THE PRIMARY LAWS OF THOUGHT.
=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
permanently identical with itself, it would be impossible to think at
all. For example: Take away the notion of permanency from the door and
thought becomes at once ridiculous. Suppose that while we are asserting
that the object is a door, it changes to a tree, and while we insist
that the object is now a tree, it changes to a cow, etc. We can readily
see that it would hardly be worth while to think at all.
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, “A man 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 the other, and if we were to draw two circles
representing them, they would be of the same size. In form, in mode
of expression, however, the notions differ and the circles, though
coinciding, would need to differ in form, the boundary of one might be
a solid line, the other a dotted. This we may call incomplete absolute
identity. All logical definitions illustrate identities of this kind.
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.
Illustration: 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.
Illustration: 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 is impossible for the same thing to be itself and
its contradictory at the same time_. Bringing out a further aspect, no
thing can have and not have the same attributes at the same time.
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 I cannot 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 the proposition “Some men
are not wise” illustrates the law of contradiction, since the _some
men_ referred to are contradicted of all which is wise. Whereas the
proposition “Some men are not-wise” illustrates relative identity,
since the subject “some men” is affirmed of a part of the predicate
“not-wise.” The student may be led to see these relations by drawing
circles, the one to represent the subject, the other the predicate.
(See page 141.)
FURTHER ILLUSTRATIONS:
Some teachers are wise }
Some teachers are not-wise } Illustrate the law of identity.
Some teachers are unwise }
Some teachers are not wise }
Some teachers are not not-wise } Illustrate the law of contradiction.
Some teachers are not unwise }
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:
A, B and C are wise. } These are mutually
A, B and C are not-wise. } destructive.
A, B and C are wise. } These are not mutually destructive,
A, B and C are not not-wise. } but virtually mean the same thing.
SYMBOLIZATION OF THE LAW OF CONTRADICTION.
A is not not-A. A is not B.
(As A is always A it would or or
be absurd to say that A is A is not not-B.
not A.)
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.
_Opposite._ _Contradictory._
──────────────── ───────────────────
bad good bad not-bad
soft hard soft not-soft
cold hot cold not-cold
rough smooth rough not-rough
good evil good not-good
warm cool warm not-warm
weak strong weak not-weak
=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
or
A is either B or not-B.
=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.=
(1) Absolute Symbols Relative Symbols.
Excluded middle.
A is either A or not-A. A is either B or not-B.
Contradiction.
A is not not-A. A is not B or A is not not-B.
Identity.
A is A. A is not-B or A is B.
(2) Propositions made to fit symbols.
Excluded middle.
A man is either a man or A man is either honest or
a not-man. not-honest.
Contradiction.
A man is not a not-man. A man is not honest, or a man
is not not-honest.
Identity.
A man is a man. A man is not-honest, or a man
is honest.
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 _con_structive while _contradiction_
is _de_structive 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: “A thing 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.
┌───────────┬───────────────────┬────────────────┬────────────────────┐
│ Name │ Stated │ Symbolized │ Illustrated │
├───────────┼───────────────────┼────────────────┼────────────────────┤
│ Absolute │ Whatever is, is │ A is A │ Work is work │
│ identity │ │ │ │
├───────────┼───────────────────┼────────────────┼────────────────────┤
│ Relative │ The whole is │ All A is B │ Work is a blessing │
│ identity │ identical with │ Some A is B │ Some play is a │
│ │ a part or a part │ │ blessing │
│ │ is identical │ │ │
│ │ with a part │ │ │
├───────────┼───────────────────┼────────────────┼────────────────────┤
│ Contra- │ Nothing can both │ A is not not-A │ Work is not │
│ diction │ be and not be at │ or │ not-work │
│ │ the same time │ A is not B │ John is not honest │
│ │ │ or │ Albert is not │
│ │ │ A is not not-B │ not-honest │
├───────────┼───────────────────┼────────────────┼────────────────────┤
│ Excluded │ Everything must │ A is either A │ Fair play is │
│ middle │ either be or not │ or not-A │ either fair play │
│ │ be │ or │ or not-fair play │
│ │ │ A is either B │ This man is either │
│ │ │ or not-B │ educated or │
│ │ │ │ not-educated │
└───────────┴───────────────────┴────────────────┴────────────────────┘
=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 I summarize 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.