  1. TWO FUNDAMENTAL LAWS.The elemental form of evolved thought is the judgment. The laws or axioms of thought may, therefore, be discovered by studying the judgment. Judging is the process of conjoining and disjoining notions. When these notions are conjoined the judgment is affirmative; when disjoined the judgment is negative. To illustrate: “Some men are wise,” is an affirmative judgment, while “Some men are not wise,” is a negative judgment. All judgments are either affirmative or negative and this suggests that there may be but two fundamental laws or axioms underlying judging or all forms of developed thinking. One law would condition the affirmative judgment; the other the negative. Such is actually the case. The law which permits the affirmative judgment is called the law of identity, while the law which allows a negative judgment is known as the law of contradiction. There is a third law termed the law of excluded middle, which is in reality a combination of the other two. 2. THE LAW OF IDENTITY.In general the law of identity implies a certain permanency throughout the material world. That door is a door and always will be a door till the conditions change. If it were not for this law, that everything is The law of identity may be stated in three ways: (1)Whatever is, is; (2)Everything remains identical with itself; (3)The same is the same. ABSOLUTE IDENTITY—COMPLETE AND INCOMPLETE. Applying the law of identity to the affirmative judgment expressed in the form of a proposition, we find two kinds of identity, absolute and relative. In the propositions, “Socrates is Socrates,” “dogs are dogs,” “honesty is honesty,” the subject is absolutely identical with the predicate—the same in form and meaning. If we were to illustrate the subject and predicate by two circles they would be of the same size and shape, the one coinciding with the other point to point. This kind of absolute identity which makes possible all truisms we may term, for want of a better name, complete absolute identity. This would imply that there is an incomplete absolute identity and such seems to be the case. Examining the definition, “Aman is a rational animal,” we observe that the notion man has the same content or meaning as the notion rational animal. In meaning, then, the two notions are absolutely identical. The one includes just as many objects or qualities as RELATIVE IDENTITY. Relative identity is best understood by thinking of it as partial identity, just as we may think of absolute identity as total identity. In relative identity the whole of one notion may be affirmed of a part of another notion; or a part of one notion may be affirmed of a part of another notion. To illustrate: (1)All men are mortal; (2)Some men are wise. These and their like are made possible because of the law of relative identity. In the first proposition all of the “men” class is identical with a part of the “mortal” class. If we were to represent this relation by circles, the “men” circle would be made smaller than the “mortal” circle and placed inside it, as in Fig.1. Fig. 1. Be it remembered that circles are surfaces, and in Fig.1 the men circle is identical with that portion of the mortal circle which is immediately underneath it. The same relation may be indicated by a small pad being placed on top of a larger pad. Then the whole of the smaller pad could be thought of as being identical with that part of the larger pad which is immediately underneath. In the case of the second proposition a part of the “men” class is identical with a portion of the “wise” class. The two circles indicating this relation must intersect each other so that a portion of each may be common ground, as in Fig.2 where the shaded part represents the identity. Fig. 2. Thus we see that the law of identity underlies all affirmative propositions. Absolute identity making possible the truism and definition, and relative identity conditioning all the universal and particular affirmative propositions which are neither truisms nor definitions. The three forms may be symbolized as follows: (1) A is A—Absolute complete (2) A is A—Absolute incomplete (3) A is B—Relative. The student will note that the “A’s” of absolute incomplete differ in form. 3. LAW OF CONTRADICTION.The law of contradiction underlies all negative propositions. It is the mission of this law to tear down or to be destructive in nature; while the law of identity builds up or is constructive in nature. The law of contradiction may be stated in this way: It is impossible for the same thing to be and not to be at the same time and in the same place. Or better, it The little word not bisects the universe. All the people in the world are either honest or not honest, virtuous or not virtuous. These are contradictory statements and what is comprehended by the one cannot be comprehended by the other at the same time, any more than a man can shake his head and nod his head at the same time. If we assert the identity between two notions then we cannot in the same breath deny their identity. ILLUSTRATIONS: (1) A red flower cannot be a red flower and not a red flower at the same time. (2) No man can be guilty and not guilty at the same time. (3) A boy cannot be working and not working at the same time. If I assert that the flower is red, then Icannot affirm in the same breath that the flower is not red. TWO USES OF NOT. The word not when used with the copula of a given proposition makes that proposition negative, as (1)“Some men are not wise.” But when not is attached to the predicate by a hyphen, the predicate is made negative, not the proposition, as (2)“Some men are not-wise.” Here the predicate not-wise is negative, but the proposition in which it appears is affirmative. It is obvious that FURTHER ILLUSTRATIONS:
The student must understand that a term and its contradictory destroy each other. If we affirm something of the one, then we must deny it of the other, or we undermine the integrity of both. If it is affirmed of teachers A, B and C that they are wise, then it must be denied that they are not-wise. ILLUSTRATIONS:
SYMBOLIZATION OF THE LAW OF CONTRADICTION.
CONTRADICTORY AND OPPOSITE TERMS. It is easy to use opposite terms in a contradictory sense. This leads to serious error. “Not-guilty” is the contradictory of “guilty,” while “innocent” is the opposite of “guilty.” We could hardly say that the water must either be cold or hot, as it might be warm. “Not-hot” is the only term which contradicts “hot.” The law of contradiction has nothing to do with opposites. Further, it is dangerous to regard words with the negative prefix as being contradictory of the affirmative form. For example: Valuable and invaluable are not contradictory. There is likewise some doubt as to the contradictory nature of such words as agreeable and disagreeable, though we are sure that agreeable and not-agreeable contradict each other. To use the “not” with a hyphen is safer than to depend upon some prefix which is supposed to mean “not.” ILLUSTRATIONS OF CONTRADICTORY AND OPPOSITE TERMS.
4. THE LAW OF EXCLUDED MIDDLE.The law of excluded middle may be considered as a combination of identity and contradiction. Identity gives the proposition, “John Doe is honest.” Contradiction, “John Doe is not honest.” Combine the two using either and or and we have the excluded middle proposition, “Either John Doe is honest or he is not honest.” Excluded middle explains itself. Of the two contradictory notions it must be either the one or the other. There is no “go-between” notion. The law may be stated in many ways, as will be seen by the following: (1)Everything must either be or not be. (2)Either a given judgment is true or its contradictory is true; there is no middle ground. (3)Of two contradictory judgments one must be true. (4)Every predicate may be affirmed or denied of every subject. ILLUSTRATIONS: (1) A man is either mortal or he is not mortal. (2)John Doe is either honest or not-honest. (3)Either you are going or you are not going. SYMBOLIZATION OF EXCLUDED MIDDLE. A is either A or not-A 5. THE LAW OF SUFFICIENT REASON.The law may be stated in this wise. Every phenomenon, event or relation must have a sufficient reason for being what it is. To illustrate: (1)If Venus is the evening star, there must be a sufficient reason. (2)If the ground is wet, there must be a cause. Many logicians argue that this law has no place in logic, its field being that of the physical sciences. The laws of identity, contradiction and excluded middle are, however, universally regarded as the Primary Laws of thought. 6. UNITY OF PRIMARY LAWS OF THOUGHT ILLUSTRATED BY SYMBOLS.
The “excluded middle” propositions of the foregoing express alternatives which are mutually contradictory. There is no middle ground. The “contradictory propositions” contradict the identity of the subject with one alternative, while the “identity” propositions affirm the identity of the subject with the other alternative. This is made possible because of the principle, “Of two mutually contradictory terms, if one is true the other must be false.” The foregoing scheme shows how closely “contradictory” and “identity” propositions are related to “excluded middle” propositions. Expressed mathematically: excluded middle = contradiction + identity. 7. OUTLINE.PRIMARY LAWS OF THOUGHT. (1) Two fundamental laws. Identity, contradiction. (2) Law of identity. Absolute—complete, incomplete. Relative. (3) Law of contradiction. Two uses of not. Contradictory and opposite terms. (4) Law of excluded middle. (5) Law of sufficient reason. (6) Unity of primary laws of thought. 8. SUMMARY.(1) The elemental forms of evolved thought are the affirmative and negative judgments. This suggests two fundamental laws of thought, the law of identity and the law of contradiction. The former conditions the affirmative judgment, the latter the negative. (2) The law of identity implies a permanency of being. “Everything remains identical with itself,” is a statement of identity. Absolute identity may be divided into complete and incomplete identity. In complete absolute identity the subject is the same as the predicate in both form and meaning. Truisms illustrate this. In incomplete absolute identity the subject is identical with the predicate in meaning only. Illustrated by definitions. In relative identity the whole of the subject may be affirmed of a part of the predicate or a part of the subject may be affirmed of a part of the predicate. (3) “It is impossible for the same thing to be itself and its contradictory at the same time,” is a statement of the law of contradiction. Identity is constructive while contradiction is destructive in nature. To make the proposition negative the word not must be used with the copula. “Not” attached to the predicate with a hyphen makes the predicate negative, but not the proposition. To use opposite terms in a contradictory sense leads to serious error. The safest way of making a positive term a contradictory negative term is to prefix “not” with a hyphen or use “non.” (4) The law of excluded middle is virtually a combination of identity and contradiction. It may be stated as follows: “Athing must either be itself or its contradictory.” (5) “Every condition must have a sufficient reason for its existence,” is the law of sufficient reason. Its distinct province is physical science rather than logic. (6) The laws may be expressed mathematically: excluded middle = identity + contradiction. SCHEMATIC STATEMENT OF PRIMARY LAWS.
9. ILLUSTRATIVE EXERCISES.(1a) Each of the following propositions is made possible because of the existence of which law of thought? In answering this question Isummarize in my mind the meaning of each law of thought. Viz.: (1) In complete absolute identity the subject and predicate are the same in form and meaning. (2) In incomplete absolute identity the subject and predicate are the same in meaning, but not in form. (3) In relative identity either the whole or a part of the subject is identical with a part of the predicate. (4) The law of contradiction always denies the identity between subject and predicate. (5) Excluded middle conditions all alternative expressions. THE PROPOSITIONS. (1) “A thief is a thief.” Complete absolute identity. (2) “Thinking is the process of affirming or denying connections.” Incomplete absolute identity. (3) “All good men are wise.” Relative identity. (4) “No triangle has interior angles whose sum is greater than two right angles.” Contradiction. (5) “A stitch in time saves nine.” Relative identity. (6) “Judging is the process of conjoining and disjoining notions.” Incomplete absolute identity. (7) “You are either a voter in this district or you are not a voter in this district.” Excluded middle. (8) “Some people do not know how to live.” Contradiction. (9) “All is well that ends well.” Incomplete absolute identity. (10) “Some men teach school.” Relative identity. (11) “None of the planets are as large as the sun.” Contradictory. (12) “All the trees in this grove are maple.” Relative identity. (1b) Indicate the law which conditions each of the following propositions: (1) “He who laughs last laughs best.” (2) “Perfect is perfect.” (3) “He is a wolf in sheep’s clothing.” (4) “Either your memory is poor or you are telling a deliberate falsehood.” (5) “Some of our greatest teachers thought they were failures.” (6) “No man of sense would ever try to get something for nothing.” (7) “Failure is not to try.” (8) “Success is the right man in the right place doing his best.” (9) “Every man is insane on some topic.” (10) “Some pupils are not industrious.” (11) “You are either a genius or a successful fakir.” (12) “Honesty is the best policy.” 10. REVIEW QUESTIONS.(1) How many kinds of judgments are there? Illustrate. (2) Name the fundamental laws of thought and explain how they are related to the kinds of judgments. (3) Show that it would be impossible to think at all were it not for the law of identity. (4) State the law of identity in three ways. (5) Explain the kinds of absolute identity. Illustrate by propositions and by circles. (6) Explain by word and by diagrammatical illustration relative identity. (7) Symbolize the three forms of identity. Fit words to these symbols. (8) State in three ways the law of contradiction. (9) Show by illustration that not bisects the world. (10) Explain the uses of not. (11) Prove that “John Doe is not-honest,” illustrates identity and not contradiction. (12) Symbolize in three ways contradiction. Fit words to these symbols. (13) Illustrate contradictory and opposite terms. (14) Show that words with negative prefixes are not necessarily the contradictory of the corresponding affirmative forms. (15) State and explain the law of excluded middle. (16) Symbolize the law of excluded middle. (17) State the law of sufficient reason. Illustrate. (18) Illustrate the unity of the three primary laws of thought. 11. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.(1) Prove that the judgment is the elemental form of evolved thought. (2) What is meant by evolved thought? (3) Show that “Whatever is, is” is a statement of complete absolute identity only. (4) State incomplete absolute identity. (5) By means of one proposition state relative identity. (6) Show that incomplete absolute identity is a term more or less illogical. (7) Show that these statements are exact expressions of relative identity: All men are some wise. Some men are some wise. (8) Why is the law of contradiction so named? (9) Show that space may be bisected by drawing a circle upon the black board. (10) Show that there is a difference in meaning between “You are not honest” and “You are not-honest.” (11) Is there any difference in meaning between disagreeable and not agreeable? (12) Which is the stronger term not-just or unjust? Why? (13) Give a list of words in which the contradictory forms are expressed by the ordinary prefixes. (14) Illustrate by circles the law of excluded middle. (15) Illustrate by a line-diagram the difference between contradictory and opposite terms. (16) Show that the province of the law of sufficient reason is physical science. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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