a link or two, and often not even that. And still, as soon as a human mind really knows what is meant, it will always assent to this proposition. Yet few uneducated persons recognize the truth of this axiom when it is mixed in daily experience. Thus countless lives have been spent in seeking for "perpetual motion"; and inexplicable events are dismissed from discussion as having "just happened." But as soon as such a person clearly sees the implication of the statement of the law of cause and effect, he at once assents to it.

Or, take another axiom just mentioned: The same object cannot be in two places at once. Experience is wholly against this axiom. In hundreds of classes of objects the individual objects are so similar that it is impossible to tell one object from another. In a bushel of peas, why don't we assume there is only one pea appearing in a thousand places at the same time? When twins are so exactly alike that one cannot be told from the other, why don't we assume there is only one person who exists at once in two places? So, I think it is safe to assert that we know some things to be true because of the very nature of the mind.

But evidently even here we must base our knowledge on faith, faith in the integrity of our intellect. It is conceivable that our minds might all be insane on some point, and hence it would be impossible for us to detect our error.

Knowledge gained from experience is also based on faith. Experience is always gained through the senses, and is reduced to knowledge by the process known as perception, and preserved by memory. Hence, we must trust our senses and our memory in every case where we rely on experience. Witness saw defendant strike plaintiff; he is sure of it. Now his certainty is based on: (a) his faith in his sense of sight and his perception (it might be an hallucination), and (b) his faith in his own memory.

Laws or principles may then become ours in two ways. Either we gain them by inductions from experience, or they are simply awakened in us by experience and then elaborated or deduced. The latter are what we call self-evident truths. Thus the law of gravitation was

induced from experience, while it is quite possible that the law of falling bodies was evolved from reason alone. The arbitrary fact, however, that if a body falls 16 feet the first second, its speed must be 32 feet per second at the end of first second, we need no experiment to know. The body began with no speed at the beginning of first second. It passed over 16 feet acted on by a constant force. Hence 16 feet per second must be the average speed, and the other extreme to 0 speed must be 2 × 16 feet or 32 feet per second.

Thus all geometry, and much of other mathematics, is deduced entirely from the axioms awakened by experience in the mind. Much of physics is a priori deduction.

All pure mathematics is based on laws of consciousness alone, as mathematics is the science of time and space as we conceive them.

DEDUCTIVE REASONING

From the law, the principle, we can descend the logical ladder to the fact, the instance; from the general we can arrive at the particular, thus reversing the process of induction. Deductive reasoning, hence, consists simply in recognizing a part of a concept as a part. The Syllogism. The explicit form of reasoning is the classical syllogism, of which there are four fundamental types. Of these four forms the following may be considered basic:

Water expands when it freezes.

The liquid in this glass is water.

Hence the liquid in this glass will expand when it freezes.

The logical relations may be expressed by the diagram shown below:

B is (in) C (Major premise).

A is (in) B (Minor premise).
Hence A is (in) C (Conclusion).

BA

C

The first sentence is called the major premise; the second the minor premise; the third the conclusion. Now the predicate of the major premise, expanding when freezing, has the greatest extension, and includes the subject, water, which is also the predicate of the minor premise. Hence the subject of the minor premise and of the conclusion, the liquid in this glass, is a fortiori included in that which includes its predicate, water.

PEDAGOGY OF REASONING

Logical Relations. — Reasoning consists in perceiving the relations of ideas to one another. Hence put all your attention on the logical relations. The facts will take care of themselves. To be exact, the fact is nothing more nor less than a center of logical relations, just as modern physics is inclined to view the atom, the unit of matter, as simply a center of forces. In studying a battle, for example, don't clog up your mind with "60,000 men, no cavalry, 6 o'clock in the morning, bombardment, charge, retreat ten miles on north road," and the like. These facts, thought of as mere facts,

will remain barren and cold in the mind, as so much lumber. Instead ask yourself: "Why 60,000 men? He could get no more, as of the army of 200,000 enlisted, only 75 per cent were effective, and of these 150,000, 50,000 were too far away to reach the commander and 40,000 had to be left guarding the route to the base of supply. The enemy were estimated at only half of this number, but the enemy fought on the defensive and in their own country; hence conditions were fairly equal." Similarly: "Why had he no cavalry? Would he have been benefited by exchanging 10,000 infantry for 10,000 cavalry? Why did he attack at 6 A.m. Was this a mistake?" In this way study becomes reasoning; in this way we learn to think.

Application of Laws to Particular Facts. Never be satisfied with your own or your pupils' knowledge of principles or laws until you have applied them to concrete examples and particular facts. This is the main reason for the existence of laboratories and experiments. A student does not know what oxygen is until he has generated it, experimented with it, stuck glowing splinters into it, and noticed how they have suddenly flared into flame. A psychological principle, like the one we just now discussed, was not understood by you half so well before you read these illustrations, and you will understand it better still when you have studied the problems and examples at the end of the chapter.

Sympathy as an Aid to Understanding. Get into sympathy with your subject; for contrary to the antique slander, love is not blind, love is the very eye of the soul. No study, from botany to theology, can be studied right, until we love it. No student does his best until