Thought Culture Part 5

The process of Synthesis is calculated to develop and cultivate the mind in several directions and exercises along these lines will give a new habit and sense of orderly arrangement, which will be most useful to the student in his every-day life. Halleck says: "Whenever a person is comparing a specimen to see whether it may be put in the same cla.s.s with other specimens, he is _thinking_. Comparison is an absolutely essential factor of thought, and cla.s.sification demands comparison. The man who has not properly cla.s.sified the myriad individual objects with which he has to deal, must advance like a cripple. He, only, can travel with seven-league boots, who has thought out the relations existing between these stray individuals and put them into their proper cla.s.ses. In a minute a business man may put his hand on any one of ten thousand letters if they are properly cla.s.sified. In the same way, the student of history, sociology or any other branch, can, if he studies the subjects aright, have all his knowledge cla.s.sified and speedily available for use.... In this way, we may make our knowledge of the world more minutely exact. We cannot cla.s.sify without seeing things under a new aspect."

The study of Natural History, in any or all of its branches, will do much to cultivate the power of Cla.s.sification. But one may practice cla.s.sification with the objects around him in his every-day life.

Arranging things mentally, into small cla.s.ses, and these into larger, one will soon be able to form a logical connection between particular ideas and general ideas; particular objects and general cla.s.ses. The practice of cla.s.sification gives to the mind a constructive turn--a "building-up" tendency, which is most desirable in these days of construction and development. Regarding some of the pitfalls of cla.s.sification, Jevons says:

"In cla.s.sifying things, we must take great care not to be misled by outward resemblances. Things may seem to be very much like each other which are not so. Whales, porpoises, seals and several other animals live in the sea exactly like fish; they have a similar shape and are usually cla.s.sed among fish. People are said to go whale-fishing. Yet these animals are not really fish at all, but are much more like dogs and horses and other quadrupeds than they are like fish. They cannot live entirely under water and breathe the air contained in the water like fish, but they have to come up to the surface at intervals to take breath. Similarly, we must not cla.s.s bats with birds because they fly about, although they have what would be called wings; these wings are not like those of birds and in truth bats are much more like rats and mice than they are like birds. Botanists used at one time to cla.s.sify plants according to their size, as trees, shrubs or herbs, but we now know that a great tree is often more similar in its character to a tiny herb than it is to other great trees. A daisy has little resemblance to a great Scotch thistle; yet the botanist regards them as very similar.

The lofty growing bamboo is a kind of gra.s.s, and the sugarcane also belongs to the same cla.s.s with wheat and oats."

Remember that a.n.a.lysis of a genus into its component species is accomplished by a separation according to _differences_; and species are built up by synthesis into a genus because of _resemblances_. The same is true regarding individual and species, building up in accordance to points of resemblance, while a.n.a.lysis or separation is according to points of difference.

The use of a good dictionary will be advantageous to the student in developing the power of Generalization or Conception. Starting with a species, he may build up to higher and still higher cla.s.ses by consulting the dictionary; likewise, starting with a large cla.s.s, he may work down to the several species composing it. An encyclopedia, of course, is still better for the purpose in many cases. Remember that Generalization is a prime requisite for clear, logical thinking.

Moreover, it is a great developer of Thought.

CHAPTER XI.

JUDGMENT

We have seen that in the several mental processes which are grouped together under the general head of Understanding, the stage or step of Abstraction is first; following which is the second step or phase, called Generalization or Conception. The third step or phase is that which is called Judgment. In the exercise of the faculty of Judgment, we determine the agreement or disagreement between two concepts, ideas, or objects of thought, by comparing them one with another. From this process of comparison arises the Judgment, which is expressed in the shape of a logical Proposition. A certain form of Judgment must be used, however, in the actual formation of a Concept, for we must first compare qualities, and make a judgment thereon, in order to form a general idea.

In this place, however, we shall confine ourselves to the consideration of the faculty of Judgment in the strictly logical usage of the term, as previously stated.

We have seen that the expression of a concept is called a Term, which is the _name_ of the concept. In the same way when we compare two terms (expressions of concepts) and pa.s.s Judgment thereon, the expression of that Judgment is called a Proposition. In every Judgment and Proposition there must be two Terms or Concepts, connected by a little word "is" or "are," or some form of the verb "to be," in the present tense indicative. This connecting word is called the Copula. For instance, we may compare the two terms _horse_ and _animal_, as follows: "A horse is an animal," the word _is_ being the Copula or symbol of the _affirmative_ Judgment, which connects the two terms. In the same way we may form a _negative_ Judgment as follows: "A horse is not a cow." In a Proposition, _the term of which something is affirmed_ is called the Subject; and _the term expressing that which is affirmed of the subject_ is called the Predicate.

Besides the distinction between affirmative Judgments, or Propositions, there is a distinction arising from _quant.i.ty_, which separates them into the respective cla.s.ses of _particular_ and _universal_. Thus, "_all_ horses are animals," is a _universal_ Judgment; while "_some_ horses are black" is a particular Judgment. Thus all Judgments must be either _affirmative_ or _negative_; and also either _particular_ or _universal_. This gives us four possible cla.s.ses of Judgments, as follows, and ill.u.s.trated symbolically:

1. Universal Affirmative, as "All A is B."

2. Universal Negative, as "No A is B."

3. Particular Affirmative, as "Some A is B."

4. Particular Negative, as "Some A is not B."

The Term or Judgment is said to be "_distributed_" (that is, extended universally) when it is used in its fullest sense, in which it is used in the sense of "each and every" of its kind or cla.s.s. Thus in the proposition "Horses are animals" the meaning is that "_each and every_"

horse is an animal--in this case the _subject_ is "distributed" or made universal. But the _predicate_ is _not_ "distributed" or made universal, but remains particular or restricted and implies merely "some." For the proposition does not mean that the cla.s.s "_horses_" includes _all_ animals. For we may say that: "_Some_ animals are _not_ horses." So you see we have several instances in which the "distribution" varies, both as regards the subject and also the predicate. The rule of logic applying in this case is as follows:

1. In _universal_ propositions, the _subject_ is distributed.

2. In _particular_ propositions, the _subject_ is _not_ distributed.

3. In _negative_ propositions, the _predicate_ is distributed.

4. In _affirmative_ propositions, the _predicate_ is _not_ distributed.

A little time devoted to the a.n.a.lysis and understanding of the above rules will repay the student for his trouble, inasmuch as it will train his mind in the direction of logical distinction and judgment. The importance of these rules will appear later.

Halleck says: "Judgment is the power revolutionizing the world. The revolution is slow because nature's forces are so complex, so hard to be reduced to their simplest forms, and so disguised and neutralized by the presence of other forces. The progress of the next hundred years will join many concepts, which now seem to have no common qualities. If the vast amount of energy latent in the sunbeams, in the rays of the stars, in the winds, in the rising and falling of the tides, is treasured up and applied to human purposes, it will be a fresh triumph for judgment. This world is rolling around in a universe of energy, of which judgment has as yet harnessed only the smallest appreciable fraction. Fortunately, judgment is ever working and silently comparing things that, to past ages, have seemed dissimilar; and it is constantly abstracting and leaving out of the field of view those qualities which have simply served to obscure the point at issue." Brooks says: "The power of judgment is of great value to its products. It is involved in or accompanies every act of the intellect, and thus lies at the foundation of all intellectual activity. It operates directly in every act of the understanding; and even aids the other faculties of the mind in completing their activities and products."

The best method of cultivating the power of Judgment is the exercise of the faculty in the direction of making comparisons, of weighing differences and resemblances, and in generally training the mind along the lines of Logical Thinking. Another volume of this series is devoted to the latter subject, and should aid the student who wishes to cultivate the habit of logical and scientific thought. The study of mathematics is calculated to develop the faculty of Judgment, because it necessitates the use of the powers of comparison and decision. Mental arithmetic, especially, will tend to strengthen, and exercise this faculty of the mind.

Geometry and Logic will give the very best exercise along these lines to those who care to devote the time, attention and work to the task.

Games, such as chess, and checkers or draughts, tend to develop the powers of Judgment. The study of the definitions of words in a good dictionary will also tend to give excellent exercise along the same lines. The exercises given in this book for the cultivation and development of the several faculties, will tend to develop this particular faculty in a general way, for the exercise of Judgment is required at each step of the way, and in each exercise.

Brooks says: "It should be one of the leading objects of the culture of young people to lead them to acquire the habit of forming judgments.

They should not only be led to see things, but to have opinions about things. They should be trained to see things in their relations, and to put these relations into definite propositions. Their ideas of objects should be worked up into thoughts concerning the objects. Those methods of teaching are best which tend to excite a thoughtful habit of mind that notices the similitudes and diversities of objects, and endeavors to read the thoughts which they embody and of which they are the symbols."

The exercises given at the close of the next chapter, ent.i.tled "Derived Judgments," will give to the mind a decided trend in the direction of logical judgment. We heartily recommend them to the student.

The student will find that he will tend to acquire the habit of clear logical comparison and judgment, if he will memorize and apply in his thinking the following excellent _Primary Rules of Thought_, stated by Jevons:

"I. _Law of Ident.i.ty_: The same quality or thing is _always_ the same quality or thing, no matter how different the conditions in which it occurs.

"II. _Law of Contradiction_: Nothing can at the same time and place _both_ be and not be.

"III. _Law of Excluded Middle_: Everything must _either_ be, or not be; there is no other alternative or middle course."

Jevons says of these laws: "Students are seldom able to see at first their full meaning and importance. All arguments may be explained when these self-evident laws are granted; and it is not too much to say that _the whole of logic will be plain to those who will constantly use these laws as their key_."

CHAPTER XII.

DERIVED JUDGMENTS

As we have seen, a Judgment is obtained by comparing two objects of thought according to their agreement or difference. The next higher step, that of logical Reasoning, consists of the comparing of two ideas through their relation to a third. This form of reasoning is called _mediate_, because it is effected through the _medium_ of the third idea. There is, however, a certain process of Understanding which comes in between this mediate reasoning on the one hand, and the formation of a plain judgment on the other. Some authorities treat it as a form of _reasoning_, calling it _Immediate Reasoning_ or Immediate Inference, while others treat it as a higher form of Judgment, calling it Derived Judgment. We shall follow the latter cla.s.sification, as best adapted for the particular purposes of this book.

The fundamental principle of Derived Judgment is that ordinary Judgments are often so related to each other that one Judgment may be derived directly and immediately from another. The two particular forms of the general method of Derived Judgment are known as those of (1) Opposition; and (2) Conversion; respectively.

In order to more clearly understand the logical processes involved in Derived Judgment, we should acquaint ourselves with the general relations of Judgments, and with the symbolic letters used by logicians as a means of simplifying the processes of thought. Logicians denote each of the four cla.s.ses of Judgments or Propositions by a certain letter, the first four vowels--A, E, I and O, being used for the purpose. It has been found very convenient to use these symbols in denoting the various forms of Propositions and Judgments. The following table should be memorized for this purpose:

_Universal Affirmative_, symbolized by "A."

_Universal Negative_, symbolized by "E."

_Particular Affirmative_, symbolized by "I."

_Particular Negative_, symbolized by "O."

It will be seen that these four forms of Judgments bear certain relations to each other, from which arises what is called opposition.

This may be better understood by reference to the following table called the Square of Opposition:

A CONTRARIES E +------------------------+ / /S C /E O /I N /R T /O S R /T S U A /C U B /I B A /D A L / L T / T E / D E R / I R N /A C N S /R T S /T O /N R /O I /C E / S / +------------------------+ I SUB-CONTRARIES O

Thus, A and E are _contraries_; I and O are _sub-contraries_; A and I, and also E and O are _subalterns_; A and O, and also E and I are _contradictories_.

The following will give a symbolic table of each of the four Judgments or Propositions with the logical symbols attached: