Mental exploration ensued. "How about following the brook?" "That won't do, for it flows down into a big swamp that we couldn't get through". "How about telling directions by the sun?" "But it has so clouded over that you can't tell east from west, or north from south."

"Yes, those old clouds! How fast they are going! They seem to go straight enough." "Well, say! How about following the clouds? If we keep on going straight, in any direction, for a couple of hours, we shall surely get out of the woods somewhere." This seems worth trying and actually brings the boys out to a road where they can inquire the way home.

What we find in this case is typical of problem solution. First, a desire is aroused, and it facilitates the observation and recall of facts relevant to itself. One pertinent fact is observed, another pertinent fact, or rule, is recalled; and in these two taken together the key to the problem is found.

2. Rationalization or self-justification.

While in the preceding case reasoning showed what to do, here it is called upon to justify what has been done, or what is going to be done anyway. The question is, what reason to a.s.sign for the act; we feel the need of meeting criticism, either from other people or from ourselves. The real motive for the act may be unknown to ourselves, as it often is unless we have made a careful study of motives; or, if known, it may not be such as we care to confess. We require a _reasonable_ motive, some acceptable general principle that explains our action.

A child is unaccountably polite and helpful to his mother some day, and when asked about it replies that he simply wants to help--while his real motive may have been to score against his brother or sister, who is to some extent his rival.

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If I have work requiring attention but want to go to the game, I should certainly be lacking in reasoning ability if I could not find something in the situation that made my attendance at the game imperative. I am stale, and the game will freshen me up and make me work better afterward. Or, I am in serious danger of degenerating into a mere "grind", and must fight against this evil tendency. Or, my presence at the game is necessary in order to encourage the team.

Thus, aspects of the situation that are in line with our desire bob to the surface and suggest acceptable general principles that make the intended action seem good and even necessary. Finding excuses for acts already performed is a reasoning exercise of the same sort. Man is a rationalizing animal as well as a rational animal, and his self-justifications and excuses, ludicrous though they often are, are still a tribute to his very laudable appreciation of rationality.

3. Explanation.

This form of reasoning, like the preceding, takes its start with something that raises the question, "Why?" Only, our interest in the question is objective rather than subjective. It is not our own actions that call for explanation, but some fact of nature or of human behavior. Why--with apologies to the Southern Hemisphere!--is it so cold in January? The fact arouses our curiosity. We search the situation for clues, and recall past information, just as in the attempt to solve a practical problem. "Is it because there is so much snow in January?" "But what, then, makes it snow? This clue leads us in a circle." "Perhaps, then, it is because the sun shines so little of the time, and never gets high in the sky, even at noon." That is a pretty good clue; it recalls the general principle that, without a continued supply of heat, cold is inevitable. To explain a phenomenon is to deduce it from {472} an accepted general principle; to understand it is to see it as an instance of the general principle.

Such understanding is very satisfactory, since it rids you of uncertainty and sometimes from fear, and gives you a sense of power and mastery.

4. Application.

The reasoning processes discussed up to this point have taken their start with the particular, and have been concerned in a search for the general principle that holds good of the given particular case.

Reasoning may also take its start at the other end, in a general statement, and seek for particular cases belonging under this general rule. But what can be the motive for this sort of reasoning? What is there about a general proposition to stimulate exploration?

Several motives may be in play. First, there may be a need for application of the general principle. Somebody whose authority you fully accept enunciates a general proposition, and you wish to apply it to special cases, either for seeing what practical use you can make of it, or simply to make its meaning more real and concrete to yourself. Your exploration here takes a different form from that thus far described. Instead of searching a concrete situation for clues, and your memory for general principles, you search your memory for particular cases where the general law should apply. If all animals are cold-blooded, excepting only birds and mammals, then fish and frogs and lizards are cold-blooded, spiders, insects, lobsters and worms; having drawn these inferences, your understanding of the general proposition becomes more complete.

5. Doubt.

A general proposition may stimulate reasoning because you doubt it, and wish to find cases where it breaks down. Perhaps somebody makes the general statement whose authority you do not accept; perhaps he says it in an a.s.sertive way that makes you want to take him down {473} a peg. Perhaps you are in the heat of an argument with him, so that every a.s.sertion he may make is a challenge. You search your memory for instances belonging under the doubted general statement, in the hope of finding one where the general statement leads to a result that is contrary to fact. "You say that all politicians are grafters. Theodore Roosevelt was a politician, therefore, according to you, he must have been a grafter. But he was not a grafter, and you will have to take back that sweeping a.s.sertion."

6. Verification.

This same general type of reasoning, which takes its start with a general proposition, and explores particular instances in order to see whether the proposition, when applied to them, gives a result in accordance with the facts, has much more serious uses; for this is the method by which a _hypothesis_ is tested in science. A hypothesis is a general proposition put forward as a guess, subject to verification.

If it is thoroughly verified, it will be accepted as a true statement, a "law of nature", but at the outset it is only a guess that may turn out to be either true or false. How shall its truth or falsity be demonstrated? By deducing its consequences, and testing these out in the realm of observed fact.

An example from the history of science is afforded by Harvey's discovery of the circulation of the blood, which was at first only a hypothesis, and a much-doubted one at that. If the blood is driven by the heart through the arteries, and returns to the heart by way of the veins, then the flow of blood in any particular artery must be away from the heart, and in any particular vein towards the heart. This deduction was readily verified. Further, there should be little tubes leading from the smallest arteries over into the smallest veins, and this discovery also was later verified, when the invention of the microscope made observation of the capillaries possible. Other deductions also were verified, {474} and in short all deductions from the hypothesis were verified, and the circulation of the blood became an accepted law.

Most hypotheses are not so fortunate as this one; most of them die by the wayside, since it is much easier to make a guess that shall fit the few facts we already know than to make one that will apply perfectly to many other facts at present unknown. A hypothesis is a great stimulus to the discovery of fresh facts. Science does not like to have unverified hypotheses lying around loose, where they may trip up the unwary. It is inc.u.mbent on any one who puts forward a hypothesis to apply it to as many special cases as possible, in order to see whether it works or not; and if the propounder of the hypothesis is so much in love with it that he fails to give it a thorough test, his scientific colleagues are sure to come to the rescue, for they, on the whole, would be rather pleased to see the other fellow's hypothesis come to grief. In this way, the rivalry motive plays a useful part in the progress and stabilizing of science.

Deductive and Inductive Reasoning

When you are sure at the outset of your general proposition, and need only to see its application to special cases, your reasoning is said to be "deductive". Such reasoning is specially used in mathematics.

But in natural science you are said to employ "inductive reasoning".

The process has already been described. You start with particular facts demanding explanation or generalization, and try to find some accepted law that explains them. Failing in that, you are driven to guess at a general law, i.e., to formulate a hypothesis that will fit the known facts. Then, having found such a conjectural general law, you proceed to deduce its consequences; you see that, _if_ the hypothesis is true, such and such facts must be true. Next you go out and see whether these facts are true, and if they are, your hypothesis {475} is verified to that extent, though it may be upset later. If the deduced facts are not true, the hypothesis is false, and you have to begin all over again.

The would-be natural scientist may fail at any one of several points.

First, he may see no question that calls for investigation. Everything seems a matter-of-course, and he concludes that science is complete, with nothing left for him to discover. Second, seeing something that still requires explanation, he may lack fertility in guessing, or may be a poor guesser and set off on a wild-goose chase. Helmholtz, an extremely fertile inventor of high-grade hypotheses, describes how he went about it. He would load up in the morning with all the knowledge he could a.s.semble on the given question, and go out in the afternoon for a leisurely ramble; when, without any strenuous effort on his part, the various facts would get together in new combinations and suggest explanations that neither he nor any one else had ever thought of before. Third, our would-be scientific investigator may lack the clear, steady vision to see the consequences of his hypothesis; and, fourth, he may lack the enterprise to go out and look for the facts that his hypothesis tells him should be found.

Psychology and Logic

Psychology is not the only science that studies reasoning; that is the subject-matter of logic as well, and logic was in the field long before psychology. Psychology studies the _process_ of reasoning, while logic checks up the result and shows whether it is valid or not.

Logic cares nothing about the exploratory process that culminates in inference, but limits itself to inference alone.

Inference, in logical terminology, consists in drawing a conclusion from two given premises. The two premises are the "two facts" which, acting together, arouse the {476} perceptive response called inference, and the "third fact" thus perceived is the conclusion.

[Footnote: The "two facts" or premises need not be true; either or both may be a.s.sumed or hypothetical, and still they may lead to a valid conclusion, i.e., a conclusion implicated in the a.s.sumed premises.] Logic cares nothing as to how the premises were found, nor as to the motive that led to the search for them, nor as to the time and effort required, nor the difficulty encountered; these matters all pertain to psychology.

Logic sets forth the premises and conclusion in the form of the "syllogism", as in the old stand-by:

Major premise: All men are mortal Minor premise: Socrates is a man Conclusion: Therefore, Socrates is mortal

The syllogism includes three "terms", which in the above instance are "Socrates", "mortal", and "man" or "men". Logic employs the letters, S, P, and M to symbolize these three terms in general. S is the "subject" (or, we might say, the "object" or the "situation") about which something is inferred. P is the "predicate", or what is inferred about S; and M is the "middle term" which corresponds to our "yardstick" or "point of reference", as we used those words at the beginning of the chapter. S is compared with P through the medium of M; or, S and P are both known to be related to M, and therefore (when the relations are of the right sort) they are related to each other.

It is part of the business of logic to examine what relations are, and what are not, suitable for yielding a valid inference.

In symbols, then, the syllogism becomes:

Major premise: M is P Minor premise: S is M Conclusion: Therefore, S is P

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Without confounding logic and psychology in the least, we may take this symbolic syllogism as a sort of map, on which to trace out the different exploratory processes that we have already described under the head of "varieties of reasoning". To do so may make these different processes stand out more distinctly.

In problem-solution, we start with S, a situation unsolved, i.e., without any P. P, when found, will be the solution. We explore the situation, and find in it M; i.e., we observe that S is M. Now M recalls our previously acquired knowledge that M is P. Having then before us the two premises, we perceive that S is P, and are saved.

In rationalization or explanation, we know, to start with, that S is P, and wish to know _why_ this is so. As before, we explore S, find M, recall that M is P, and see that S, therefore, is P. Our final conclusion is, really, that S is P because it is M; that January is cold because it gets little sunlight.

In application, doubt or verification, we start with the major premise, M is P, and explore our memories for an S which, being M, should therefore be P according to our hypothesis. If we find an S which is _not_ P, then our final conclusion is that the major premise is false.

Reference to our "map" indicates that there might be several other varieties of reasoning, and there are, indeed, though they are scarcely as important as those already mentioned. Reasoning sometimes starts with the observation of P, which means something that might prove useful on some future occasion. Your attention is caught by these prominent words in an advertis.e.m.e.nt, "$100 a week!" That might come in handy on some future occasion, and you look further to see how all that money can be attached to S, yourself on some future occasion.

You soon learn that you have only to secure subscriptions for a certain magazine, {478} and that income may be yours. P is the money, and M is the occupation that gives the money, while S is yourself supposedly entering on this occupation and earning the money. This type of reasoning is really quite common. If we see a person making a great success of anything, we try to discover how he does it, reasoning that if we do the same, we shall also be successful; or, if we see some one come to grief, we try to see how it happened, so as to avoid his mistake and so the bad consequences of that mistake. We plan to perform M so as to secure P, or to avoid M in the hope of avoiding P.

Sometimes, not so rarely, we have both premises handed out to us and have only to draw the conclusion. More often, we hear a person drawing a conclusion from only one expressed premise, and try to make out what the missing premise can be. Sometimes this is easy, as when one says, "I like him because he is always cheerful", from which you see that the person speaking must like cheerful persons. But if you hear it said that such a one "cannot be a real thinker, he is so positive in his opinions" or that another "is unfeeling and unsympathetic from lack of a touch of cruelty in his nature", you may have to explore about considerably before finding acceptable major premises from which such conclusions can be deduced.

Finally, in asking what are the _qualifications of a good reasoner_ we can help ourselves once more by reference to the syllogistic map. To reason successfully on a given topic, you need good major premises, good minor premises, and valid conclusions therefrom.

(a) A good stock of major premises is necessary, a good stock of rules and principles acquired in previous experience. Without some knowledge of a subject, you have only vague generalities to draw upon, and your reasoning process will be slow and probably lead only to indefinite conclusions. {479} Experience, knowledge, memory are important in reasoning, though they do not by any means guarantee success.

(b) The "detective instinct" for finding the right clues, and rejecting false leads, amounts to the same as sagacity in picking out the useful minor premises. In problem solution, you have to find both of your premises, and often the minor premise is the first to be found and in turn recalls the appropriate major premise. Finding the minor premise is a matter of observation, and if you fail to observe the significant fact about the problem, the really useful major premise may lie dormant, known and retained but not recalled, while false clues suggest inapplicable major premises and give birth to plenty of reasoning but all to no purpose. Some persons with abundant knowledge are ineffective reasoners from lack of a sense for probability. The efficient reasoner must be a good guesser.

(c) The reasoner needs a clear and steady mental eye, in order to see the conclusion that is implicated in the premises. Without this, he falls into confusion and fallacy, or fails, with the premises both before him, to get the conclusion. The "clear and steady mental eye", in less figurative language, means the ability to check hasty responses to either premise alone, or to extraneous features of the situation, so as to insure that "unitary response" to the combination of premises which const.i.tutes the perceptive act of inference.