Reasoning

All the mental processes which we have so far described find their

culmination and highest utility in reasoning. Not that reasoning comes

last in the list of mental activities, and cannot take place until all

the others have been completed, for reasoning is in some degree present

almost from the dawn of consciousness. The difference between the

reasoning of the child and that of the adult is largely one of

degree--of r ach. Reasoning goes farther than any of the other processes

of cognition, for it takes the relations expressed in judgments and out

of these relations evolves still other and more ultimate relations.



NATURE OF REASONING.--It is hard to define reasoning so as to describe

the precise process which occurs; for it is so intermingled with

perception, conception, and judgment, that one can hardly separate them

even for purposes of analysis, much less to separate them functionally.

We may, however, define reasoning provisionally as thinking by means of

a series of judgments with the purpose of arriving at some definite end

or conclusion. What does this mean? Professor Angell has stated the

matter so clearly that I will quote his illustration of the case:



Suppose that we are about to make a long journey which necessitates

the choice from among a number of possible routes. This is a case of the

genuinely problematic kind. It requires reflection, a weighing of the

pros and cons, and giving of the final decision in favor of one or

other of several alternatives. In such a case the procedure of most of

us is after this order. We think of one route as being picturesque and

wholly novel, but also as being expensive. We think of another as less

interesting, but also as less expensive. A third is, we discover, the

most expedient, but also the most costly of the three. We find ourselves

confronted, then, with the necessity of choosing with regard to the

relative merits of cheapness, beauty, and speed. We proceed to consider

these points in the light of all our interests, and the decision more or

less makes itself. We find, for instance, that we must, under the

circumstances, select the cheapest route.



HOW JUDGMENTS FUNCTION IN REASONING.--Such a line of thinking is very

common to everyone, and one that we carry out in one form or another a

thousand times every day we live. When we come to look closely at the

steps involved in arriving at a conclusion, we detect a series of

judgments--often not very logically arranged, to be sure, but yet so

related that the result is safely reached in the end. We compare our

concept of, say, the first route and our concept of picturesqueness,

decide they agree, and affirm the judgment, This route is picturesque.

Likewise we arrive at the judgment, This route is also expensive, it is

interesting, etc. Then we take the other routes and form our judgments

concerning them. These judgments are all related to each other in some

way, some of them being more intimately related than others. Which

judgments remain as the significant ones, the ones which are used to

solve the problem finally, depends on which concepts are the most vital

for us with reference to the ultimate end in view. If time is the chief

element, then the form of our reasoning would be something like this:

Two of the routes require more than three days: hence I must take the

third route. If economy is the important end, the solution would be as

follows: Two routes cost more than $1,000; I cannot afford to pay more

than $800; I therefore must patronize the third route.



In both cases it is evident that the conclusion is reached through a

comparison of two or more judgments. This is the essential difference

between judgment and reasoning. Whereas judgment discovers relations

between concepts, reasoning discovers relations between judgments, and

from this evolves a new judgment which is the conclusion sought. The

example given well illustrates the ordinary method by which we reason to

conclusions.



DEDUCTION AND THE SYLLOGISM.--Logic may take the conclusion, with the

two judgments on which it is based, and form the three into what is

called a syllogism, of which the following is a classical type:



All men are mortal;

Socrates is a man,

Therefore

Socrates is mortal.



The first judgment is in the form of a proposition which is called the

major premise, because it is general in its nature, including all men.

The second is the minor premise, since it deals with a particular man.

The third is the conclusion, in which a new relation is discovered

between Socrates and mortality.



This form of reasoning is deductive, that is, it proceeds from the

general to the particular. Much of our reasoning is an abbreviated form

of the syllogism, and will readily expand into it. For instance, we say,

It will rain tonight, for there is lightning in the west. Expanded

into the syllogism form it would be, Lightning in the west is a sure

sign of rain; there is lightning in the west this evening; therefore, it

will rain tonight. While we do not commonly think in complete

syllogisms, it is often convenient to cast our reasoning in this form to

test its validity. For example, a fallacy lurks in the generalization,

Lightning in the west is a sure sign of rain. Hence the conclusion is

of doubtful validity.



INDUCTION.--Deduction is a valuable form of reasoning, but a moment's

reflection will show that something must precede the syllogism in our

reasoning. The major premise must be accounted for. How are we able to

say that all men are mortal, and that lightning in the west is a sure

sign of rain? How was this general truth arrived at? There is only one

way, namely, through the observation of a large number of particular

instances, or through induction.



Induction is the method of proceeding from the particular to the

general. Many men are observed, and it is found that all who have been

observed have died under a certain age. It is true that not all men have

been observed to die, since many are now living, and many more will no

doubt come and live in the world whom we cannot observe, since

mortality will have overtaken us before their advent. To this it may be

answered that the men now living have not yet lived up to the limit of

their time, and, besides, they have within them the causes working whose

inevitable effect has always been and always will be death; likewise

with the men yet unborn, they will possess the same organism as we,

whose very nature necessitates mortality. In the case of the

premonitions of rain, the generalization is not so safe, for there have

been exceptions. Lightning in the west at night is not always followed

by rain, nor can we find inherent causes as in the other case which

necessitates rain as an effect.



THE NECESSITY FOR BROAD INDUCTION.--Thus it is seen that our

generalizations, or major premises, are of all degrees of validity. In

the case of some, as the mortality of man, millions of cases have been

observed and no exceptions found, but on the contrary, causes discovered

whose operation renders the result inevitable. In others, as, for

instance, in the generalization once made, All cloven-footed animals

chew their cud, not only had the examination of individual cases not

been carried so far as in the former case when the generalization was

made, but there were found no inherent causes residing in cloven-footed

animals which make it necessary for them to chew their cud. That is,

cloven feet and cud-chewing do not of necessity go together, and the

case of the pig disproves the generalization.



In practically no instance, however, is it possible for us to examine

every case upon which a generalization is based; after examining a

sufficient number of cases, and particularly if there are supporting

causes, we are warranted in making the inductive leap, or in

proceeding at once to state our generalization as a working hypothesis.

Of course it is easy to see that if we have a wrong generalization, if

our major premise is invalid, all that follows in our chain of reasoning

will be worthless. This fact should render us careful in making

generalizations on too narrow a basis of induction. We may have observed

that certain red-haired people of our acquaintance are quick-tempered,

but we are not justified from this in making the general statement that

all red-haired people are quick-tempered. Not only have we not examined

a sufficient number of cases to warrant such a conclusion, but we have

found in the red hair not even a cause of quick temper, but only an

occasional concomitant.



THE INTERRELATION OF INDUCTION AND DEDUCTION.--Induction and deduction

must go hand in hand in building up our world of knowledge. Induction

gives us the particular facts out of which our system of knowledge is

built, furnishes us with the data out of which general truths are

formed; deduction allows us to start with the generalization furnished

us by induction, and from this vantage ground to organize and

systematize our knowledge and, through the discovery of its relations,

to unify it and make it usable. Deduction starts with a general truth

and asks the question, What new relations are made necessary among

particular facts by this truth? Induction starts with particulars, and

asks the question, To what general truth do these separate facts lead?

Each method of reasoning needs the other. Deduction must have induction

to furnish the facts for its premises; induction must have deduction to

organize these separate facts into a unified body of knowledge. He only

sees well who sees the whole in the parts, and the parts in the whole.