HYPOTHETICAL ARGUMENTS, AND DISJUNCTIVE ARGUMENTS
INCLUDING THE DILEMMA.
=1. THREE KINDS OF ARGUMENTS.=
The proposition, constituting the basic unit of the argument, would
of necessity be indicative of the nature of said argument; therefore
the three general kinds of propositions, categorical, hypothetical and
disjunctive, suggest the three kinds of arguments which are in turn
categorical, hypothetical and disjunctive. Categorical arguments are
those in which all of the propositions are categorical. Since this kind
has been treated, it remains for us to consider the other two.
=2. HYPOTHETICAL ARGUMENTS.=
We have observed that a hypothetical proposition is one in which the
assertion depends on a condition; for example, in the proposition, “If
it is pleasant, I will call on you to-morrow,” the _calling_ depends
on the state of the weather. “I will call on you to-morrow,” is the
_assertion_ which is limited by the _condition_, “If the weather is
pleasant.” Definition:
_The hypothetical argument or syllogism is one in which the major
premise is hypothetical and the minor premise categorical._
ILLUSTRATION:
If the people are right more than half of the time, the world will
progress;
And the people _are_ right more than half of the time,
Hence the world will progress.
In contradistinction to _disjunctives_, hypothetical propositions and
hypothetical syllogisms are frequently referred to as “_conjunctive_.”
=3. THE ANTECEDENT AND CONSEQUENT.=
Facility in detecting the antecedent and consequent of hypotheticals
is required in order to deal intelligently with the argument. The
hypothetical proposition has been defined as one in which the assertion
is limited by a condition. The _consequent_ is the assertion and
usually follows (though not always) the _antecedent_ which is the
limiting condition. _First the antecedent and then the consequent is
the logical order_ as the derivative meaning of the words antecedent
and consequent would indicate. The antecedent is introduced by such
words as “if,” “though,” “unless,” “suppose,” “granted that,” “when,”
etc.
ILLUSTRATIONS:
_Antecedent._ _Consequent._
1. If you study, you will pass.
2. If it rains, it is cloudy.
3. If two is added to three, the result is five.
4. If you are temperate, you will live to a ripe old age.
_Consequent._ _Antecedent._
5. I will go, unless you wire me to the
contrary.
6. I will pay you, when you present your bill.
7. I shall make the trip in granted that I have no accidents.
ten hours,
8. My overcoat would not have if the door had been locked.
been stolen,
=4. TWO KINDS OF HYPOTHETICAL ARGUMENTS.=
The two kinds of hypothetical syllogisms are the _constructive_ and
_destructive_.
_A constructive hypothetical syllogism is one in which the minor
premise affirms the antecedent._
_A destructive hypothetical syllogism is one in which the minor premise
denies the consequent._
The constructive hypothetical is sometimes referred to as the “_modus
ponens_”; whereas the destructive hypothetical is called the “_modus
tollens_.”
ILLUSTRATIONS:
_Constructive_ Hypothetical Syllogisms.
_Symbols._ _Words._
If A is B, C is D If you are diligent, you will succeed;
A is B And you _are_ diligent,
∴ C is D Therefore you will succeed.
_Destructive_ Hypothetical Syllogisms.
If A is B, C is D If you had been diligent, you would have
succeeded;
C is not D But you did not succeed,
∴ A is not B Therefore you were not diligent.
=5. THE RULE AND TWO FALLACIES OF THE HYPOTHETICAL ARGUMENT.=
From a given hypothetical proposition it is possible to construct
_four_ different hypothetical syllogisms, as the attending
illustrations make evident:
Consider the hypothetical proposition “If it has rained, the ground is
damp.”
(1) Minor premise affirms antecedent.
If it has rained, the ground is damp;
It has rained,
Therefore the ground is damp.
(2) Minor premise denies antecedent.
If it has rained, the ground is damp;
It has not rained,
Therefore the ground is not damp.
(3) Minor premise affirms consequent.
If it has rained, the ground is damp;
The ground is damp,
Therefore it has rained.
(4) Minor premise denies the consequent.
If it has rained, the ground is damp;
The ground is not damp,
Therefore it has not rained.
Without any knowledge of the rules of the hypothetical syllogism let
us strive to determine how many of the foregoing are valid. Relative to
the first, it would be impossible for any rain to fall without making
the ground somewhat damp; a few drops would be sufficient. In short,
if the antecedent happens, the consequent _must_ follow. It seems,
therefore, that the first argument is _valid_. Considering the second:
rain is not the only cause for the dampness of the ground, as it might
result from the falling of dew, or from a dense fog; _no rain_ does not
necessarily mean _no dampness_. It is clear that if the antecedent does
not happen, the consequent may or may not follow. Thus it appears that
the second argument is _invalid_. Attention to the third makes evident
a condition similar to the second: the ground may be made damp by
agencies other than rain, such as fog and dew. Thus the third argument
is likewise _invalid_. But in the fourth argument it is obvious that
if the ground is not damp, then there could have been neither rain, nor
fog, nor dew. No dampness shuts out _all_ of the conditions, including
the rain. Therefore the fourth argument is _valid_.
This investigation suggests a rule for hypothetical arguments. Since
only the first and fourth arguments are valid, this is the rule which
must obtain: _The minor premise should either affirm the antecedent or
deny the consequent._
Any violation of this rule would result in the fallacies of _denying
the antecedent_ or _affirming the consequent_.
There is one exception to this rule which must not be overlooked;
viz.: If the antecedent and consequent of the hypothetical proposition
are _co-extensive_ then both may be either affirmed or denied.
ILLUSTRATIONS:
(1) If the rectangle is equilateral, then it is a square;
The rectangle is equilateral,
∴ It is a square.
(2) If the rectangle is equilateral, then it is a square;
The rectangle is not equilateral,
∴ The rectangle is not a square.
(3) If the rectangle is equilateral, then it is a square;
It is a square,
∴ The rectangle is equilateral.
(4) If the rectangle is equilateral, then it is a square;
It is not a square,
∴ The rectangle is not equilateral.
=6. HYPOTHETICAL ARGUMENTS REDUCED TO THE CATEGORICAL FORM.=
The hypothetical syllogism so closely resembles the categorical that
it may be changed to it by a slight alteration in the wording. After
testing the hypothetical by its own rule, it may be expedient to reduce
the argument to the categorical form, and subject it to a second test
in which the categorical rules are applied. This reduction usually
necessitates two steps; first, _change the propositions which represent
the antecedent and consequent to a subject term and a predicate term
respectively and then unite them to form the major premise_; second,
_supply a new minor term, if necessary_.
Illustrations of Reduction; and Comparison of Hypothetical and
Categorical Fallacies:
_Hypothetical Form_:
(1) If it has rained, the ground is damp;
It has rained,
∴ The ground is damp.
_Categorical Form_:
M G
A The falling rain makes the ground damp,
―――――――――――――――― ―――――――――――
S M
A In this case rain has fallen,
―――――――――――――――――
S G
A ∴ In this case the ground is damp ground.
――――――――――――
It is seen that the argument in the hypothetical form is valid as the
minor premise affirms the antecedent. Reducing to the categorical gives
{ A
to the argument the mode { A in the first figure which we know to be
{ A
valid.
_Hypothetical_:
(2) If one were wise, he would study;
But you will not study,
∴ You are not wise.
_Categorical_:
G M
A A wise person would study,
―――――――――――
S M
E ∴ You will not study,
――― ―――――
S G
E ∴ You are not wise.
――― ――――
In the hypothetical form the argument is valid since the minor premise
{ A
denies the consequent. Reducing to the categorical gives mood { E in
{ E
the second figure. This is valid.
_Hypothetical_:
(3) If the wind blows from the south, it will rain;
But the wind is not blowing from the south,
Hence it is not going to rain.
_Categorical_:
M G
A South wind brings rain,
――――――――――
S M
E This wind is not a south wind,
――――――――― ――――――――――
S G
E ∴ This wind will not bring rain.
――――――――― ――――――――――
Hypothetically considered, the minor premise denies the antecedent and
consequently the argument is invalid. Reducing to the categorical form,
it is found that the major term is distributed in the conclusion, but
is not distributed in the major premise; hence the fallacy of _illicit
major_ is committed.
_Hypothetical_:
(4) If a man is just, he will obey the golden rule;
This judge has obeyed the golden rule,
Hence he is just.
_Categorical_:
G M
A A just man will obey the golden rule,
――――――――
S M
A This judge has obeyed the golden rule,
―――――
S G
A ∴ This judge is a just man.
―――――
Hypothetically considered, the minor premise affirms the consequent
and thus the argument is fallacious; when changed to the categorical
we find the fallacy of _undistributed middle_. If other examples were
taken, it could be proved that the hypothetical fallacy of _denying
the antecedent_ is usually equivalent to the categorical fallacy of
_illicit major_; whereas the hypothetical fallacy of _affirming the
consequent_ amounts to _undistributed middle_.
In reducing some hypotheticals it is necessary to make use of such
expressions as, “_the case of_” or “_the circumstances that_.” The
attending argument will illustrate this:
If Jefferson was right, man was created free and equal;
(but) Man was not created free and equal,
∴ Jefferson was not right.
_Reduced to the categorical_:
G
The case of Jefferson being right is the case of man being created
―――――――――――――――――――――――――――――
M
free and equal;
S M
Man was not created free and equal,
――― ――――――――――――――
S G
∴ Jefferson (this man) was not right.
――――――――― ―――――
The argument is valid in both cases.
=7. ILLUSTRATIVE EXERCISE TESTING HYPOTHETICAL ARGUMENTS OF ALL KINDS.=
The following brief outline may be followed in testing hypothetical
arguments:
1. Arrange logically.
2. Determine antecedent and consequent.
3. Apply the hypothetical rule; name fallacies giving reasons.
4. Reduce to categorical form.
5. Apply the categorical rules, giving fallacies with reasons.
(1) If a man is properly educated, he will not despise manual labor;
therefore I conclude that you have not been properly educated,
since you dislike to work with your hands.
_Arranged logically and antecedent and consequent indicated_:
If a man is properly educated (antecedent), he will not despise
manual labor (consequent);
You despise manual labor (dislike to work with your hands),
∴ You have not been properly educated.
The minor premise denies the consequent, hence the argument is valid
according to the rule, “The minor premise must affirm the antecedent
or deny the consequent.” The student should note that the consequent is
negative and therefore its denial must be an affirmative proposition.
_Reduced to the categorical_:
G M
E A properly educated man will not despise manual labor;
――――――――――――――――――――― ――――――――――――――――――――
S M
A You despise manual labor,
―――
S G
E ∴ You have not been properly educated.
――― ―――――――――――――――――
Regarded categorically this is valid. Why?
(2) “If one believes in the tenets of the democratic party, then he
should vote for its candidates; and since A does believe in them I have
asked him to vote for me.”
_Arranged, and antecedent and consequent indicated._
If one believes in the tenets of the democratic party (antecedent),
then he should vote for its candidates (consequent);
And A does believe in these tenets,
∴ He should vote for its candidates (I have asked him to vote for
me).
The minor premise affirms the antecedent and thus the argument is valid
according to rule.
_Reduced to the categorical_:
M
A One who believes in the tenets of the democratic party should
――――――――――――――――――――――――――――――――――――――――――――――――――――――
G
vote for its candidates,
S M
A A believes in these tenets,
―
S G
A ∴ A should vote for its candidates.
―
{ A
Reduced to the categorical gives mood { A in the first figure and this
{ A
we know to be valid.
(3) “If the weather had not been pleasant, I could not have come; but
as the weather is pleasant, here I am.”
_Arranged and antecedent and consequent indicated_:
If the weather had not been pleasant (antecedent), I could not have
come (consequent);
The weather is pleasant,
∴ I have come (here I am).
The minor premise _denies_ the antecedent and consequently the argument
is invalid according to the rule. (An affirmative minor premise denies
a negative antecedent.)
_Reduced to the categorical_:
E Unpleasant weather would not permit me to come,
E This weather is not unpleasant,
A ∴ This weather enabled me to come.
Fallacy of two negative premises.
(4) “If one pays his debts, he will not be ‘black-listed’; but since
you are ‘black-listed,’ I conclude that you have not paid your debts.”
_Arranged logically and antecedent and consequent indicated_:
If one pays his debts (antecedent), he will not be “black-listed”
(consequent);
You are “black-listed,”
∴ You have not paid your debts.
The minor premise denies the consequent hence the argument is valid.
_Reduced to categorical form_:
G M
E No one who pays his debts is black listed,
―――――――――――――――――――――― ――――――――――――
S M
A You are black listed,
―――
S G
E ∴ You have not paid your debts.
――― ―――――――――――――――
{ E
The mood { A in the second figure is valid.
{ E
(5) “Men would do right for the sake of themselves, if they appreciated
the law of retribution; but they never think of that.”
_Arranged, completed, and tested_:
If they appreciated the law of retribution (antecedent), men would
do right for the sake of themselves (consequent);
But they do not appreciate the law of retribution (never think of
that),
Hence they do not do right for the sake of themselves.
Fallacy of denying the antecedent.
_Reduced to the categorical_:
M
A The case of men appreciating the law of retribution, is the case
――――――――――――――――――――――――――――――――――――――――――
G
of men doing right for the sake of themselves;
S M
E But men do not appreciate the law of retribution,
――― ―――――――――――――――――――――――――――――――――
S G
E ∴ Men do not do right for the sake of themselves.
――― ――――――――――――――――――――――――――――――――
Fallacy of illicit major.
(6) “If an animal is a vertebrate, then it must have a backbone; but
the books say that this animal is not a vertebrate, hence it cannot
have a backbone.”
Since the minor premise denies the antecedent it would appear that the
argument is invalid; yet common knowledge and common sense dictate that
the conclusion is true. Surely no invertebrate can have a backbone. As
a matter of fact the antecedent and consequent are _co-extensive_ and
therefore the hypothetical rule is not applicable.
_Reduced to the categorical_:
M G
A Vertebrates must have a backbone (Co-extensive),
――――――――――― ――――――――――
S M
E This animal is not a vertebrate,
―――――― ――――――――――
E ∴ This animal cannot have a backbone.
―――――― ――――――――――
As co-extensive A’s distribute their predicates the possibility of
there being a fallacy of illicit major is forestalled.
Categorically considered the argument is likewise valid.
=8. DISJUNCTIVE ARGUMENTS.=
It has been observed that a disjunctive proposition is one which
expresses an alternative. _A disjunctive syllogism is one in which the
major premise is a disjunctive proposition._
ILLUSTRATION:
The boy is either honest or dishonest,
He is honest,
∴ He is not dishonest.
=9. THE TWO KINDS OF DISJUNCTIVE ARGUMENTS.=
The two forms of disjunctive arguments are _the one which by affirming
denies_ and _the one which by denying affirms_. The former is known by
the Latin words “_modus ponendo tollens_”; while the latter is termed
the “_modus tollendo ponens_.”
ILLUSTRATIONS:
(1) By affirming denies.
The defendant is either guilty or innocent,
He is guilty,
∴ He is not innocent.
or
The defendant is either guilty or innocent,
He is innocent,
∴ He is not guilty.
(2) By denying affirms.
The defendant is either guilty or innocent,
He is not guilty,
∴ He is innocent.
or
The defendant is either guilty or innocent,
He is not innocent,
∴ He is guilty.
=10. THE FIRST RULE OF DISJUNCTIVE ARGUMENTS.=
It may be said that disjunctive arguments depend on _two_ rules. This
is the first: _The major premise must assert a logical disjunction._
A logical disjunction involves two requisites; first, the alternatives
must be _mutually exclusive_; second, the _enumeration_ must be
_complete_.
_Illustrations of illogical major premise._
_Terms not mutually exclusive_:
This boy is either inattentive or indolent,
He is not inattentive,
∴ He is indolent.
It is obvious that the boy might be _both_ inattentive and indolent.
Experience teaches that the qualities are usually concurrent, and to
assume that the boy must be either one or the other is a clear case of
“begging the question.”
Some logicians maintain that “_either――or_” signify that both
alternatives _cannot be false_, but that both _may be true_. If this
viewpoint were adopted, the major premise of the illustration would
_not_ be a case of begging the question. It is unnecessary to argue the
point, if it is made perfectly clear which view is to obtain in this
discussion. Briefly stated the two points are these. First opinion:
“_Either――or_” when used logically, mean that if the first alternative
is false the second must be true, or if the first alternative is true
the second must be false. Second opinion: “_Either――or_” when used
logically mean that if the first alternative is false, the second must
be true; but if the first alternative is true, the other may or may
not be true. _This treatise adopts the first opinion._ With us all
alternative arguments to be logical must be mutually contradictory;
i. e., _when one is false, the other must be true and when one is true
the other must be false; both_ cannot be false, neither can _both_
be true. When it is intended that this implication should not obtain,
then the expressed alternative will take this form, “The boy is either
inattentive or indolent or _both_.”
Other examples where the terms of the disjunctive may not be mutually
exclusive:
(1) “Lord Bacon was either exceedingly studious or phenomenally
bright.” (Undoubtedly he was both.)
(2) “This teacher is a graduate either of Harvard or of Yale.”
(Perhaps both.)
(3) “The defendant is either a liar or a thief.” (The one often
leads to the other.)
(4) “To succeed one must either seize the opportunity as it passes
or make his own.” (The best success results from doing both.)
_Incomplete enumeration_:
The cause of the disease was either the water or the milk,
It was not the milk,
∴ It was the water.
When such an argument as this is advanced, it must be with the
knowledge that every other alternative has received satisfactory
investigation. Without this assurance one could justly claim that the
disease might have been caused by the _meat_ or _fish_ supply. Complete
enumeration means that the investigation has narrowed the facts to
the boundary of the field covered by the alternatives. The fallacy
of incomplete enumeration is also one of “begging the question.”
Other examples of a possible incomplete enumeration:
(1) “Jones lives either in Boston or New York.”
(2) “Mary is studying either algebra or geometry.”
(3) “He either committed suicide or was lynched.”
(4) “Either the Giants or the Boston Americans will win the pennant.”
=11. SECOND RULE OF DISJUNCTIVE ARGUMENTS.=
The second rule is made so self evident by the first that there is
little need of a detailed discussion concerning it. The rule is this:
_When the minor premise affirms or denies one of the alternatives of
a logical disjunction, the conclusion must, in order, deny or affirm
all of the others._ To put it differently: When the “minor” affirms,
the conclusion must deny every other alternative, and vice versa.
When there are but two alternatives reference to any of the foregoing
disjunctive arguments will make the rule clear. There may be, however,
_more_ than two alternatives. In such a case, if the first rule is
observed then the second becomes applicable.
ILLUSTRATIONS:
(1) John Doe lives either in Boston, Albany, or New York;
He lives in New York,
∴ He does not live in either Boston or Albany.
or
He does not live in New York,
∴ He lives in either Boston or Albany.
(2) The season must have been either summer, or autumn, or winter,
or spring;
It was neither autumn, nor winter, nor spring,
∴ It must have been summer.
or
It was either autumn, or winter, or spring,
∴ It could not have been summer.
=12. REDUCTION OF THE DISJUNCTIVE ARGUMENT TO THE HYPOTHETICAL AND
THEN TO THE CATEGORICAL.=
It would seem that the laws of the disjunctive contradict those of the
categorical syllogism; for we apparently derive from two affirmatives a
negative conclusion, and we also derive an affirmative conclusion when
one premise is negative. This objection is seen to be nugatory when the
disjunctive is reduced to the categorical form. The reduction involves
the two steps of first changing the disjunctive to the hypothetical
form and then to the categorical form. The following illustrations will
suffice to make the matter clear:
(1) _Disjunctive._
A is either B or C
A is B
∴ A is not C
_Hypothetical._
If A is B, then A is not C
A is B
∴ A is not C
_Categorical._
The case of A being B is the case of A not being C
In this case A is B
∴ A is not C
(2) _Disjunctive._
The defendant is either guilty or innocent;
He is not innocent,
∴ He is guilty.
_Hypothetical._
If the defendant is guilty, then he is not innocent;
But he is guilty,
∴ He is not innocent.
_Categorical._
The case of the defendant being guilty is the case of the
defendant not being innocent,
In this case the defendant is guilty,
∴ In this case the defendant is not innocent.
=13. THE DILEMMA.=
The majority of us are acquainted with the dilemma as related to the
activities of life. One is in a dilemma when there are two courses open
to him but neither is particularly enticing. One is placed in a dilemma
when he is forced to choose the lesser of two evils. For example, one
may, without the proper equipment, be overtaken by a heavy rain storm;
he seeks the shelter of a wayside shed; the rain continues so that
he is forced either to miss his train, or to endure the discomfort of
a drenching. Thus the logical dilemma limits one to a choice between
alternatives, either one of which might well be avoided.
_Definition._
_The dilemma is a syllogism in which the major premise consists of
two or more hypothetical propositions, while the minor premise is a
disjunctive proposition._
It being a combination of hypothetical and disjunctive propositions
the dilemma is sometimes appropriately referred to as the
“hypothetico-disjunctive” argument. The order of the premises is
indifferent, yet it seems to be more natural to use the hypothetical
first; thus the definition.
=14. FOUR FORMS.=
The four forms of the dilemma are the _simple constructive_, the
_simple destructive_, the _complex constructive_, and the _complex
destructive_. The following symbolizations illustrate these four kinds:
_Simple Constructive Dilemma._
If A is B, W is X; and if C is D, W is X,
But either A is B or C is D,
Hence W is X.
This is termed a simple dilemma because there is but _one_
consequent; namely, W is X. The conclusion being affirmative makes it
_constructive_.
_Simple Destructive Dilemma._
If A is B, W is X; and if A is B, Y is Z,
But either W is not X or Y is not Z,
Hence A is not B.
This is simple because there is but one antecedent, A is B, and
destructive because the conclusion is _negative_.
_Complex Constructive Dilemma._
If A is B, W is X; and if C is D, Y is Z,
But either A is B or C is D,
Hence either W is X or Y is Z.
This is complex because there are two antecedents and two consequents;
constructive, inasmuch as the conclusion is affirmative.
_Complex Destructive Dilemma._
If A is B, W is X; and if C is D, Y is Z,
But either W is not X or Y is not Z,
Hence either A is not B or C is not D.
This is complex because there are two antecedents as well as two
consequents, and destructive because the conclusion is negative.
Briefly: (1) A simple dilemma is one where either the antecedent or
consequent is repeated; whereas if neither is repeated the dilemma is
complex. (2) A constructive dilemma contains an affirmative conclusion;
while a destructive dilemma uses a negative conclusion. (3) A simple
dilemma has as its conclusion a categorical proposition; whereas the
conclusion of a complex dilemma is always disjunctive.
If the number of antecedents and consequents be increased, a trilemma,
tetralemma, etc., may result.
ILLUSTRATION――_Trilemma._
If A is B, W is X; and if C is D, Y is Z; and if E is F, U is V,
But either A is B, or C is D, or E is F,
Hence either W is X, or Y is Z, or U is V.
Some authorities define a dilemma as a syllogism in which the
“major-hypothetical” has _more than one antecedent_ while the “minor”
must be disjunctive. This viewpoint necessarily _excludes_ the second
form or the simple destructive dilemma. The weight of authority,
however, appears to favor the classification here recommended.
=15. THE ONE RULE INVOLVED IN DILEMMATIC ARGUMENTS.=
Since the major premise of the dilemma is hypothetical, the rule for
testing such would of necessity be the hypothetical rule; namely, “The
minor premise must either affirm the antecedent or deny the consequent.”
As this rule and the fallacies incident to it have been treated in
detail, further discussion is unnecessary.
=16. ILLUSTRATIVE EXERCISE TESTING DISJUNCTIVE AND DILEMMATIC
ARGUMENTS.=
(1) If the arithmetic contains useful facts, it will help to good
citizenship; and if it trains the powers of reason, it will
help to good citizenship,
But the arithmetic either contains useful facts or trains the
powers of reason,
Hence it will help to good citizenship.
This is a simple constructive dilemma in which the minor premise
affirms the antecedents. The argument is, therefore, valid since it
conforms to the rules of the hypothetical syllogism. The fact that the
minor premise may not be a perfect disjunctive does not invalidate the
conclusion, inasmuch as it is perfectly obvious that if the arithmetic
fulfilled both the requirements of the antecedents, the conclusion
would still obtain. It may, therefore, be inferred that if the dilemma
conforms to the rules of the hypothetical argument, it is valid, though
the disjunctive proposition which it contains may not be strictly
logical.
(2) A man is either temperate or intemperate; and, as I have seen you
drunk several times, I conclude that you are intemperate.
_Arranged logically._
A man is either temperate or intemperate,
You are not temperate,
∴ You are intemperate.
It would seem that the major premise is a logical disjunctive, since
temperate and intemperate indicate that the alternatives are _mutually
exclusive_ and the _enumeration complete_. And since the minor premise
denies one alternative while the conclusion affirms the other, we may
infer that the argument is valid.
(3) If a man is honest, he will either pay his debts or explain; but
this fellow paid no heed to the repeated notifications.
_Arranged logically._
If a man is honest, he will pay his debts; and if he is honest, he
will explain in case he cannot pay,
This man neither paid his debt, nor explained,
∴ This man is not honest.
This is a simple destructive dilemma, and since the minor premise
denies the consequents it is valid.
(4) A voter must either favor protection or free trade; and since you
do not favor protection, you must be a free trader. The disjunctive is
not logical as one might believe in universal reciprocity. The argument
is, therefore, invalid. _Why?_
(5) If a man were loyal, he would not be unduly critical; and if he
were wise, he would not be too loquacious; but I find this clerk has
been both unduly critical and too loquacious; hence I consider that he
has been not only unwise but strikingly disloyal.
This complex dilemma is valid since the minor premise denies the two
consequents.
=17. ORDINARY EXPERIENCES RELATED TO THE DISJUNCTIVE PROPOSITION AND
HYPOTHETICAL ARGUMENT.=
(1) One desires to take a certain trip which involves various routes;
information from time tables reveals the fact that there are three
routes A, B, and C. Concerning the conditions of the journey the most
important factor is the _matter of comfort_. Further investigation
makes evident that route B will be the most comfortable one, and
consequently is the route selected. Putting this ordinary experience
in argumentative form gives the following:
The route is to be either A, or B, or C;
I will take route A; if it is the most comfortable; (co-extensive)
A is not the most comfortable route,
Hence I will not take route A.
If B is the most comfortable route, I will take it;
B is the most comfortable route,
Hence I will take route B.
(2) The symptoms suggest either malarial or typhoid fever; the
physician is undecided till a blood test makes evident that it is not
typhoid.
_Considered argumentatively._
This disease is either malarial or typhoid fever;
If it is typhoid, the blood will reveal certain evidences;
But the blood does not reveal these evidences,
Hence the disease is not typhoid.
(3) The natural bent of the youth suggests the profession of either the
ministry or teaching. He finally decides to follow the one in which he
can best serve his fellows. This, after mature deliberation, appears to
him to be the work of the teacher. Thrown into the form of an argument
the following results:
I am best fitted for either the pulpit or the schoolroom;
If the schoolroom furnishes the richest field for helping my fellows,
I will choose that work;
The schoolroom _does_ appear to furnish such a field,
Hence I will choose the work of the teacher.
It would appear from these ordinary experiences that frequently we
are brought face to face with a choice of alternatives which are not
unattractive, as in the case of the dilemma. Moreover, some condition
suggests itself which, if proved or disproved, will lead to a choice
of _one_ of these alternatives. Such circumstances when thrown into
the form of an argument present a _disjunctive proposition_ followed
by a _hypothetical argument_. To put it differently: Often in our daily
affairs a most prominent limiting condition induces us to select one
out of several alternatives. These alternatives are _not_ dilemmatic
in nature.
=18. OUTLINE.=
HYPOTHETICAL ARGUMENTS, AND DISJUNCTIVE ARGUMENTS INCLUDING THE
DILEMMA.
(1) Three kinds of arguments
Categorical, hypothetical, disjunctive.
(2) Hypothetical arguments
Defined, illustrated.
(3) Antecedent and consequent.
How determined, illustrations.
(4) Two kinds of hypothetical arguments
Constructive, destructive, illustrations.
(5) Rule and two fallacies of the hypothetical argument.
Illustrations and application of rules.
Fallacy of denying antecedent.
Fallacy of affirming consequent.
Co-extensive hypotheticals.
(6) Hypothetical arguments reduced to the categorical form.
Rule, illustrations.
Hypothetical and categorical arguments compared.
(7) Illustrative exercises testing hypothetical arguments of all
kinds.
(8) Disjunctive arguments.
Defined, illustrated.
(9) Two kinds of disjunctive arguments.
By “affirming denies,” by “denying affirms.” Illustration.
(10) First rule.
Stated, illustrated.
(11) Second rule
Stated, illustrated.
(12) Reduction of disjunctive argument
Two steps.
(13) The dilemma
Definition.
(14) Four forms of dilemmatic arguments
Simple constructive, simple destructive,
Complex constructive, complex destructive.
Illustrations.
(15) The rule.
(16) Illustrative exercises testing disjunctive and dilemmatic
arguments.
(17) Ordinary experiences related to the disjunctive proposition and
hypothetical argument.
=19. SUMMARY.=
(1) Just as there are three kinds of propositions so there are three
kinds of arguments; namely, categorical, hypothetical, disjunctive.
(2) Categorical syllogistic arguments are those in which all of the
propositions are categorical.
Hypothetical syllogistic arguments are those in which the major premise
is hypothetical.
In contradistinction to disjunctives, hypothetical arguments may be
referred to as “_conjunctive_”.
(3) The hypothetical proposition is composed of antecedent and
consequent; the former being the limiting condition; while the latter
is the direct assertion. As the words indicate the antecedent usually
precedes the consequent. The signs of the antecedent are “if,” “though,”
“unless,” “suppose,” “granted that,” “when,” etc.
(4) The two kinds of hypothetical syllogisms are the constructive and
destructive; the former is involved when the minor premise affirms the
antecedent; the latter when the minor premise denies the consequent.
These two kinds are sometimes referred to as “_modus ponens_” and
“_modus tollens_” respectively.
(5) Out of the four possible hypothetical syllogisms only _two_ are
valid as investigation proves this rule: _The minor premise must affirm
the antecedent or deny the consequent._ In the case of the hypothetical
proposition being _co-extensive_, the rule does not apply.
(6) Hypothetical arguments may be reduced to the categorical by
contracting the antecedent of the hypothetical proposition to form
the subject-term, and by contracting the consequent of the hypothetical
proposition to form the predicate-term of the major premise of the
categorical syllogism. If it is necessary, supply a new minor term.
Denying the antecedent is a matter of illicit major; whereas affirming
the consequent is equivalent to undistributed middle.
(7) Hypothetical arguments may be tested by following this outline:
(1) Arrange logically.
(2) Determine antecedent and consequent.
(3) Apply hypothetical rule.
(4) Reduce to categorical form.
(5) Apply categorical rules.
(8) A disjunctive syllogism is one in which the major premise is a
disjunctive proposition.
(9) The two kinds of disjunctives are those which “_by affirming deny_”
and those which “_by denying affirm_.”
(10) In testing disjunctive arguments there are _two_ rules involved:
_First_, “The major premise must assert a _logical disjunction_.” This
necessitates the two requisites “_the alternatives must be mutually
exclusive_” and the “_enumeration must be complete_.” The two opinions
relative to the nature of an alternative assertion are, first, if one
is false, the other must be true and vice versa; and second, if one
is false, the other must be true, but _both_ may be true. The first is
adopted in this discussion.
_Second._ The second rule involved is “When the minor premise affirms
or denies _one_ of the alternatives of a logical disjunctive the
conclusion must deny or affirm all of the others.”
(11) Subjecting the disjunctive arguments to the categorical test
gives evidence to the close relation existing between the two forms.
A logical disjunctive proves to be logical when reduced to the
categorical. The reduction entails the two steps, first, reduce to
the hypothetical; second, reduce to the categorical.
(12) The logical meaning of the dilemma is suggested by the popular
conception. One is said to be in a dilemma when two courses are open
to him, neither of which is specially attractive.
A logical dilemma presents two alternatives either one of which might
well be avoided.
The major premise of the dilemma is hypothetical; while the minor is
disjunctive.
(13) The four forms of the dilemma are the simple constructive,
the simple destructive, the complex constructive and the complex
destructive.
(14) The dilemma is subject to the hypothetical rule which is, “The
minor premise must either affirm the antecedent or deny the consequent.”
(15) The minor premise need not be a logical disjunctive provided the
major conforms to the hypothetical rule.
(16) Frequently when ordinary experiences are reduced to augmentative
form they present a disjunctive proposition followed by a hypothetical
argument.
=20. REVIEW QUESTIONS.=
(1) Relate the three kinds of arguments to the three general kinds
of propositions.
(2) Define and illustrate the hypothetical argument.
(3) Explain the term conjunctive with reference to hypothetical
arguments.
(4) Explain and illustrate antecedent and consequent in hypothetical
arguments.
(5) Select from the following the antecedent and consequent:
(1) “I usually succeed when I try.”
(2) “I will not undertake it unless you guarantee half of the
sum needed.”
(3) “Though I speak with the tongues of men and of angels,
and have not charity, I am become as sounding brass or a
tinkling cymbal.”
(6) Illustrate the two kinds of hypothetical syllogisms which are
valid.
(7) State and explain the rule to which hypothetical arguments must
conform.
(8) State and exemplify the one exception to the hypothetical rule.
(9) Explain how hypothetical arguments may be reduced to the
categorical form. Illustrate.
(10) Show by illustration that denying the antecedent is equivalent
to _illicit major_, while affirming the consequent is equivalent
to _undistributed middle_.
(11) Reduce to the categorical form and test:
“If Napoleon had possessed more of the spirit of Washington, he
would have been less famous but a better man than he was; but
he did not possess the spirit of the ‘Father of His Country.’”
(12) Test according to outline the following hypothetical arguments:
(1) “If it be a good thing to have faith, then certainly he who
believes in the bible of a pagan has faith and must have a
good thing.”
(2) “If a 10-inch charge burst inside of a tank, there would
be nothing left of the tank. It would be blown into small
pieces.”
(3) “If the plate found had been originally on the outside of
the ship, I should have judged that there must be green
paint on it, but I could not find green paint on that part
of the ship.”
(4) “If I mistake not, you are the man who did not pay me for
that pair of shoes. I am sure that you are the man as I
never forget a face.”
(5) “If the maxim ‘Early to bed and early to rise makes one
healthy, wealthy and wise’ were true, I would have been a
millionaire long ago.”
(13) Define and illustrate a disjunctive argument.
(14) Exemplify the two kinds of disjunctive arguments.
(15) What is meant by a logical disjunction?
(16) “The alternatives must be mutually exclusive.” Explain this,
illustrating fully.
(17) Cite cases where the enumeration is not complete.
(18) State in complete form both of the rules to which all disjunctive
arguments must conform.
(19) Show by illustration how the disjunctive syllogism may be reduced
to the categorical.
(20) Define and illustrate the dilemma.
(21) Give examples, using symbols, of the four dilemmatic forms.
Explain why these forms are so named.
(22) Why does the hypothetical rule apply to the dilemmatic syllogism?
(23) Test the validity of the following: Give reasons.
(1) “If a substance is solid it possesses elasticity and
so also it does if it be a liquid or gaseous; but all
substances are either solid, liquid or gaseous; therefore,
all substances possess elasticity.”
(2) “If men were prudent, they would act morally for their own
good; if benevolent, for the good of others. But many men
will not act morally, either for their own good or that of
others; such men, therefore, are not prudent or benevolent.”
(3) “If the majority of those who use public houses are
prepared to close them, legislation is unnecessary; but if
they are not prepared for such a measure, then to force it
upon them by outside pressure is both dangerous and unjust.”
(4) “The man is either a liar or a fool and in either case he
is beneath my attention.”
(5) “Either he is sincere or else he is the most astute
impostor the world has ever produced; for me I prefer to
think him sincere.”
(24) Explain the relation that many experiences appear to bear toward
an argument introduced by a disjunctive proposition and followed
by a hypothetical syllogism. Illustrate.
=21. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=
(1) May both premises of a hypothetical argument be hypothetical
propositions? Explain. See Fowler p. 115.
(2) Which of the two is valid? Explain.
(1) If A is B, C is D
If A is B, E is F
∴ If C is D, E is F
(2) If A is B, C is D
If C is D, E is F
∴ If A is B, E is F
(3) Show by circles that two of the possible four hypothetical
arguments are invalid.
(4) What categorical rules does the hypothetical argument seem to
violate? Explain.
(5) Originate a hypothetical syllogism whose antecedent and
consequent are both negative. Test its validity.
(6) Originate a co-extensive hypothetical argument and show that four
valid syllogisms may be derived from it.
(7) Explain by word and illustration the two meanings which may be
attached to “either-or.”
(8) If we accepted the opinion that both alternates of a disjunctive
may be true, which kind of disjunctive argument would it
invalidate?
(9) In a logical disjunction what law of thought is involved?
Explain.
(10) Why do the laws of the disjunctive seem to contradict the
categorical rules? Explain fully.
(11) Show by drawing on common experience that a logical dilemma is
closely related to the popular conception of dilemma.
(12) Illustrate by symbols and then place in good English a pentalemma.
(13) State a definition of a dilemma which excludes the simple
destructive form.
(14) Give a common experience which, when thrown into argumentative
form, results in a disjunctive proposition followed by a
hypothetical syllogism. Coin a name for such a combination.