Selected Areas In Cryptography 16th Annual International Workshop Sac 2009 Calgary Alberta Canada August 1314 2009 Revised Selected Papers 1st Edition Sebastiaan Indesteege
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Fallacies.
Formal(Indictione)
1. Opposition
2. Obversion
1. Immediate inference
2. Categorical arguments
3. Hypothetical arguments
4. Disjunctive arguments
3. Conversion
4. Contraversion
5. Four terms
6. Undistributed middle
7. Illicit major
8. Illicit minor
9. Negative premises
10. Particular premises
11. Denying the antecedent
12. Affirming the consequent
13. Illogical disjunction
Material(Indictionem)
1. Ambiguous middle
2. Amphibology
3. Accent
1. In Language Equivocation
4. Composition
5. Division
6. Figure of speech
2. In Thought Assumption
1. Accident
2. Converse accident
3. Irrelevant conclusion
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 inlanguage. 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 nomenarehonest.
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 distributingan 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.
I
LLUSTRATIONS 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) Ambiguousmiddle.
Ambiguous middle explains itself. Itisthefallacyofgivingtothe middle term a doublemeaning. 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 formis given a doublemeaning.
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.
Ambiguousmiddle.
(a) “Necessityis the mother of invention,”
Bread is a necessity,
∴ Bread is the mother of invention.
(b) “Nothingisbetter than wisdom,”
Dry bread is better than nothing,
∴ Dry bread is better than wisdom.
(c) A churchis 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.
Fallaciesoffourterms.
(a) All trueteachersare just,
John Doe is an educator,
∴ John Doe is just.
(b) Milkis nourishing,
This substance is a whitefluid,
∴ This substance is nourishing.
(c) Thievesshould be imprisoned,
This man hastakenwhatdoesnotbelongtohim,
∴ 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 nonsequiturhas been committed.
(2) Amphibology(oramphiboly).
Amphibology is a fallacy resulting from an ambiguous proposition rather than from the ambiguity of any particular term. Thefallacyof 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 everyemergency.
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 fallacysprings from placing undueemphasis 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 notneighbors.
(b) “You must not crib when taking myexaminations.”
(c) Whatthe“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.” Whatthenewspaperreported.
(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.
Thefallacyofcompositioniscommittedwhenitisassumedthat whatistruedistributivelyislikewisetruecollectively. 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.
Thefallacyofdivisioniscommittedwhenitisassumedthatwhat 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) FigureofSpeech.
This fallacy results from assuming that words of the same root have thesamemeaning.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 designingperson should be trusted,
This architect is a designer,
∴ This architect should not be trusted.
(b) Justifiable investigationis 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 closelyresembleeach other in form, and yet they are not fallacies of ambiguous middle; since the middle terms are not identicalin 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 fallacyofaccidentoccurs whenone 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) ConverseAccident.
As the title implies this is the fallacy of reasoning from an accidentalcasetoageneraltruth.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 AccidentDistinguished 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 résumémay be of value:
(1) Division is similar in movement to accident, while compositionresembles converseaccident.
(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 accidentalsense, or vice versa.
IrrelevantConclusion(IgnoratioElenchi).
The fallacy of irrelevant conclusion results when the argument doesnotsquarelymeetthepointatissue.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 “rhetoricalthinking” 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 notto think.”
Definite names have been given to the various forms of irrelevant conclusion which may be summarized as follows:
Argumentumadpopulum.
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.
Argumentumadhominem.
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.
Argumentumadignorantiam.
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.
Argumentumadbaculum.
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.”
Argumentumadverecundiam.
This fallacy comes from supposing that the whole thing may be settled by citing some noted authority who apparently substantiates the argument advanced.
EpitomeoffiveformsofIrrelevantConclusion:
(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.
NonSequitur(FalseConsequent).
Thisisthefallacyofderivinga conclusionwhichdoesnot follow fromthepremises.The fallacy obtains whenever material appears in the conclusion, which has no bearing on the case under discussion. “Irrelevantconclusion” pertains to the establishment of the premises while “nonsequitur” 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.
“Nonsequitur” 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.
FalseCause.
Thisisthefallacyofassumingthatbecausetwohappeningshave occurredtogether 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 “NonSequitur.”
ComplexQuestion(DoubleQuestion).
This fallacy obtains when an assumption isput 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?”
BeggingtheQuestion(PetitioPrincipii).
This is a fallacy of deriving a conclusion from notions which in themselvesdemandproof.
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 toprove 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 twoplaces in order to move.” Abody cannot move in the place where it is, but must be moved fromplace toplace.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) ReasoninginaCircle(Circulusinprobando).
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.
Examplesofbeggingthequestionbyreasoninginacircle:
(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) QuestionBeggingEpithetsandAppellations.
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 animatedfeatherduster.
(c) They call him BlueCharlie.
(d) It is the policy of the bigstick.
(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 (ignoratioelenchi).
Argumentumadpopulum.
Argumentumadhominem.
Argumentumadignorantiam.
Argumentumadbaculum.
Argumentumadverecundiam.
Nonsequitur(false consequent).
False cause.
Complex question.
Begging the question (petitioprincipii).
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 loosenessinthinkingand the latter to lackofprecisioninexpression.
(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 collectivelyis 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.
In form we know this argument to be valid since it is in mood
of 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.”
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