THE LOGICAL FALLACIES OF DEDUCTIVE REASONING.
=1. A NEGATIVE ASPECT.=
It has been remarked that “Logic as a science makes known the laws
and forms of thought and as an art suggests conditions which must
be fulfilled to think rightly.” In recent chapters we have discussed
the second aspect of the definition; in these we have attempted to
answer the question, “What _rules_ must be followed in order to reason
correctly?” We are now ready to treat the same aspect from a negative
point of view namely, what _errors_ must be avoided in order to reason
correctly? What are the fallacies which we must strive to avoid in our
_own_ thinking, and attempt to correct in the thinking of _others_?
=2. PARALOGISM AND SOPHISM.=
“Fallacy” comes from the Latin _fallacia_, meaning deceptive or
erroneous, and therefore _a fallacy in logic is any error in reasoning
which has an appearance of correctness_. If the writer or speaker is
_himself_ deceived by the fallacy, then such is called a _Paralogism_;
but if the fallacy is committed by him for the expressed purpose of
deceiving others, then such becomes a _Sophism_. During the time of the
Schoolmen the Sophism was in such high repute that it required even a
Socrates to puncture this ignominious bubble of vain trickery. In fact,
Socrates, the greatest of all pagan educators, _led_ the crusade which
has relegated to the “logical dust bin” the notion that _skill in the
art of framing sophisms is a scholarly accomplishment_. Many believe
modern sophistry to be the chief social and commercial evil of the
day, and to Socrates must be given the credit for teaching us to look
upon those who would practice sophism with righteous indignation and
pronounced disgust. However, paralogism and not sophism is the more
legitimate field for the student of logic; his problem being, “What
are the common errors which I, as a writer and speaker, must strive to
avoid?”
=3. A DIVISION OF THE DEDUCTIVE FALLACIES.=
The mistakes of induction will occupy our attention in a later
chapter. We are now concerned with the fallacies of deduction. Any
classification or division of the deductive fallacies must of necessity
be faulty. Even the labors of Aristotle in this regard are now
pronounced crude and unsatisfactory. This is due to the divergence of
opinion as to the signification of some of the fallacies, as well as
to the fact that no division is free from the fault of an _overlapping_
of the species. As a result of this lack of unanimity in definition and
lack of ability in making the species mutually exclusive, any division
of the deductive fallacies must be more or less illogical.
Aristotle divides the fallacies of deduction into two groups:
(1) Fallacies _in dictione_, or formal fallacies. (2) Fallacies _extra
dictionem_, or material fallacies. This division has received universal
approval and though many distinctions made by him have been abandoned,
yet most logicians retain his phraseology. Since many of the technical
terms which Aristotle used have lived through the generations under
the conventional meaning which he assigned to them, it becomes less
confusing to adhere as closely as possible to these terms. Therefore,
in the attending division only those changes have been made which
progress and experience have forced upon us. What remains of this
chapter will be devoted to explaining these fallacies as they appear
in this division. For the sake of clearness and definiteness it is
strongly recommended that the student study the outline extensively
enough to be able to reproduce it.
_Fallacies._
_Formal_ (_In dictione_)
{ 1. Opposition
1. Immediate { 2. Obversion
inference { 3. Conversion
{ 4. Contraversion
{ 5. Four terms
{ 6. Undistributed middle
2. Categorical { 7. Illicit major
arguments { 8. Illicit minor
{ 9. Negative premises
{ 10. Particular premises
3. Hypothetical { 11. Denying the antecedent
arguments { 12. Affirming the consequent
4. Disjunctive { 13. Illogical disjunction
arguments {
_Material_ (_In dictionem_)
{ 1. Ambiguous middle
{ 2. Amphibology
1. In Language { 3. Accent
Equivocation { 4. Composition
{ 5. Division
{ 6. Figure of speech
{ 1. Accident
{ 2. Converse accident
2. In Thought { 3. Irrelevant conclusion
Assumption { 4. Non sequitur
{ 5. False cause
{ 6. Complex question
{ 7. Begging the question
=4. GENERAL DIVISIONS EXPLAINED.=
The _formal fallacies_ are those which concern the _form_ of the
argument rather than the meaning. These fallacies arise from an
improper use of words as arbitrary signs of thought, not from any
inconsistency in the thought itself. To commit a formal fallacy we
must violate one of the specific rules of logic. For this reason the
formal fallacies are easier of comprehension. Moreover, because of this
definiteness logicians are better able to come to some agreement as to
their content and import. Classing the fallacies of immediate inference
as formal is somewhat of an innovation; but since they occur because of
the breaking of certain definite rules, and since immediate inference
is a matter of changing the form without altering the meaning, we
believe there is some justification for this position. Some would class
“immediate inference” fallacies with the material fallacies of language.
The _material fallacies_ are fallacies of meaning and not of form. They
are those arising from inconsistency in thought, and from imperfect
ways of interpreting this thought as it appears in language. No very
specific rules of logic are violated by them and for this reason there
are those who would entirely eliminate the material fallacies from the
field of logic. But since _thought_ is even more subtle than _form_ in
its deceitful machinations, we believe that the material fallacy calls
for special attention on the part of the logician.
Material fallacies are divided into two kinds. First, those which have
reference to wrong thinking, or fallacies _in thought_; and, second,
those which are due mainly to an incorrect interpretation of words,
or fallacies _in language_. The former result from inconsistency and
unreasonableness in thought, whereas the latter come from lack of
precision in expression.
=5. FALLACIES OF IMMEDIATE INFERENCE.=
Fallacies of immediate inference arise from some violation of the rules
which this topic enunciates.
(1) _Opposition._
Among other statements opposition posits these two: (1) When the
particular is true its opposing universal is indeterminate; (2) A
universal negative does not necessarily contradict a universal
affirmative.
These signify that neither an A nor an E must be assumed to be true
when the corresponding I or O is true, and that E may not always
contradict A, nor O contradict I.
ILLUSTRATIONS OF FALLACIES OF OPPOSITION.
(1) Since some men are wise, then I may conclude that all men are wise.
(2) I have contradicted his statement “all men are honest” by proving
that _no men are honest_.
There is little difference between fallacies like (1) and fallacies of
converse accident. Concerning illustration (2), _both_ statements are
false; but to contradict we know that if one is false, the other must
be true.
(2) _Obversion._
“Two negatives are equivalent to one affirmative,” is the principle
underlying obversion. The most common fallacy in obversion springs from
using one negative instead of two.
ILLUSTRATIONS OF FALLACIOUS OBVERSION.
(a) Original: Some men are not wise. Obverse: (incorrect) Some men are
wise.
(b) Original: All true teachers are just. Obverse: (incorrect) All true
teachers are not just.
(3) _Conversion._
Conversion involves the interchanging of the subject and predicate
of a proposition without affecting the distribution; in consequence
the usual fallacy incident to this interchange is _distributing_ an
undistributed term.
ILLUSTRATIONS OF FALLACY OF CONVERSION.
(a) Original: All fixed stars are heavenly bodies. Converted:
(incorrectly) All heavenly bodies are fixed stars.
(b) Original: Some men are not wise. Converted: (incorrectly) Some wise
beings are not men.
(4) _Contraversion._
As this process involves the two steps of obversion and conversion,
fallacies appertaining to contraversion would relate to these two steps.
ILLUSTRATIONS OF FALLACIES OF CONTRAVERSION.
(a) Original: No honest man fails to pay his debts. Contraverted:
(incorrectly) Some who do not pay their debts are honest men.
(b) Original: Some animals are quadrupeds. Contraverted: (incorrectly)
Some not-quadrupeds are not animals.
The formal fallacies of categorical, hypothetical, and disjunctive
arguments have received detailed treatment in chapters 11, 14 and 15;
we may, therefore, devote our attention to the material fallacies
without further delay.
=6. FALLACIES OF LANGUAGE. (Equivocation.)=
These are the fallacies of _double meaning_. It is known that an
equivocal term is one which permits two or more interpretations;
similarly a _proposition_ which admits of two or more interpretations
may be denominated equivocal. Thus the term equivocation has come to
stand for all errors in language resulting from a possibility of more
than one interpretation. This justifies the position of referring to
all of the six fallacies in language as fallacies also of equivocation.
(1) _Ambiguous middle._
Ambiguous middle explains itself. _It is the fallacy of giving to the
middle term a double meaning._ In form the argument may contain but
three terms, yet in meaning there are in reality four terms. For this
reason ambiguous middle and the fallacy of four terms appear to be
about one and the same thing; but in this treatment we shall regard
them as mutually exclusive, and this is the distinction:
Invalid arguments of “ambiguous middle” have only _three_ terms in form
but _four_ terms in meaning. This signifies that the middle term though
identical in _form_ is given a _double meaning_.
Invalid arguments of “four terms” always have four terms in both _form_
and _meaning_; they are “logical quadrupeds” in every sense of the word.
ILLUSTRATIONS.
_Ambiguous middle._
(a) “_Necessity_ is the mother of invention,”
Bread is a _necessity_,
∴ Bread is the mother of invention.
(b) “_Nothing is_ better than wisdom,”
Dry bread is better than _nothing_,
∴ Dry bread is better than wisdom.
(c) A _church_ is a force for good in any community,
A slate roof is good for a _church_,
∴ A slate roof is a force for good in any community.
_Fallacies of four terms._
(a) All _true teachers_ are just,
John Doe is an _educator_,
∴ John Doe is just.
(b) _Milk_ is nourishing,
This substance is a _white fluid_,
∴ This substance is nourishing.
(c) _Thieves_ should be imprisoned,
This man _has taken what does not belong to him_,
∴ This man should be imprisoned.
In the “four-term” fallacies, observe that the four terms occur in
the _premises_. When a fourth term is introduced in the conclusion,
the material fallacy of _non sequitur_ has been committed.
(2) _Amphibology_ (_or amphiboly_).
Amphibology is a fallacy resulting from an ambiguous proposition
rather than from the ambiguity of any particular term. _The fallacy of
amphibology is committed when the spoken or written proposition conveys
more than one meaning._ The ancient oracles indulged in this sort of
fallacy, the reason for such indulgence being obvious; the oracles
were not too positive as to the outcome of their prognostications, and
therefore were especially careful to cover _every emergency_.
A careless use of relative clauses and prepositional phrases often
results in the fallacy of amphibology.
ILLUSTRATIONS OF THE FALLACY OF AMPHIBOLOGY.
(a) “You the enemy will slay.”
(b) “The Duke yet lives that Henry shall depose.”
(c) “Wanted a piano by a young lady made of mahogany.”
(d) “You your father will punish.”
(3) _Accent._
_This fallacy springs from placing undue emphasis on some word or group
of words._ Naturally such accentuation may convey a meaning entirely
foreign to the author’s intent. Newspapers are guilty of this fallacy
when they select a few words from a speech and use them as headlines
without further explanation. A politician may quote a sentence uttered
by an opponent and fail to relate it to what preceded or followed.
A cartoonist may arouse the prejudice of public opinion by giving
ridiculous emphasis to some idiosyncracy possessed by the subject of
his attack.
ILLUSTRATIONS OF FALLACIES OF ACCENT.
(a) “Thou shalt not bear false witness against thy _neighbor_.”
By giving undue emphasis to _neighbor_, the notion is clearly
conveyed that one may bear false witness against all who are
_not_ neighbors.
(b) “You must not crib when taking _my_ examinations.”
(c) _What the “Spellbinder” said._
“I may say, as a side remark, that the labor unions are guilty of
developing a nation of shirks, when they prohibit a phenomenally
efficient workman from doing his best.” “I do not wish to be
misunderstood in this.” “I believe in labor unions but in this
particular they are dead wrong.”
_What the newspaper reported._
(Headline) “The Labor Union Scored as a Training School for
Shirks.” “―――― said in his speech in ―――― Hall that the Union was
responsible for the development of a nation of shirks.” “A good
man,” said he, “is not permitted to do his best work.”
(4) _Composition._
_The fallacy of composition is committed when it is assumed that what
is true distributively is likewise true collectively._ A term is used
in a distributive sense when it is applied to _each individual_ of
the class; whereas a term is used in a collective sense when it is
applied to the class considered as _one whole_. “All” meaning _each
one considered separately_ and “all” meaning _the whole_ furnishes a
frequent pitfall for this fallacy.
ILLUSTRATIONS OF THE FALLACY OF COMPOSITION.
(a) “Every member of the team is a star player; hence I expect that
the entire aggregation will be a winner.”
(b) “All the men of the jury are fair minded; therefore we have good
reason for supposing that the jury’s verdict will be in accord
with the rules of justice.”
(c) “Thirteen and twenty-three are odd numbers; thirty-six is equal
to thirteen and twenty-three; hence thirty-six is an odd number.”
(d) “All the angles of a triangle are less than two right angles;
hence the angles X, Y and Z are less than two right angles.”
(e) In governmental affairs the assumption, that a law which benefits
one section will benefit all, is a fallacy of composition.
(5) _Division._
_The fallacy of division is committed when it is assumed that what is
true collectively is true distributively._ Division is the converse of
composition. Composition is a fallacious procedure from a distributive
to a collective use; while division is a fallacious procedure from
a collective to a distributive use. The fallacy of division may
be illustrated by giving the converse of the illustrations under
composition:
(a) “The team is a star playing team; and since Smith is the ‘first
baseman’ of the team, he must be a star player.”
(b) “The jury rendered a just decision; hence the foreman is a fair
minded man.”
(c) Thirty-seven is an odd number,
Nine and twenty-eight are thirty-seven,
∴ Nine and twenty-eight are odd numbers.
(d) All the angles of a triangle are equal to two right angles,
A is an angle of a triangle,
∴ A is equal to two right angles.
(6) _Figure of Speech._
_This fallacy results from assuming that words of the same root have
the same meaning._ Since the same root-word may be used as a noun,
verb, adjective, etc., it does not follow that in these various forms
it retains a common meaning. “Address” as a noun and “address” as a
verb convey two distinct meanings.
The following are examples of this fallacy:
(a) No _designing_ person should be trusted,
This architect is a _designer_,
∴ This architect should not be trusted.
(b) Justifiable _investigation_ is wise,
This man is a just _investigator_,
∴ This man is wise.
These fallacies are not classed as those of “four terms” because two
terms so _closely resemble_ each other in _form_, and yet they are
not fallacies of ambiguous middle; since the middle terms are _not
identical_ in form.
=7. FALLACIES IN THOUGHT.=
The fallacies in thought arise through a tendency to assume as true
that which demands further proof. Any one who is more anxious to
be _right_ than to _win_ will make sure that nothing has been taken
for granted which should receive further investigation, or that no
truth has been given a presumptuous twist in order to make it fit the
particular case under discussion. Because these errors in thought may
be attributed chiefly to undue assumptions, we may denominate them as
the fallacies of assumption.
(1) _Accident._
_The fallacy of accident occurs when one reasons from a general truth
to an accidental case._ Doctrinaires and theoretic enthusiasts are
partial to this fallacy. It is so easy to lay down a general formula or
remedy and then attempt to apply it to every accidental circumstance.
Grandmother with her catnip tea and mustard plaster, however we may
cherish the memory of the dear old soul, was nevertheless guilty of
the fallacy of accident. Applying maxims and proverbs to particular
instances is still another way of committing the fallacy.
EXAMPLES OF FALLACIES OF ACCIDENT.
(a) “Honesty is the best policy,” thinks the physician as he reveals
the cold, hard truth to his patient and thus shortens the
patient’s life.
(b) Spirituous liquor in excess acts as a poison, and therefore
should not be used to resuscitate an extreme case.
(c) “What is bought in the market is eaten; raw meat is bought in the
market; therefore it is eaten.”
(d) “Early to bed and early to rise makes one healthy, wealthy and
wise.” I shall practice this for ten years and by that time hope
to be healthy, wealthy and wise.
(e) John has earned the enviable (?) reputation of being the “worst
boy in school,” hence he is going to be the worst boy in “my
grade.”
(f) Mary is an inveterate whisperer; and since I know that some one
is whispering, I am sure that that some one is Mary.
(g) Being a convict, he is not to be trusted.
(2) _Converse Accident._
_As the title implies this is the fallacy of reasoning from an
accidental case to a general truth._ Illustrations:
(a) “John has been a bad boy to-day; and hence he is going to make
trouble during the entire term.”
(b) “This food is good for hens; and hence it is good for all
domestic fowls.”
(c) “I know of several men who have been phenomenally serviceable
to mankind, and none of these men were college trained; hence
I conclude that college education is not essential to the
attainment of the highest state of efficiency.”
Relative to both accident and converse accident, it may be said that
they obtain because all general truths, such as rules, principles,
definitions, maxims, etc., have their _exceptions_; and it is through
these exceptions that the two fallacies are made possible.
_Accident and Converse Accident Distinguished from Division and
Composition._
The fallacy of accident, we have learned, occurs when one reasons
from a _general truth_ to an _accidental case_; whereas the fallacy
of division obtains when one reasons from a _collective_ use of a
term to a _distributive_ use; in both cases the procedure is from a
_larger unit_ to a _smaller unit_. Moreover, with converse accident and
composition, the movement is from the _smaller unit_ to the _larger_.
Because of this similarity there is danger of confusing the two kinds
of fallacies. As a matter of distinction between the fallacies of
accident, and composition and division the attending comparative
_résumé_ may be of value:
(1) _Division_ is similar in movement to _accident_, while
_composition_ resembles _converse accident_.
(2) A valuable cue for remembering which way division and accident
move, is to recall that division in arithmetic is a procedure
from the larger unit to the smaller, and therefore that division
in logic would have the same signification.
(3) Division and composition pertain to _mathematical_ wholes; while
accident and converse accident relate to _logical_ wholes.
(4) The aggregates of division and composition may be counted or
enumerated easily; while the accident and converse accident
aggregates (or generals) are not easily enumerated.
(5) Division and composition relate to logical _terms_, whereas
accident and converse accident relate to general _truths_.
(6) Division and composition use a _term_ in a _collective_ sense
and then in a separate or _distributive_ sense, or vice versa;
accident and converse accident use a _thought_ in a _general_
and then in an _accidental_ sense, or vice versa.
_Irrelevant Conclusion_ (_Ignoratio Elenchi_).
_The fallacy of irrelevant conclusion results when the argument does
not squarely meet the point at issue._ It is the fallacy of arguing to
the wrong point either purposely or through ignorance. One in defense,
who has a weak case, may be tempted to divert attention from the point
in hand, realizing that a close analysis of the matter in dispute
will tend to his undoing. In such instances (1) the lawyer will abuse
the plaintiff, (2) the demagogue will tell humorous stories, (3) the
teacher will take advantage of the ignorance of the pupil, (4) the
scholar will refer to authority and (5) the magnate will fall back
upon the power of position and wealth. These forms of “_rhetorical
thinking_” are as harmful as they are popular, and furnish one of the
chief reasons for giving to the common people a better understanding
of “how to think” as well as “how _not_ to think.”
Definite names have been given to the various forms of irrelevant
conclusion which may be summarized as follows:
_Argumentum ad populum._
This is the fallacy of appealing to the feelings, passions and
prejudices of an audience rather than to their good sense and powers of
reason. It is probably the most common of the group. To excite sympathy,
the lawyer for the defense may speak feelingly of the _suffering_
that an unfavorable verdict will bring to the wife and children of the
accused.
_Argumentum ad hominem._
Here the character of the opponent is defamed with a view of
discrediting him with the court or audience. “Mud throwing” in times of
political agitation is a good example of this fallacy.
_Argumentum ad ignorantiam._
This fallacy comes from taking advantage of the ignorance of the
opponent; the fallacy assumes that the original supposition has been
proved if one is unable to prove the _contradictory_ of the original.
Illustration: Mars is inhabited because no one is able to prove that
Mars is not inhabited.
_Argumentum ad baculum._
In this all argumentation is made to give way to the forces of personal
opposition and to the power of money. Illustration: A political
committee seating those delegates only, who will vote _their_ way; and,
doing this, not from the merits of the case, but because said committee
happen to have a sufficient number of votes to “put the thing through.”
_Argumentum ad verecundiam._
This fallacy comes from supposing that the whole thing may be settled
by citing some noted authority who apparently substantiates the
argument advanced.
_Epitome of five forms of Irrelevant Conclusion_:
(1) Appealing to the audience.
(2) Defaming the character of the opponent.
(3) Inability to prove the contradictory.
(4) Gaining the point by force.
(5) Citing authority.
_Non Sequitur (False Consequent)._
_This is the fallacy of deriving a conclusion which does not follow
from the premises._ The fallacy obtains whenever material appears in
the conclusion, which has no bearing on the case under discussion.
“_Irrelevant conclusion_” pertains to the establishment of the premises
while “_non sequitur_” is concerned with the conclusion only. We know
that a logical thinker constructs the conclusion from material already
presented by the premises; “_Non sequitur_” uses material in the
conclusion which is found in neither premise.
“_Non sequitur_” differs from the fallacy of four terms in that the
latter uses the fourth term in the premises while the former introduces
the fourth term in the conclusion, and in a form so well obscured that
it sometimes escapes notice. Illustration:
All men are thinking animals,
Socrates was a man,
∴ Socrates was a scholar.
It does not follow that because a man is a thinking animal that he will
become scholarly.
_False Cause._
_This is the fallacy of assuming that because two happenings have
occurred together several times, the one is the cause of the other._
This very common fallacy is due to lack of discrimination, and to the
exaggerations incident to fear and superstition. Illustrations:
(a) Planting vegetables which grow down, such as the beet, during
the last two days of the waxing moon in order to have a larger
yield. So far as we know the moon has no influence over growing
vegetables.
(b) Thirteen seated at a table is an indication that one of the
number will die during the year. This is one of the most absurd
fallacies that has ever been visited upon an intelligent people.
It is seen that “False Cause” is closely related to “_Non Sequitur_.”
_Complex Question_ (_Double Question_).
_This fallacy obtains when an assumption is put in the form of a
question._
ILLUSTRATIONS:
(a) A wise father who did not want to tempt beyond the yielding
point his three-year-old son, asked, pointing to the scratches on
the new mahogany piano, “Freddie, did you do that last night or
this morning?”
(b) What caused you to desist from slandering your neighbors; New
Year’s resolutions or the preaching of Dominie X?
(c) A daily paper anecdote:
“Charles Bradlaugh, the noted English free-thinker, once engaged
in a discussion with a dissenting minister. He insisted that
the minister should answer questions by a simple yes or no,
asserting that every question should be replied to in that
manner.” The reverend gentleman arose and said, “Mr. Bradlaugh,
will you allow me to ask you a question on these terms?”
“Certainly,” said Mr. Bradlaugh. “Then, may I ask, have you
given up beating your wife?”
_Begging the Question_ (_Petitio Principii_).
This is a fallacy _of deriving a conclusion from notions which in
themselves demand proof_.
The fallacy is not committed when the assertion is self-evident. It
is easy to claim that our opponent is begging the question as soon as
we see that he is getting the better of us. One may himself beg the
question by being too ready to charge others with begging the question.
When the opponent adopts premises which are commonly accepted, he does
not beg the question. One commits the fallacy when he _seems to prove_
the conclusion more satisfactorily than he really does. This he may
accomplish by covertly taking for granted the truth of notions which
have not the stamp of universal approval. The fallacy of begging the
question assumes three forms:
(1) _The assumption of an unproved premise_ (_assumptio non probata_).
In this either the major or the minor premise, or both may demand
more substantial proof. It must be borne in mind, however, that the
disputant must not ask for further proof after he has once accepted the
premises, or after the opponent has met his demands to the satisfaction
of commonly accepted authority.
_Examples of begging the question by assuming unproved premises_:
(a) All patriotic citizens are honest at heart,
This man charged with graft is a patriotic citizen,
∴ This man charged with graft is honest at heart.
“All patriotic citizens are honest at heart,” is not an accepted
truth and thus demands proof.
(b) A famous sophism of the Greek philosopher by which he proved that
motion was impossible, is an excellent illustration of an assumed
premise:
“If motion is possible, a body must move either in the place
where it is, or in the place where it is not;
But a body cannot move in the place where it is; and of course
it cannot move where it is not,
Therefore, motion is impossible.”
Referring to this, De Morgan claims “Movement is change, and so a
body requires _two_ places in order to move.” _A body cannot move
in the place where it is, but must be moved from place to place._
The major premise being assumed, this sophism illustrates the
fallacy of begging the question.
(c) The most subtle form of begging the question is an enthymeme
where the suppressed premise is the one assumed; e. g., “You,
being a teacher, should not do as other people do.”
Completed and arranged the argument becomes:
No teacher should do as other people do,
You are a teacher,
∴ You should not do as other people do.
Surely the major premise demands proof.
(2) _Reasoning in a Circle_ (_Circulus in probando_).
This form of begging the question occurs, “When a conclusion is based
upon a premise which in an earlier stage of the argument was itself
based upon this very conclusion.” To put it in another way: Reasoning
in a circle involves proving the truth of a conclusion by using a
particular premise, and then proving the truth of the particular
premise by using the conclusion. From premise to conclusion and from
conclusion to premise completes the circle.
_Examples of begging the question by reasoning in a circle_:
(a) It is wrong because my conscience pricks me, and my conscience
pricks me because it is wrong.
(b) “The effeminate walk shows a lack of force; because no forceful
man walks that way.”
(c) Says Hamilton, “Plato, in his _Phoedo_, demonstrates the
immortality of the soul from its simplicity; and in the
_Republic_, he demonstrates its simplicity from its immortality.”
(3) _Question Begging Epithets and Appellations._
This is the fallacy of assuming the point at issue by means of a
carefully selected epithet.
Scientists sometimes assume to clarify an inexplicable phenomenon by
giving it a technical name. Politicians are exceedingly free with their
epithets and appellations, and the records of religious disputes prove
that the theologian often resorted to this device.
_Examples of begging the question by using epithets and appellations_:
(a) We must attribute the disease to _heredity_.
(b) The candidate for governor is an _animated feather duster_.
(c) They call him _Blue Charlie_.
(d) It is the policy of the _big stick_.
(e) The _muck-raker_ seldom makes an efficient servant of the people.
It is seen that the use of these epithets and appellations is simply a
rhetorical device for the purpose of creating either a favorable or
unfavorable impression.
=8. OUTLINE.=
THE LOGICAL FALLACIES OF DEDUCTIVE REASONING.
(1) A negative aspect of definition of logic.
(2) Paralogism and sophism.
Distinguished. Mission of Socrates.
(3) A division of the deductive fallacies.
More or less faulty. Aristotle’s phraseology retained.
Division given.
(4) General divisions explained.
Formal and material. Material fallacies in _language_ and in
_thought_.
(5) Fallacies of immediate inference.
Opposition, obversion, conversion, contraversion.
(6) Fallacies in language (also fallacies of equivocation).
Ambiguous middle――distinguished from four terms.
Amphibology.
Accent.
Composition――“all” a pitfall.
Division.
Figure of speech.
(7) Fallacies in thought――(also fallacies of assumption).
Accident.
Converse accident. Made possible by exceptions.
Accident and converse accident distinguished from composition
and division.
Comparative résumé.
Irrelevant conclusion (_ignoratio elenchi_).
_Argumentum ad populum._
_Argumentum ad hominem._
_Argumentum ad ignorantiam._
_Argumentum ad baculum._
_Argumentum ad verecundiam._
_Non sequitur_ (false consequent).
False cause.
Complex question.
Begging the question (_petitio principii_).
Assumption of premise.
Reasoning in a circle.
Question begging epithets and appellations.
=9. SUMMARY.=
(1) Logic as a science makes known the laws and forms of thought and as
an art suggests conditions which must be fulfilled in order to think
rightly.
A discussion of the second phase of the definition would be incomplete
without a consideration of the negative aspect as well as the positive.
Such a viewpoint makes evident the question “What errors must be
avoided in order to reason correctly?” An answer to this question is
given under the caption of Logical Fallacies.
(2) A logical fallacy is any error in reasoning which has the
appearance of correctness.
A fallacy which deceives the writer or speaker himself is termed
a paralogism, whereas a fallacy formed for the express purpose of
deceiving another is denominated a sophism.
It was the pagan teacher Socrates who taught modern thought to frown
upon all forms of sophism; these exist to-day much as they did in the
olden time.
(3) Because of disagreement as to definition, and because of inability
to prevent an overlapping of species, any logical division of the
deductive fallacies must be faulty.
In the division of the deductive fallacies, this treatise retains the
phraseology and form worked out by Aristotle, so far as such retention
is consistent with the changes incident to the advances of time.
(4) Formal fallacies occur because of careless and improper use of
words as arbitrary signs. Formal fallacies are definite and easy of
comprehension.
The material fallacies are due to certain inconsistencies in thought
and to imperfect ways of interpreting language. They are more subtle
and thus more difficult of comprehension than the formal fallacies.
There are material fallacies in thought and material fallacies in
language; the former are due to _looseness in thinking_ and the latter
to _lack of precision in expression_.
(5) Fallacies of opposition result most frequently from deriving
universals from their corresponding particulars, and from assuming
to contradict affirmative universals by negative universals and
affirmative particulars by negative particulars.
The common fallacy in the process of obversion consists in using one
negative instead of two, whereas the ordinary error of conversion is a
matter of distributing an undistributed term.
Fallacies of contraversion must involve either those of obversion or
conversion since the process is a combination of the two.
(6) Fallacies in language, because they result from permitting
more than one interpretation, may be also denominated fallacies of
equivocation.
(1) Ambiguous middle is the fallacy of giving to the middle term a
double meaning.
The fallacy of four terms, as the name signifies, exists when
the argument has four terms in both form and meaning. Ambiguous
middle is a matter of four terms in meaning but only three in
form.
(2) The fallacy of amphibology is committed when the given
proposition conveys more than one meaning. In order to maintain
their prestige the ancient oracles made use of this fallacy.
(3) The fallacy of accent springs from placing undue emphasis on some
word or group of words. Newspaper and demagogues are prone to
this error, that they may thus create an unfavorable impression
towards those whom they oppose.
(4) The fallacy of composition is committed when it is assumed that
what is true _distributively_ is likewise true _collectively_.
“All” meaning _each one_ and “all” meaning the _whole class_
often leads to the fallacy of composition.
(5) The fallacy of division is committed when it is assumed that what
is true _collectively_ is true _distributively_.
Division is the converse of composition.
(6) The fallacy of figure of speech is occasioned by assuming that
words of the same root have the same meaning.
(7) Fallacies in thought are likewise called fallacies of assumption,
because of the tendency to assume as true something which demands
further proof.
(1) The fallacy of accident occurs when one reasons from a general
truth to an accident case. It is the favored fallacy of the
doctrinaire, the reformer and the vender of “cure-alls.”
(2) The fallacy of converse accident occurs when one reasons from an
accidental case to a general truth.
Both accident and converse accident are made possible because rules,
definitions, maxims, etc., have _exceptions_. It is easy to confuse
division and composition with the fallacies of accident. Division and
composition are concerned with the _collective and distributive use of
terms_, whereas the fallacies of accident involve the use of notions
in a _general and accidental sense_. The former represent notions which
may be _counted or enumerated_ while the latter concern notions which
are _logical_ rather than numerical. Composition and division involve
“number of,” accident, “meaning of.”
(3) The fallacy of irrelevant conclusion results when the argument
does not squarely meet the point at issue. It is the fallacy of
arguing to the wrong point either purposely or ignorantly. This
may be accomplished by (1) appealing to sympathy of audience,
(2) defaming character of opponent, (3) assuming that the fact is
true because of inability to prove the contradictory, (4) gaining
point by force, (5) citing authority.
(4) “_Non sequitur_” is the fallacy of deriving a conclusion which
does not follow from the premises. It involves introducing new
material in the conclusion.
(5) “False cause” is the fallacy of assuming that because two
happenings have occurred together several times the one is
the cause of the other. The fallacy is due largely to the
exaggerations of fear and superstition.
(6) The fallacy of complex question consists in putting an assumption
in the form of a question.
(7) Begging the question is the fallacy of deriving a conclusion from
notions which in themselves demand proof.
This fallacy takes the three forms of (1) the assumption of an
unproved premise, (2) reasoning in a circle, (3) question begging
epithets and appellations.
=10. ILLUSTRATIVE EXERCISES IN THE TESTING OF ARGUMENTS IN BOTH FORM
AND MEANING.=
(1a) He who wilfully takes the life of another should be
electrocuted, This sharp shooter has wilfully taken the life
of another, Hence he should be electrocuted.
{ A
In form we know this argument to be valid since it is in mood { A of
{ A
the first figure. But as the conclusion does not meet with our approval,
we are forced to the belief that there must be a material fallacy.
Such proves to be the case. In the first instance, “Wilfully takes
the life of another” is used in a personal, individual, selfish sense,
whereas in the second instance the expression is used in a general,
“servant-of-the-government” signification. The argument is, therefore,
invalid, the fallacy being ambiguous middle.
(1b) From the viewpoint of both _form_ and _meaning_ test the following:
“Events which are not probable happen almost every day; but what
happens every day are very probable events; therefore events which are
not probable are very probable.”
(2a) The planets have those attributes needed in the support of life,
Mars is a planet,
Hence Mars has those attributes needed in the support of life.
{ A
This is valid in form { A in the first figure. The major premise posits
{ A
a fact which has not been proved; the argument is therefore invalid in
meaning, the fallacy being that of _begging the question_.
(2b) “The end of a thing is its perfection; death is the end of life,
therefore death is the perfection of life.”
Indicate the fallacy in the foregoing, giving reasons.
(3a) The countries of Europe abound in beggars,
France is a country in Europe,
∴ France abounds in beggars.
“The countries of Europe” in the major premise is used in a collective
sense, while the same expression in the minor premise is used in a
distributive sense. The argument is, therefore, invalid in meaning;
_fallacy of division_.
(3b) State and explain the material fallacy in the following:
The states believe in the income tax principle; hence Vermont’s vote
will be favorable to this.
(4a) “On general principles I believe that one is better off when he
abstains from both tea and coffee; and this is the reason why I offer
you a cup of hot water.”
The individual to whom the hot water was offered might have been
in great need of a mild stimulant. Here, then, is an exception to
the general principle and the fallacy committed is clearly that of
_accident_.
(4b) “Books are a source both of instruction and amusement; a table of
logarithms is a book; therefore it is a source both of instruction and
amusement.” Jevons.
Designate with explanations the fallacy in the above argument.
(5) “Twice have I started out on Friday and both times I had tire
trouble.” Fallacy of _false cause_.
(6) “Where do you spend your vacation, in Palestine or Rome?” Fallacy
of _complex question_.
(7) “Of all the men of that department he seemed to be the most
trustworthy, and I pride myself on my ability to judge men in this
regard; but now even the police cannot find him.”
The fact that the police cannot find him has nothing to do with the
argument. The fallacy is that of _non sequitur_.
(8) “You must not whisper in _my_ classes.” Fallacy of _accent_.
(9) “I am a Progressive because I believe in progress.” Fallacy of
_figure of speech_.
(10) “I know it is true because I found it in our text book.” Fallacy
of _irrelevant conclusion_.
=11. REVIEW QUESTIONS.=
(1) Give the negative aspect of the second part of the definition of
logic.
(2) Define and illustrate the term fallacy as it is used in logic.
(3) Distinguish between a paralogism and a sophism.
(4) Tell of the mission of Socrates.
(5) What reasons may be given for such a divergence of opinion on a
proper classification of the fallacies of deduction?
(6) Give a complete outline, without explanation, of the deductive
fallacies.
(7) Distinguish between formal and material fallacies.
(8) Explain the two kinds of material fallacies.
(9) Illustrate the fallacies of immediate inference.
(10) Why should the fallacies in language be likewise termed fallacies
of equivocation?
(11) Explain and illustrate ambiguous middle.
(12) Illustrate the fallacy of amphibology.
(13) Explain by illustration the fallacy of accent.
(14) Explain and exemplify the fallacies of composition and division.
(15) Illustrate the fallacy of figure of speech.
(16) Give reasons for denominating the fallacies in thought as
fallacies also of assumption.
(17) Define and illustrate the fallacies of accident and converse
accident.
(18) Distinguish between the fallacies of composition and division and
the two fallacies of accident.
(19) “Every rule has its exception,” what has this to do with the
fallacies of accident?
(20) Explain and illustrate the fallacy of irrelevant conclusion.
(21) Name the various ways in which irrelevant conclusion may be
committed.
(22) Illustrate the fallacy of _non sequitur_.
(23) Explain the fallacy of false cause.
(24) Give examples of the complex question.
(25) How may the teacher use the complex question to advantage?
(26) Explain the fallacy of begging the question.
(27) Illustrate the three forms of begging the question.
(28) From the viewpoint of form and meaning, test the validity of the
following:
(1) “No soldiers should be brought into the field who are not
well qualified to perform their part; none but veterans are
well qualified to perform their part, therefore, none but
veterans should be brought into the field.” Whately.
(2) “For the proverb is true, ‘That light gains make heavy
purses;’ for light gains come thick, whereas great gains come
but now and then.” Bacon.
(3) “Whatever is given on the evidence of sense may be taken as a
fact; the existence of God, therefore, is not a fact, for it
is not evident to sense.” St. Andrew. 1896.
(4) “All the trees in the park make a thick shade; this is one of
them, therefore this tree makes a thick shade.” Jevons.
(5) “What we eat grew in the field; loaves of bread are what we
eat; therefore loaves of bread grew in the fields.” Jevons.
(6) “Who is most hungry eats most; who eats least is most hungry;
therefore who eats least eats most.” Jevons.
(7) “Great talkers should be cropped, for they have no need of
ears.” Franklin.
(8) “Love your enemies, for they tell you your faults.” Franklin.
(9) “All the works of Shakespeare cannot be read in a day;
therefore the play of Hamlet, being one of the works of
Shakespeare, cannot be read in a day.” Jevons.
(10) “Logic as it was cultivated by the schoolmen proved a
fruitless study; therefore logic as it is cultivated at the
present day must be a fruitless study likewise.” Jevons.
=12. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=
(1) Is there any difference in content between error and fallacy?
Illustrate.
(2) In what ways do trusts indulge in sophisms?
(3) May the sophism be used conscientiously by the country doctor?
Explain.
(4) Give in substance Aristotle’s classification of fallacies.
(5) Select the fallacies which could with justice be called fallacies
of interpretation. See Creighton.
(6) Explain in full the popular conception of equivocation.
(7) Indicate the marks which distinguish the following: Ambiguous
middle, fallacy of four terms, non sequitur, figure of speech.
(8) “Why should Jeremy Bentham employ a person to read to him who
habitually read in a monotonous tone of voice?” Jevons――Hill.
(9) Originate a sentence of about ten words and through the fallacy
of accent secure as many different meanings as possible.
(10) Show that the fallacy of figure of speech might be classed as a
fallacy of four terms.
(11) To what fallacies, in your opinion, are teachers especially
given?
(12) Show that the fallacy of accident could be classed as one of
ambiguous middle.
(13) “When the Puritan settlers in New England passed their three
famous resolutions――Resolved, _first_, that the earth is the
Lord’s and the fullness thereof; _secondly_, that he hath given
it to his Saints; _thirdly_, that we are his Saints. What fallacy
did the Puritan Fathers commit?” Ryland.
(14) A Dutchman afflicted with pneumonia arises at midnight and eats
a large quantity of sauerkraut. The Dutchman gets well, whereat
his physician writes in his little book on remedies, “_Sauerkraut
sure cure for pneumonia_.” The physician was guilty of what
fallacy? Why?
(15) De Morgan quotes from Boccaccio this: “A servant who was roasting
a stork for his master was prevailed upon by his sweetheart to
cut off a leg for her to eat. When the bird came upon the table
the master desired to know what had become of the other leg. The
man answered that storks never had more than one leg. The master,
very angry, but determined to strike his servant dumb before
he punished him, took him next day into the fields where they
saw storks, standing each on one leg, as storks do. The servant
turned triumphantly to his master; on which the latter shouted,
and the birds put down their other legs and flew away. Ah, sir,
said the servant, you did not shout to the stork at dinner
yesterday; if you had done so he would have shown his other leg.”
What fallacy does this quotation from Boccaccio illustrate?
(16) Why should begging the question and irrelevant conclusion be
classed as fallacies of the “forgotten issue?”
(17) From the standpoint of both form and meaning test the validity of
the following:
(1) “Virtue is the child of knowledge and vice of ignorance;
therefore education, periodical literature, traveling,
ventilation, drainage and the arts of life, when fully
carried out, serve to make a population moral and happy.”
Hibben.
(2) “The civil power has the right of ecclesiastical jurisdiction
and administration, therefore parliament may impose articles
of faith on the church or suppress dioceses.” Hibben.
(3) “Seeing that abundance of work is a sure sign of industrial
prosperity, it follows that fire and hurricane benefit
industry, because they undoubtedly create work.”
St. Andrews――1895.
(4) “Riches are for spending, and spending for honor and good
action; therefore, extraordinary expense must be limited by
the worth of the occasion.” Bacon.
(5) “And let a man beware how he keepeth company with choleric
and quarrelsome persons; for they will engage him into their
own quarrels.” Bacon.
(6) “He that resteth upon gains certain, shall hardly grow to
great riches; and he that puts all upon adventures, doth
oftentimes break and come to poverty. It is good, therefore,
to guard adventures with certainties that they may uphold
losses.” Bacon.