Frank van Dun        Ph.D., Dr.Jur.     -    Senior lecturer Philosophy of Law.


  
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FALLACIES

SECTION 1
LOGIC

Introduction
Principles
Subject, Predicate, and Context

Logic and Rhetoric
 
Inferences and Proofs

SECTION 2
FALLACIES

Argumentation
Non-sequitur
 
Category Errors 
Fallacies of distraction 
Appeal to motives 
Changing the subject 
Inductive fallacies 
Statistical syllogisms 
Causal fallacies 
Missing the point 
Ambiguity 
Syllogistic fallacies 
Fallacious explanation 
Fallacies of definition 


Argumentation & FALLACY

The point of an argumentation is to give objective reasons (or arguments) in support of some statement S. An argumentation is a fallacy when the reasons offered do not objectively support the statement S. 

Argumentation
The point of an argumentation is to give objective reasons (or arguments) in support of some statement S. 

Obviously, 'support of a statement' is a vague term. Support can be logically sufficient and then it proves the statement; or it can be logically insufficient and then it merely gives one an objective reason for believing the statement, without necessarily removing all reasons for disbelieving or doubting it. 

Argumentation involves one who argues ("the speaker"), an audience that the speaker wishes to convince (so that it becomes [more] willing to accept the statement in support of which he adduces his reasons or arguments). Moreover, it involves the use of language and an appeal to rules of logic and knowledge, which may be made explicit or merely assumed or presupposed in the argumentation. 

Argumentation is not concerned with purely subjective reasons or arguments. For example, "I believe this because I want to believe it", "I believe such and such out of respect for my mother", or "Paris is a wonderful city because I know you love to hear me say that it is" do give one's reasons for believing / saying that some proposition or other is true, but in argumentation the speaker purports to give the audience [additional or better] reasons why it should believe or accept the proposition.

If an argumentation is intended to prove a statement S, it is called an intended proof of S. Otherwise it is called a supportive argumentation. An intended proof may fail as a proof and still be considered a good argumentation, if it adds support for its conclusion, despite the fact that it does not remove all doubts about it. 

Proofs
A proof is an argumentation-structure of the following form:

                      B: Unstated background assumptions 
                             [common knowledge, presuppositions, language
                             rules, definitions, mathematics, ...]
                      P: Premises
                             [the reasons given explicitly in the argumentation for S]
                      _____________________________________________
                     
                      C: Conclusion
                             [the statement S that is to be proven]   

where the conditional inference rule
                      If (B and P) then C   is a formal tautology
 and the conditions 
                      B and P are true
[A formal tautology is a statement that is true by its form alone (independent of what B, P and C stand for). Thus, If A then A is a formal tautology, as is If A and B then A .]

Where a proof is given, one cannot maintain, without contradicting oneself,  that while (B and P) is true C is false. 

To challenge a purported proof one may question
a) the truth of at least one of the premises
b) the validity of the conditional inference rule
c) at least one of the unstated but effectively used background assumptions, if there is any.

(a) and (b) are common challenges. In many contexts of argumentation the speaker and his audience share exactly the same background assumptions. Consequently, doubts about the purported proof concern only the truth of the premises and the validity of the inference rule. 
However, occasionally a challenge will be directed at one or more of the background assumptions. Such a challenge often will be called 'philosophical', if it questions things which the speaker and most of his audience take for granted as  obvious and beyond criticism. It is a challenge of received wisdom. 

Examples: 
(i) The following argumentation
                   B: [basic arithmetic; meaning of 'cheaper', 'cost', 'lower', 'price'] 
                   P: This book costs $15; that book costs $28.
                   C: Therefore, This book is cheaper than that book
is a proof of the statement that This book is cheaper than that book, only if 
a) If the price of this book is lower than the price of that book then this book is cheaper than that book is a formal tautology--which it is; and
b) The price of this book is lower than the price of that book (which is the case here: 15<28).

(ii) The following argumentation
                   B: ['Bachelor' refers to an unmarried person; 'John' to a person]
                   P: John is not married
                   C: Therefore, John is a bachelor
is a proof of the statement that John is a bachelor, only if 
a) If John is a person and John is not married then John is an unmarried person (i.e. a bachelor) is a formal tautology--which it is; and
b) the argument is about a person called 'John' who is not married.

Note that to one who does not know the English language sufficiently
                   If John is not married then John is a bachelor
does not appear as a formal tautology. Its form seems to be
                   If A then B  
which is not true by its form alone (For example: If Brussels is in Europe then Paris is in Asia is not true). However, speakers of English know the meaning of 'bachelor' and the fact that normally 'John' is the name of a person (and should be interpreted as such, if no indication to the contrary is given). Thus, in normal English argumentation
                  P: John is not married
                  C: Therefore, John is a bachelor
will be considered a conclusive proof of the statement that John is bachelor, although its conclusiveness will appear formally only after we have spelled out and verified the background assumptions. 

Supportive argumentations
Many argumentations are not intended as conclusive supports (or proofs in the strict sense). In general an argumentation for a statement S has the form: 

                      B: Unstated background assumptions 
                             [common knowledge, presuppositions, language
                             rules, definitions, mathematics...]
                      P: Arguments
                             [the reasons given explicitly in the argumentation for S]
                      _____________________________________________
                     
                      C: Conclusion
                             [the statement S that is to be supported]   

It actually supports the statement S if the conditions
                      B and P are true;
the conditional
                      If (B and P) then C is more likely than not-C is true;
and 
                      (B and P) and C is not logically inconsistent.
(If it were logically inconsistent then if (B and P) then not-C would be a formal tautology; and the argumentation would prove that C is not true. In short, no argumentation can support the negation of what it proves).

Note that 'more likely' is a vague expression. There is no suggestion that it must refer to a measurable or quantifiable probability. 

With a merely supportive argumentation, unlike a proof, one is not necessarily contradicting oneself if one maintains that (B and P) is true and that C is false.  

The strength of the argumentation depends on the assessment of the conditional inference rule. Compare:
              If (B and P) then C is almost certainly true
              If (B and P) then C is much more likely than not-C  
              If (B and P) then C is only slightly more likely than not-C
              If (B and P) then C is as likely as not-C
The problem with these assessments is that we often have no independent way to determine which one of them, if any, is true. Thus, there may be no conclusive answer to a challenge of these conditional inference rules. In this respect they are quite unlike the formal tautologies underlying rigorous proofs. Consequently, the same argument may lead one person to conclude that C is almost certainly true; another that C is more likely to be true than false; and a third that it does not support C at all. 
Nevertheless, in many (but by no means in all) contexts, speaker and audience share sufficient background to agree that if one accepts the premises one has good (though not necessarily sufficient) reason to believe that the conclusion should be accepted also. 

Inductive argumentations (which draw conclusions about all instances of some kind of thing on the basis of knowledge or observation of a limited number of instances) are supportive:

                     No one has ever seen a white raven
                     Therefore, no ravens are white

This induction does not prove that there are no white ravens because there may be ravens that no one has ever observed, some of which may be white. However,  (assuming the premise is true) we certainly have better reason to  believe the conclusion than its negation 'Some ravens are white'.

Retroductive argumentations (which draw conclusions about some property of a particular thing on the basis of knowledge or observation of some other properties it has) are supportive:

          Zebras are white-skinned animals with black stripes on their backs
          This animal is white-skinned with black stripes on its back
          Therefore, it is a zebra

This retroduction does not prove that the animal in question is a zebra because there may be white-skinned animals with black stripes on their backs that are not zebras. However, if we assume that the only known or the most common white-skinned animals with black stripes on their backs are zebras, then we certainly have a better reason to believe that the conclusion is true rather than its opposite 'This animal is not a zebra' or something like 'This animal is a white raven with black stripes'. 


Fallacies
Fallacies are argumentations in which the arguments do not objectively support the statement that the argumentation aims to defend.  

Fallacies may be intentional (the speaker seeks to mislead his audience, say, for self-interested or propagandistic reasons) or they may be unintentional (the speaker made a mistake, was ignorant or confused, got carried away by his own rhetoric, or inadvertently oversimplified his argumentation in a misguided effort to make it easier for his audience to understand it). Some audiences are more critical and more likely to point out fallacies to the speaker than other audiences.

Fallacies occur when the speaker appeals to rules of inference that are not logically valid, or to linguistic, mathematical, scientific data or statements of fact that are false, insufficient, inappropriate or irrelevant for his argumentation. 

Knowledge of formal logic is not enough to guard against fallacies. 
The logical structures that formal logic studies are not always clearly detectable in natural language texts--which moreover often are ambiguous, so that there can be genuine controversy about their representation in formal logic. 

On the one hand, the conditional form 
                     If all A's are not-B's and x is a B then x is not an A  
is formally valid. However, the argumentation
                     All sadists are inhuman
                     Mr Xyz is human
                     Therefore Mr Xyz is not a sadist
is fallacious. In the first sentence 'inhuman' does not mean 'not human' or 'not a human being'. Instead it means 'not humane'. Hence, the argumentation goes as follows:
                     All sadists are not-humane
                     Mr Xyz is human
                     Therefore Mr Xyz is not a sadist
 the conditional form of which is
                     If all A's are not-B's and x is a C then x is not an A
which is not formally valid.

On the other hand, the argumentation
                     All bachelors are permitted to enter
                     John is not married
                     Therefore, John is permitted to enter
is valid even if superficially its conditional form seems to be
                    If all A's are B's and x is not-C then x is B
which is not valid. However, given the common meaning of 'bachelor', we can reformulate the argumentation as follows:
                     All persons who are not married are permitted to enter
                     John is a person who is not married
                     Therefore, John is permitted to enter
the conditional form of which is 
                    
If all not-A's are B's and x is not-A then x is B
which is formally valid. 

Below is a discussion of some common fallacies. It is based on the list compiled by Stephen Downes (Stephen's Guide to the Logical Fallacies), which can be consulted at http://www.datanation.com/fallacies/index.htm. I have maintained his categorisation of fallacies but added certain types of fallacy that he did not cover, amended some of his definitions, and in most cases substituted other examples. 

Three things should be noted:
- different authors may propose different categorisations (but our aim here is not to propose a fully worked out theory of fallacies, only help in identifying fallacies);
- often more than one thing is wrong with an argumentation; hence it may fit under two or more different categories;
- the list is not meant to be exhaustive: there is no end to the ways in which argumentation can go wrong, or fallacies can be classified. 

Caution: Often a fallacy can be detected only by those who sufficiently master appropriate technical or analytical skills or some intricate scientific theory. For example, many statistical fallacies will escape notice because only people well-versed in statistics, probability theory, or some other branch of mathematics have the requisite skills to expose them. Such fallacies fall outside the scope of this overview, which is concerned only with fallacies that any person with a modicum of common sense should be able to discover. 

Each fallacy is described in the following format:
  Name:          this is the widely accepted name of the fallacy
  Definition:    the fallacy is defined
  Examples:    examples of the fallacy are given
  Proof:           the steps needed to prove that the fallacy is committed

As a rule the examples are such that the fallacy is easy to spot. In 'real life' that is not always the case. Many fallacies are hidden deep below the surface of a text. It may take repeated close reading or listening to discover them. 

 


Non-Sequitur

Non sequitur is Latin for It does not follow
A non-sequitur is argument that is formally invalid. 


Affirming the Consequent
Definition: 
In a conditional statement If A then B A is called the antecedent and B the consequent
Any argument of the following form is invalid:
                    Premise 1:   If A then B
                    Premise 2:   B (affirmation of the consequent)
                    Conclusion: Therefore, A

Examples: 
(i) If I am in Brussels, then I am in Europe. I am in Europe; therefore, I am in Brussels. 
(The inference is invalid: even if the premises are true, the conclusion need not be.  I may be in Europe without being in Brussels; I may be, say, in Paris or London.)
(ii) If the government spends more money on public works then the rate of employment increases. The rate of employment increases; therefore the government is spending more money on public works. 
(The inference is invalid: even if the premises are true it is possible that the actual increase in the rate of employment has nothing to do with government spending on public works. It may be the result of, say, lower taxes, the abolition of protective tariffs, increased foreign investment.) 

Proof: 
Find or construct a counterexample to show that even though the premises are true, the conclusion could be false. In general, show that B might be true even if A is false.  

Remark:
*
Arguments of the following forms are valid:
                    Premise 1:   Only if A then B
                    Premise 2:   B 
                    Conclusion: Therefore, A

                    Premise 1:   If and only if A then B
                    Premise 2:   B 
                    Conclusion: Therefore, A

* Of course, arguments of this form are valid:
                    Premise 1:   If B then A
                    Premise 2:   B
                    Conclusion: Therefore, A
Note, however, that in many argumentations statements often are hedged, explicitly or implicitly, with qualifying clauses such as ceteris paribus (i.e. other things remaining as they are). Such a qualifying clause adds a condition! Thus
                    If B then ceteris paribus A 
is equivalent to
                    If (B and other things remain as they are) then A     
Consequently, to infer A one needs to argue
       Premise 1:    If (B and other things remain as they are) then A
       Premise 2:    B
       Premise 3:    Other things have not changed
       Conclusion:  A
The problem, of course, is that in most contexts "other things" is vague in the extreme. Moreover, it may not be clear which criteria are to be used for deciding whether we are dealing with two different independent things, two different but related or interacting things, or one thing under different names. 
For example, the expressions 'the rate of consumption' and 'the rate of saving' are different. Therefore, one who has no knowledge of economics might think of these rates as different things and say "The rate of consumption increases while the rate of savings remains the same". Such a speaker assumes that he can speak about the rate of consumption and include the rate of savings among 'the other things'.
However, a student of economics probably would object that the expressions merely refer in different ways to the same phenomenon and that therefore if one of those rates changes then the other also must change. (If you consume less of your income then you save more of your income; if you save less of your income then you consume more of it.) Thus, he assumes that if one is discussing the rate of consumption then one cannot include the rate of savings among 'the other things'.
Of course, different authors may have different technical definitions that diverge from the common understanding of the terms 'consumption' and 'savings'. Such definitions should be made explicit in any argumentation that uses them.


Denying the Antecedent
Definition: 
Any argument of the following form is invalid:
                     If A then B
                     Not A  (denial of the antecedent)
                     Therefore, Not B

This fallacy is formally equivalent to Affirming the consequent. That is so because
If A then B is logically equivalent to If not B then not A .
Hence Denying the antecedent amounts to Affirming the consequent
                    If not B then not A
                    Not A  (affirming the consequent)
                    Therefore, Not B

Examples: 
(i) If I am in Brussels then I am in Europe. I am not in Brussels; therefore, I am not in Europe.
(ii) If the government spends more money on public works then the rate of employment increases. The government does not spend more money on public works; therefore the rate of employment does not increase.  

Proof: 
Find or construct a counterexample to show that even though the premises are true, the conclusion could be false. In general, show that B might be true even if A is false.  


Inconsistency
Definition: 
The conclusion cannot be true if the premises of the argument are true.            

Examples: 
(i) Mary is the wife of John. Therefore, John is a bachelor.
(X is the wife of Y implies Y is married and this in turn implies Y is not a bachelor.)
(ii-a)  Tom is older than Harry and Harry is older than Dick. Therefore, Dick is older than Tom. 
(ii-b)  Tom is older than Harry and Harry is older than Dick. Therefore, Tom is younger than Dick.
(If the premises are true then Tom must be older than Dick--which contradicts the first conclusion that Dick is older than Tom, because if X is older than Y then Y is not older than X. It also contradicts the second conclusion that Tom is younger than Dick, because X is older than Y implies X is not younger than Y.)

Proof: 
Show that the premises imply a statement that contradicts or is incompatible with the purported conclusion.


Ex falso sequitur quodlibet
Definition:
Ex falso sequitur quodlibet means From a logically false premise anything whatsoever follows . This principle rests on the fact that if a premise of the argumentation cannot possibly be true, by any stretch of the imagination, then it is impossible to find or construct a counterexample in which the premise is true and the conclusion false--no matter what the conclusion may be. Assume that F stands for a necessarily false proposition; then both
                    If F then A and If F then not-A are formal tautologies.
Thus, an argument with inconsistent premises is always valid, no matter what the conclusion may be! Consequently, it neither proves nor supports any statement. 

Examples: 
(i) "Tom is older than Harry, Harry is older than Dick, and Tom is younger than Dick. Therefore, Dick is younger than Harry."
(ii)
(i) "Tom is older than Harry, Harry is older than Dick, and Tom is younger than Dick. Therefore, Dick is not younger than Harry."
(The first two premises imply that Tom is older than Dick and therefore that Tom is not younger than Dick--which contradicts the third premise that Tom is younger than Dick. In other words, the premises of the argument are inconsistent.  
Thus, while the arguments above are logically valid, they do not prove that Dick is younger than Harry; and they do not prove that Dick is not younger than Harry.) 

Proof: 
Show that the premises (or, if necessary the background assumptions) are inconsistent.


Mixed-up quantifiers
Definition:
Quantifiers (for example, all, some, none, one, two, most) tell us about how many objects in a class the speaker is referring, without naming or identifying any object in particular.
The fallacy of mixed-up quantifiers occurs when the speaker misidentifies the scope of particular quantifiers or replaces one quantifier by another..

Examples:
(i) Every living person has a biological father; therefore there is a person who is the biological father of every living person.
(Compare this to "There is a person who is the biological father of every living person; therefore every living person has a biological father", which is a valid inference, although the premise is false.)
(ii) He said that nobody agreed with him; therefore, he does not even agree with himself.
(Obviously, the person referred to meant 'nobody other than myself [i.e. I am the only one who] believes this'.)
(iii)  They say that men like to smoke. Well, let me tell you, I am a man and I don't like to smoke. Therefore, it is not true that men like to smoke.
(What 'they' meant was that some or even most men like to smoke, not that all men without exception like to smoke.)

Proof:
Identify the quantifiers used in the argument as well as their scope and point out where they were mixed up or replaced by another


Category Errors

These fallacies occur because the author mistakenly assigns something to a category in which it does not belong. Remember that things that belong to different categories are... categorically different.
Categories that often are confused are "whole" and "part" (things joined together may have different properties as a whole than any of them do separately) and "goal" and "means". 

Mistaken classification
Definition:
Things are assigned to a category to which they do not belong.

Examples:
(i) Red is a warm colour, blue is a cold colour. Therefore, painting a blue object red will raise its temperature.
(Colours and objects are categorically different. The words 'warm' and 'cold' have different meanings with respect to colours than they have with respect to objects.)
(ii) To celebrate the centennial of the nation the government will distribute a cheque drawable on the Central Bank of $100 to every citizen. Thus, thanks to this new money, we all shall be wealthier to the tune of $100, come next Wednesday.
(Wealth consists of useful and valuable goods, more wealth means more goods. Money is not wealth but a medium of exchange. More money does not mean more goods, merely more tickets to exchange for goods. Analogy: printing more entrance tickets to a cinema is not the same as adding more seats.)
(iii) Social security is a good thing. Therefore, it is irresponsible to oppose Social Security.
(Goals and means to that goal do not necessarily belong to the same category of things, even if they have the same name. It would be great if people had more social security. It does not follow that the existing system of administrations, entitlements, etc. that people call Social Security is a means, let alone a good means, to achieve that outcome.)
(iv) Demonstrating that there is a brain basis for adolescents' misdeeds allows us to blame adolescents' brains instead of the adolescents themselves.
(A brain by itself cannot commit misdeeds and neither can a brainless body, only persons can commit misdeeds. If one removes a person's brain then neither he nor his brain is a person.)

Proof:
Identify the things and the categories to which they belong and show where a thing is placed in the wrong category or where there is confusion of categories. 

Improper relation
Definition:
*
Some relations are reflexive: x is as old as x is necessarily true
*Some relations are anti-reflexive: x is wiser than x is necessarily false
*Some relations are symmetrical: if x is family of y is true then necessarily y is family of x is true.
*Some relations are anti-symmetrical: if x is longer than y is true then necessarily y is longer than x is false
*Some relations are transitive: if x older than y and y is older than z are true then necessarily x is older than z is true.
*Some relations are anti-transitive: if x is the biological father of  y and y is the biological father of z are true then necessarily x is the biological father of z is false.

The fallacy of improper relations occurs if the properties of a relation are mistaken

Examples: 
(i) John knows Mary and Mary knows Peter; therefore John knows Peter
(ii) Tom owes money to Dick, Dick owes money to Harry, and Harry owes money to Tom. Therefore, Tom owes money to Tom.
(Neither X knows Y nor X owes money to Y is a transitive relation.)
(iii) John dislikes Peter. Therefore, Peter dislikes John
( X dislikes Y is not a symmetrical relation.)
(iv) The friends of my friends are my friends. Therefore, the friends of his friends are his friends.

Proof:
Show that the relation in question does not have the properties presupposed in the argumentation. 

Composition
Definition 
Because the parts of a whole have a certain property, it is argued that the whole has that property. That whole may be either an object composed of different parts, or it may be a collection or set of individual members. 

Examples: 
(i) The French are rational. Therefore, France is rational.
(ii) A conventional bomb does less damage than a nuclear bomb. Therefore, conventional warfare is less damaging than nuclear warfare. 
(iii) All objects are finite. Therefore, the universe is finite.
(iv) Hydrogen is an atom, oxygen is an atom; therefore water is an atom.

Proof: 
Show that the properties in question are the properties of the parts, and not of the whole. If necessary, describe the parts to show that they could not have the properties of the whole.


Division
Definition: 
Because the whole has a certain property, it is argued that the parts have that property. The whole in question may be either a whole object or a collection or set of individual members.

Examples: 
(i) Europe is dying. Therefore, all Europeans are dying. 
(ii) France is a socialist country. Therefore, all the French are socialists.
(ii) Conventional warfare has killed many more people than nuclear warfare. Therefore, a conventional bomb is more lethal than a nuclear bomb. 
(iii) Because the universe is infinite, no object in it is finite.
(iv) At room temperature, water is liquid and water is a compound of hydrogen and oxygen; therefore, at room temperature, hydrogen and oxygen are liquid. 
(v) The construction industry has been losing money. Therefore, there all construction firms are in decline.

Proof: 
Show that the properties in question are the properties of the whole, and not of each part or member or the whole. If necessary, describe the parts to show that they could not have the properties of the whole.


Fallacies of Distraction

Each of these fallacies is characterized by the illegitimate use of a logical operator in order to distract the reader from the apparent falsity of a certain proposition.

False dilemma
Definition: 
An argument in an argumentation that specifies a limited number of options (usually two), while in reality there are more options. 

Examples: 
(i) Either you're for me or you're against me.
(ii) You save your money or you waste it.
(iii) Only a barbarian will oppose state-funding of schooling.

Proof: 
Identify the options given and show (with an example) that there is at least one additional option.


Argument from ignorance
(argumentum ad ignorantiam )
Definition: 
Argumentations of this form assume that what has not been proven false, is therefore true; or that what has not been proven true, is therefore false. 
(This is a special case of a false dilemma, the assumption here being that all propositions must either be known to be true or known to be false. The fact that there is no proof for statement S is not a proof of not-S.)

Examples: 
(i-a) I cannot prove your innocence; therefore, you must be guilty as charged. 
(i-b) I cannot prove your guilt; therefore, you are innocent.
(ii-a) Since scientists cannot prove that human activity does not cause global warming, it most likely is the result of human activity. 
(ii-b) Since scientists cannot prove that human activity causes global warming, it most likely is not the result of human activity. 
(iii-a) You can never prove that what I didn't do would have been better than what I did do. Therefore, what I did do was the best I could do.
(iii-b) You can never prove that what I didn't do would not have been better than what I did do. Therefore, what I did do was not the best I could do.

Proof: 
Ask if there is a direct proof of the conclusion. If there is none, show that by similar fallacious reasoning one would have to accept the opposite conclusion. 

Slippery slope
Definition: 
In order to show that a proposition P is unacceptable, a sequence of increasingly unacceptable events is alleged to follow from P (without proof that they must follow from it).. 

Examples: 
(i) If we pass laws against fully-automatic weapons, then it won't be long before we pass laws against all weapons, and then we will begin to restrict other rights, and finally we will end up living in a communist state. Thus, only communists will favour a ban on fully-automatic weapons.
(ii) You should never gamble. Once you start gambling you cannot to stop. Soon you are spending all your money on gambling, and eventually you will turn to crime to
support your earnings. Therefore, if you want to stay clear of crime, don't ever gamble.

(iii) If I make an exception for you then I have to make an exception for everyone.

Proof: 
Identify the proposition P being refuted and identify the final event in the series of events. Then show that this final event need not occur as a consequence of P.

Remark:
The slippery slope fallacy has the form P leads to Q . Do not confuse it with a warning of the form P may lead to Q (if one is not careful) .

Complex question
Definition: 
Two unrelated points are conjoined and treated as a single proposition. The audience is expected to accept or reject both together, when in reality one is acceptable while the other is not. The fallacy occurs most often as a move in debates and interrogations.

Examples: 
(i) - You said you do not beat your wife. When did you stop doing that?
    - I didn't stop... 
    - So, you admit being a wife-beater!

(If the person being questioned did not beat his wife ever then he could not have stopped beating his wife.)
(ii) Would you want us to believe that you care for the poor when you are on record as an opponent of minimum-wage legislation that aids the poor? Answer yes or no.
(One may oppose minimum-wage legislation precisely because one believes it hurts the poor, for example by pricing them out of the labour market.)
(iii) Did you or didn't you kill him with this knife? Answer yes or no.
(A negative answer, even a truthful one, does not rule out that the person being questioned killed the victim with his bare hands, some other instrument, perhaps another knife.)

Proof: 
Identify the two propositions illegitimately conjoined and show that believing one does not mean that you have to believe the other.



Appeals to Motives in Place of Support

The fallacies in this section have in common the practise of appealing to emotions or other psychological factors. But what causes an emotional response to a proposition is not a reason for believing it to be true, or false.

Appeal to force 
(argumentum ad baculum)
Definition: 
The audience is told that unpleasant consequences will follow if it does not agree with the author.

Examples: 
(i) You had better agree that this policy will save the country or you will never again be nominated for public office. 
(ii) Not paying your taxes is morally wrong, as you will find out when we throw you in jail. 
(iii) Those who do not support this war will suffer the righteous vengeance of their fellow citizens.  

Proof: 
Identify the threat and the proposition and point out that the threat is unrelated to the truth or falsity of the proposition. 


Appeal to pity
(argumentum ad misericordiam)
Definition: 
The reader is told to agree to the proposition out of pity with the speaker or others.

Examples: 
(i) This is a genuine gold watch, believe me, I am an honest hard-working poor man with a large family to support.
(ii) Increasing the minimum-wage will solve many of the problems related to poverty. So, support this legislation, if you care at all for the poor.  

Proof: 
Identify the proposition and the appeal to pity and point out that the pitiful state of the speaker or others has nothing to do with the truth or falsity of the proposition.


Appeal to consequences
(argumentum ad consequentiam)
Definition: 
The speaker mentions disagreeable consequences of holding a particular belief in order to show that this belief is false. Alternatively, the speaker mentions agreeable consequences of holding a particular belief in order to show that this belief is true.

Examples: 
(i) You can't agree that evolution is true, because if it were then we would be no better than monkeys and apes.
(ii) You must believe that evolution is true, because if it were not then we should accept that worms and vermin are our equals.
(iii) You must believe in God, for otherwise life would have no meaning. 
(iv) You cannot possibly believe in God, because if you did then you'd be no better than any religious zealot. 
(v) You shouldn't say that Mussolini made the trains run on time or people will think you're a neo-fascist.

Proof: 
Identify the consequences referred to and ask for a pertinent argument for or against the belief to which they are attached. 


Prejudicial language
Definition: 
By means of loaded or emotive terms the speaker positive or negative [moral] value to believing the proposition.

Examples: 
(i) All reasonable men will agree that taxes are the price we pay for civilisation.
(ii) A true feminist is a socialist and a democrat. 
(iii) Some critics allege that pay-as-you-go social security actually will make life more insecure. 
(iv) Some 'critics' say that pay-as-you-go social security actually will make life more insecure. 
(Note the use of scare quotes.)
(iv) That deficits do not matter is exactly what the Robber-in-chief said yesterday at his press conference. 
(A reference to the head of state or the government.)

Proof: 
Identify the prejudicial terms and ask for a pertinent argument for or against the proposition to which they are attached. 


Appeal to popularity
(argumentum ad populum)
Definition: 
A proposition is held to be true because it is widely held to be true or is held to be true by some part of the population with which the audience is believed to sympathise.

Examples: 
(i) Immigrants steal our jobs. Everybody knows that.
(ii) Exposing youngsters to explicit sex on television hampers their moral education? Only a few old people still believe that. 
(iii) This cream does wonders to your skin. Why else should so many of your favourite actresses and singers use it?  

Proof: 
Identify the appeal to popularity and ask for a pertinent argument for or against the proposition to which it is attached.


Changing the Subject

The fallacies in this section change the subject by discussing the person making the argument instead of discussing reasons to believe or disbelieve the conclusion.

While on some occasions it is useful to cite authorities, it is almost never appropriate to discuss the person instead of the argument.


Attacking the person 
(argumentum ad hominem)
Definition: 
The person presenting an argument is attacked instead of the argument itself. This takes many forms. For example, the person's character, nationality or religion may be attacked. Alternatively, it may be pointed out that a person stands to gain from a favourable outcome. Or, finally, a person may be attacked by association, or by the company he keeps.

There are three major forms of Attacking the Person:
(1) abusive ad hominem: instead of attacking an assertion, the argument attacks the person who made it.
(2) circumstantial ad hominem: instead of attacking an assertion the speaker points to the relationship between the person making the assertion and the person's circumstances.
(3) tu quoque ('you do the same'): this form of attack on the person notes that he does not exemplify or practise what he preaches or has no stronger case than one has oneself.

Examples: 
(i) Some say that HIV does not cause AIDS. They are merely attention seekers. (abusive ad hominem)
(ii) Fred is a libertarian. Libertarians favour the free market. Therefore, Fred is a stooge for the big corporations. 
(abusive ad hominem)
(ii) Politicians are in favour of pension reform. No wonder, they know their pensions will not be affected. 
(circumstantial ad hominem)
(iii) That company got the defense contract because it made the best offer? Don't you know that the sister-in-law of the Minister of Defence is on the Board of that company? 
(circumstantial ad hominem)
(iv) The senator opposes an open immigration policy. He should remember that his parents could come to this country only because of its open immigration policy. 
(tu quoque)
(v) You ask if I can prove that God created man. Can you prove that Man descended from the apes?
(tu quoque)

Proof: 
Identify the attack and show that the character or circumstances of the person has nothing to do with the truth or falsity of the proposition being defended.


Appeal to Authority
(argumentum ad verecundiam)
Definition: 
While sometimes it may be appropriate to cite an authority to support a point, often it is not. In particular, an appeal to authority is inappropriate if: 
(i) the person is not qualified to have an expert opinion on the subject,
(ii) experts in the field disagree on this issue.
(iii) the authority was making a joke, drunk, or otherwise not being serious 
A variation is the appeal to anonymous authorities and hearsay. An argument from hearsay is an argument which depends on second or third hand sources. 

Examples: 
(i) Socialist organisation of the economy is the one truly humane economic system. [Physicist] Albert Einstein and [philosopher] Bertrand Russell, among many others, said so. 
(ii) Saddam Hussein had weapons of mass destruction ready for use against the West in 2003. The President of the U.S.A said so and who would be better placed than he to know it? 
(iii) Saddam Hussein had no weapons of mass destruction ready for use against the West in 2003. The President of the France said so and who would be better placed than he to know it?
(iv) God does not play with dice. Not my words, but Einstein's.
(v) In Rome at one time one of the consuls was a horse. You can read it in Sallustius.
(vi) Franklin Delano Roosevelt ended the Great Depression of the 30's. It's true, most people you talk to will confirm it. 
(vii) Experts agree that deregulating the airlines will make flying more dangerous.

Proof: 
Always ask where the person cited argued for the reported view  and whether he was serious. At least ask whether his views on the matter at hand are generally accepted among people with a comparable or better claim to expertise. Dismiss arguments based on hearsay, at least until you are shown the evidence. 

Style Over Substance
Definition: 
The manner in which an argument (or arguer) is presented is taken to affect the likelihood that the conclusion is true.

Examples: 
(i) Who will doubt that our kids are in for a golden future, after hearing the stylish, witty and heartwarming lecture of Ms Xyz? 
(ii) Given his appeal to women, we can be sure this man will be a president of peace. 
(iii) He looks like Sherlock Holmes, he talks like Sherlock Holmes, he even dresses like Sherlock Holmes. He's a great detective. 

Proof: 
The truth or falsity of a statement does not depend on the manner in which the argument (or the arguer) is presented. Point this out and ask for pertinent arguments for or against the proposition that the speaker wants the audience to believe. 


Inductive Fallacies

Inductive reasoning consists in inferring from the properties of a sample to the properties of a population as a whole.


For example, suppose we have a barrel containing of 1,000 beans. Some of the beans are black and some of the beans are white. Suppose now we take a sample of 100 beans from the barrel and that 50 of them are white and 50 of them are black. Then we could infer inductively that half the beans in the barrel (that is, 500 of them) are black and half are white.
All inductive reasoning depends on the similarity of the sample and the population. The more similar the same is to the population as a whole, the more reliable will be the inductive inference. On the other hand, if the sample is relevantly dissimilar to the population, then the inductive inference will be unreliable.
No inductive inference is perfect. That means that any inductive inference can sometimes fail. Even though the premises are true, the conclusion might be false.
Nonetheless, a good inductive inference gives us a reason to believe that the conclusion is probably true.


Hasty Generalization
Definition: 
The size of the sample is too small to support the conclusion. 

Examples: 
(i) Osama bin Laden, probably the best known Muslim in the world today, is an enemy of the United States of America. This shows how any Muslim really thinks about the free world. 
(The inference from one Muslim to all Muslims is fallacious; so is the inference from 'enemy of the U.S.A.' to 'enemy of the [entire] free world'.)
(ii) All the people I talked to tonight said they liked my music. My music therefore really is popular. 

Proof: 
Identify the size of the sample and the size of the population, then show that the sample size is too small. Note: a formal proof would require a mathematical calculation. This is the subject of probability theory. For now, you must rely on common sense.


Unrepresentative Sample
Definition: 
The sample used in an inductive inference is relevantly different from the population as a whole.

Examples: 
(i) From our interviews with hundreds of prison inmates, most of them sex-offenders, we learned that many more men have homosexual experiences than is commonly believed. 
(ii) Having visited several Model Farms in the Soviet Union, I can assure you that collective farming guarantees the rural population a comfortable, rewarding life. 

Proof: 
Show how the sample is relevantly different from the population as a whole, then show that because the sample is different, the conclusion is probably different.


False Analogy
Definition: 
In an analogy, two objects (or events), A and B are shown to be similar. Then it is argued that since A has property P, so also B must have property P. An analogy fails when the two objects, A and B, are different in a way which affects whether they both have property P.

Examples: 
(i) Employees are like nails. Just as nails must be hit in the head in order to make them work, so must employees.
(ii)  Government is like a business, so just as a business will lose revenue if its customers are not satisfied with its services, just so government will lose revenue if the citizens don't like its policies.  
(Selling things to willing customers is not like taxing people that are within the area where a government has the effective power to tax.)
(iii) Socialists support socialism; therefore, capitalists support capitalism.
(A socialist is a supporter of socialism but a capitalist is a person with sizeable capital: nothing follows from this with respect to his ideology or political preferences. Some capitalists are / have been strong supporters of socialism.)
(iv) Society is like one person whose body is composed of many individual cells. Now, an individual person cannot hold a cell responsible for its actions. Therefore, society cannot hold individuals responsible for their actions.
(Society is an association of individual persons, all of whom are capable of responsibility, that is, asking and responding to questions; it is not like a biological organism, which consists of parts that are not capable of responsibility.)

Proof: 
Identify the two objects or events being compared and the property which both are said to possess. Show that the two objects are different in a way which will affect whether they both have that property.


Slothful Induction
Definition: 
The conclusion of an inductive argument is contrary to the evidence given.

Examples: 
(i) Having been rejected by more than ten publishers, I can only conclude that they don't even bother to read submissions from unknown authors.  
(ii) The government has been spending millions of euros and hundreds of thousands of man-hours on this problem, but it is still there. Clearly, we have underestimated how serious it is and we need to intensify our efforts. We need a bigger budget, more money and more powers to deal with it. 

Proof: 
Point to alternative conclusions that might be drawn from the evidence and show that they are at least as strongly supported by it as the conclusion proposed by the speaker. 


Fallacy of Exclusion
Definition: 
Important evidence which would undermine an inductive argument is excluded from consideration. The requirement that all relevant information be included is called the "principle of total evidence".

Examples: 
(i) Henri Lepage is French. The French overwhelmingly support the welfare state. Therefore Henri Lepage almost certainly supports the welfare state. 
(The information left out is that Henri Lepage is a French author who is a long-time critic of the welfare state.)
(ii) The records of the past fifteen years show that it is safe to invest in Company Xyz. I recommend that you put your money in it. 
(The information left out is that Company Xyz is now under investigation for serious accounting fraud and faces huge liability claims in connection with a series of accidents.) 

Proof: 
Give the missing evidence and show that it changes the outcome of the inductive argument. Note that it is not sufficient simply to show that not all of the evidence was included; it must be shown that the missing evidence will change the conclusion. 


Fallacies Involving Statistical Syllogisms

A statistical generalization is a statement which is usually true, but not always true. 

Very often these are expressed using the word "most", as in "Most conservatives favour welfare cuts." Sometimes the word "generally" is used, as in "Conservatives generally favour welfare cuts." Or, sometimes, no specific word is used at all, as in: "Conservatives favour welfare cuts."

Fallacies involving statistical generalizations occur because the generalization is not always true. Thus, when an author treats a statistical generalization as though it were always true, the author commits a fallacy. 


Accident
Definition: 
A general rule is applied when circumstances suggest that an exception to the rule should apply.

Examples: 
(i) Thou shall not kill. Therefore, you committed a mortal sin in shooting the raiders that attacked your family. 
(ii) It is forbidden to work without registration and a permit. Therefore, you should not help your mother with her housekeeping until you have acquired a permit and registered as domestic help. 
(iii) You say that people have a right to marry;  then you cannot deny that homosexual men have the right to marry.
(iv) Pornography has become a generally accepted fixture of our culture as well as a billion dollar business. Therefore, it is hypocritical to keep it out of the reach of youngsters.

Proof: 
Identify the generalization in question and show that it s not a universal generalization. Then show that the circumstances of this case suggest that the generalization ought not to apply.


Converse Accident
Definition: 
An exception to a general rule is presented as a general rule. 

Examples: 
(i) Because we allow some people to use marihuana for medicinal purposes, we should allow everyone to use it freely.
(ii) The King has the legal right to live at the expense of others; therefore, everybody should have the right to live at the expense of others. 
(iii) A married couple should be able to adopt children. Therefore, every person should be able to adopt a child otherwise we'll be practising discrimination.
(iv) While under hypnosis a person is not responsible for his actions; this shows that we are not responsible for for our actions. 

Proof: 
Identify the generalization in question and show how the case mentioned was an exception to the generalization.


Causal Fallacies

It is common for arguments to conclude that one thing causes another. But the relation between cause and effect is a complex one. It is easy to make a mistake.


In general, we say that C is the cause of an effect E if and only if:
(i) Most of the time, if C occurs, then E will occur, and
(ii) Most of the time, if C does not occur, then E will not occur ether.
We say "most of the time" because there always may be exceptions. For example:
We say that striking the match causes the match to light, because:
(i) Most of the time, when the match is struck, it lights (except, say, when the match is dunked in water), and
(ii) Most of the time, when the match is not struck, it does not light (except, say, when it is lit with a blowtorch).
Many writers also require that a causal statement be supported with a natural law.
For example, the statement that "striking the match causes it to light" is 
supported by the principle that "friction produces heat, and heat applied to an inflammable substance produces fire".


Coincidental Correlation 
(post hoc ergo prompter hoc)
Definition: 
The name in Latin means "after this therefore because of this". This describes the fallacy. A speaker commits the fallacy when he assumes that because one thing follows another the one thing was caused by the other, without considering other possible causes.

Examples: 
(i) Living standards in Europe rose enormously after the Second World War, when all European nations installed huge Social Security Administrations. Thus, we see that Social Security causes economic growth. 
(What about the return to a peace-time economy, the resumption of international trade, the availability of new technologies, and other factors?)
(ii) The Great Depression of the 1930's was caused by excessive speculation in the stock market in the late 1920's..
(iii) Prayers work. I prayed that my son would pass the examination and he did. 

Proof: 
Show that the correlation is coincidental by showing that: 
(i) the effect would have occurred even if the cause did not occur, or
(ii) that the effect was caused by something other than the suggested cause.


Joint Effect
Definition: 
One thing is held to cause another when in fact both are the effect of a single underlying cause. This fallacy is often understood as a special case of post hoc ergo prompter hoc.

Examples: 
(i) We are experiencing high unemployment which is being caused by a low consumer demand. 
(In fact, both may be caused by tax increases.)
(ii) You have a fever and this is causing you to break out in spots
(In fact, both symptoms are caused by the measles.)
(iii) The increase in AIDS was caused by more sex education in the schools.
(In fact, both phenomena may be caused by the sexual liberation ideology, which encouraged sexual experimentation and held that all varieties of sex are equally 'natural' or 'normal', and which was propagated by the mass media.) 
(iv) The Great Depression was caused by excessive speculation in the .
(But why was there excessive speculation? The causal explanation fails if the speculation was merely an early symptom of the economic malfunctioning that became evident to all in the Depression years. So, what caused this malfunctioning of the economy?)


Proof: 
Identify the two effects and show that they are caused by the same underlying cause. It is necessary to describe the underlying cause and prove that it causes each symptom.


Genuine but Insignificant Cause
Definition: 
The object or event identified as the cause of an effect is a genuine cause, but insignificant when compared to the other causes of that event.
Note that this fallacy does not apply when all other contributing causes are equally insignificant. Thus, it is not a fallacy to say that you helped to elect the present majority by voting for it, for your vote had as much weight as any other vote, and hence is equally a part of the cause. 

Examples: 
(i) Tax evasion causes the budget to be in deficit.
(This may be true but since tax evasion is more or less predictable it is largely accounted for in the budget; in any case, the major cause of budget deficits in any year is likely to be political reluctance to cut spending or to raise taxes.)
(ii) By leaving your kitchen lights on overnight you are contributing to the rise in energy prices. 

Proof: 
Identify the much more significant cause.


Wrong Direction
Definition: 
The relation between cause and effect is reversed.

Examples: 
(i) Among smokers we find more symptoms of stress than among non-smokers. This shows that, contrary to popular belief, smoking does not alleviate but tends to exacerbate stress.
(However, it is more likely that people who suffer from stress are more inclined to find relief in smoking or another stress alleviating practice. Also, persistent anti-smoking propaganda may induce stress in smokers.)
(ii) Costs determine prices.
(In fact, prices determine costs. If costs determined prices then no producer would ever suffer a loss, except if he had failed to add up his costs correctly. However, producers know that if they cannot keep the sum of all their costs below the price at which their product will sell, their enterprise will be unprofitable and will have to be scaled down, shut down or should not be undertaken at all.) 

Proof: 
Give a causal argument showing that the relation between cause and effect has been reversed.


Complex Cause
Definition: 
The effect is caused by a number of objects or events, of which the cause identified is only a part. A variation of this is the feedback loop where the effect is itself a part of the cause. 

Examples: 
(i) The building burnt down because much of the interior decoration was not fireproof.
(True, but the building would not have burnt down if there had not been a gas explosion, if the sprinkler system had been functioning, or if the flameproof doors had been closed.)
(ii) Price inflation in the 1970's was caused by the restriction of oil production instigated by the Organisation of Petroleum Exporting Countries (OPEC). 
(Assuming relatively inelastic demand for many petroleum products, that restriction certainly increased the price of such products but it did not explain the rise of other prices. The cause of the inflated price level must have been more complex than the one given in the statement.) 
(iii) Social and economic problems cause an increase in regulation. 
(This may be true, in some loose sense of the word 'cause', but regulations often lead people to change their way of life and of doing business. Thus regulations often upset previously existing practices and relationships and so create new problems in unforeseen areas, which then cause some people to call for more regulations. Thus, regulations become the cause of other regulations: a feedback loop.)

Proof: 
Show that all of the causes, and not just the one mentioned, are required to produce the effect.


Missing the Point

These fallacies have in common a general failure to prove that the conclusion is true.

Begging the Question ( petitio principii )
Definition: 
The truth of the conclusion is assumed by the premises.
Often, the conclusion is simply restated in the premises in a slightly different form. In more difficult cases, the premise is a consequence of the conclusion.

Examples: 
(i) Since I'm not mistaken, it follows that I'm telling the truth.
(ii) Since I'm not lying, it follows that I'm telling the truth.
(Here it may be argued that if lying implies the intention not to tell the truth then the speaker is presenting a false dilemma: either I lie or I tell the truth, without considering the possibility that he may be mistaken or misinformed.)
(ii) We know that God exists, since the Bible says God exists. What the Bible says must be true, since it is God's Word and God never lies. 
(Here, we must agree that God exists in order to believe that the Bible is the Word of God.)
(iii) Being a self-owner, I can sell myself  
(The argument presupposes that X owns Y implies X can sell Y , and therefore that only saleable things can be owned; but this is far from an uncontroversial background assumption. Thus, the argument begs the question it seeks to answer.)

Proof: 
Show that in order to believe that the premises are true we must already agree that the conclusion is true.


Irrelevant Conclusion ( ignoratio elenchi )
Definition: 
An argument which purports to prove one thing instead proves a different conclusion.

Examples: 
(i) You should support the new housing bill. We can't continue to see people living in the streets; we must have cheaper housing. 
(We may agree that housing is important even though we disagree with the housing bill.)
(ii) I say we should support affirmative action. White males have run the country for 500 years. They run most of government and industry today. You can't deny that this sort of discrimination is intolerable. 
(The speaker wants fewer white males in government and business but he has proven neither that the historical record shows discrimination, let alone intolerable discrimination, in favour of white males nor that affirmative action will reduce their numbers in government or business. Note the use of the prejudicial term 'intolerable')


Proof: 
Show that the conclusion proved by the author is not the conclusion that the author set out to prove.


Straw Man
Definition: 
The speaker attacks an argument which is different from, and usually weaker than, the opposition's best argument.

Examples: 
(i) He will not accept the evolutionary explanation of the origins of life because he neglects to consider the vastness of space and time and therefore underestimates the probability of a chance generation of life.
(Suppose that the person who is the subject of this critique actually said that to prove that something might have happened in some improbable way is not the same as proving that it did happen in that way. Then the speaker is attacking a straw man.) 
(ii) We should have conscription. People don't want to enter the military because they find it an inconvenience. But they should realize that there are more important things than convenience. 
(Most opponents of conscription have ethical / political reasons for their opposition. Moreover, the fact that a person does not want to enter the military because he finds it inconvenient does not make him a opponent of the conscription of others.)

Proof: 
Show that the opposition's argument has been misrepresented by showing that the opposition has a stronger argument. Describe the stronger argument.


Fallacies of Ambiguity

The fallacies in this section are all cases where a word or phrase is used unclearly.

There are two ways in which this can occur.
(i) The word or phrase may be ambiguous, in which case it has more than one distinct meaning.
(ii) The word or phrase may be vague, in which case it has no distinct meaning.


Equivocation
Definition: 
The same word is used with two different meanings.

Examples: 
(i) The sign said "fine for parking here", and since it was fine, I parked there.
(fine: a sum imposed as punishment for an offense, or all right)
(ii) Criminal actions are illegal; therefore criminal justice should be illegal too.
(criminal: having the nature of a crime, or pertaining to crimes or criminals.)
(iii) All child-murderers are inhuman, thus, no child-murderer is human
(iv) War is a human activity, so don't tell me war is inhuman.
(inhuman: not humane, lacking pity, kindness, mercy, or belonging to a class of things or beings other than human things or beings)

Proof:
Identify the word which is used twice, then show that a definition which is appropriate for one use of the word would not be appropriate for the second use.


Amphiboly
Definition: 
An amphiboly occurs when the construction of a sentence allows it to have two different meanings.

Examples: 
(i) Save soap and waste paper.
([Save soap] and [Waste paper], or Save [soap and paper])
(ii) I laughed at the postman in my tuxedo.
([I laughed at [the postman in my tuxedo]; or I [in my tuxedo] laughed at the postman) 
(iii) Charity gives poor free meals.
(Charity gives free meals to the poor; or Charity gives meals that are free and poor in quality)

Proof: 
Identify the ambiguous phrase and show the two possible interpretations.


Accent
Definition: 
Emphasis is used to suggest a meaning different from the actual content of the proposition.

Examples: 
(i) He did not kill a man.
(i-a) He did not kill a man.
(i-b) He did not kill a man.
(i-c) He did not kill a man.
(ii) The captain was sober when the accident occurred.
(ii-a) The captain was sober when the accident occurred.
(ii-b) The captain was sober when the accident occurred.
(iii) There were no violent crimes yesterday.
(iii-a) There were no violent crimes yesterday.
(iii-b) There were no violent crimes yesterday.

Proof: 
Show how the accentuation adds / suggests meaning that is not part of the proposition without the accent. 



Syllogistic Fallacies

The fallacies in this section are all cases of invalid categorical syllogisms. 
The following list does not include all types of fallacious syllogisms.


Fallacy of the Four Terms
(quaternio terminorum)
Definition: 
A standard categorical syllogism has three terms, e.g.
                     Maior premise: All swans are birds
                    
Minor premise: All birds are animals
                     Conclusio:        All swans are animals
The three terms are swans, birds and animals. The term birds, which occurs in both the maior and the minor premise is called the middle term. The fallacy of the four terms occurs when four terms are used.

Examples:
(i) All swans are birds, all ravens are animals; therefore all swans are animals. 
(The four terms are: swans, ravens, birds and animals.)

Note: In many cases, the fallacy of four terms is a special case of equivocation. While the same word is used, the word has different meanings, and hence the word should be treated as two different terms. Consider the following example:
(ii) Only man is capable of reason, and no woman is a man; therefore, no woman is capable of reason. 
(The four terms are: man, in the sense of human being, man, in the sense of male, women and capable of reason.)

Proof:
Identify the four terms and where necessary state the meaning of each term.


Undistributed Middle
Definition:
The middle term in the premises of a standard form categorical syllogism is assumed to identify the only relevant property of the things it describes. 

Examples:
(i) All swans are birds, and all ravens are birds, therefore, all ravens are swans.
(The middle term is 'birds'. The assumption here is that since ravens and swans both are birds, they are identical in all respects.) 
(ii) All the defenders died. One attacker died. Therefore, one attacker was a defender.
(The middle term is 'died'.)
(iii) All mice are animals, and some animals are not dangerous, therefore some mice are not dangerous.
(The middle term is 'animals'. The assumption is that since mice and beings that are not dangerous are animals, they are identical in all respects.)

Proof:
Show how each of the two categories identified in the conclusion could be separate groups even though they share a common property.


Illicit Major
Definition:
The predicate term of the conclusion refers to all members of that category, but the same term in the premises refers only to some members of that category.

Examples:
(i) All swans are birds, and no sparrows are swans; therefore, no sparrows are birds.
(The predicate term in the conclusion is 'birds'. The conclusion refers to all birds: not one bird is a sparrow. However, the premises refer only to some birds, namely swans).

Proof:
Show that there may be other members of the predicate category not mentioned in the premises which are contrary to the conclusion.

Concluding an Affirmative From a Negative
Definition:
The conclusion of a standard form categorical syllogism is affirmative, but at least one of the premises is negative.

Examples:
(i) All mice are animals, and some animals are not dangerous, therefore some mice are dangerous.
(ii) No honest people are thieves, and no honest people are liars; therefore, some thieves are liars

Proof:
Assume that the premises are true. Find an example which allows the premises to be true but which clearly contradicts the conclusion.



Fallacies of Explanation

An explanation is a form of reasoning which attempts to answer the question "why?" A good explanation will be based on a scientific or empirical theory. 

 

Subverted Support
Definition:
An explanation is intended to explain why some phenomenon happens. The explanation is fallacious if the phenomenon does not actually happen of if there is no evidence that it does happen.

Examples
(i) The airplane disappeared from the radar because it was flying too low.
(However, the airplane did not disappear from the radar; perhaps the radar operator is looking for an excuse for his own inattentiveness: he failed to notice the airplane's blip on the screen.)
(ii) Xyz killed the shopkeeper for the money.
(However, Xyz did not kill the shopkeeper.)

Proof
Identify the phenomenon which is being explained. Show that there is no reason to believe that the phenomenon has actually occurred.

Non-Support
Definition:
An explanation is intended to explain why some phenomenon happens. In this case, there is evidence that the phenomenon occurred, but it is trumped up, biased or ad hoc evidence.

Examples
(i) The reason why most bachelors are timid is that their mothers were domineering.
(A fallacy when said by a speaker who bases his generalization on two bachelors he once knew, both of whom were timid. See also hasty generalisaton.)
(ii) I never lost a game of chess. That's because I have an analytical mind. 
(A fallacy when said by a speaker who never played chess before or only played against pre-school children.) 

Proof
Identify the phenomenon which is being explained. Show that the evidence advanced to support the existence of the phenomenon was manipulated in some way.

Untestability
Definition
The theory advanced to explain why some phenomenon occurs cannot be tested.

We test a theory by means of its predictions. For example, a theory may predict that light bends under certain conditions, or that a liquid will change colour if sprayed with acid, or that a psychotic person will respond badly to particular stimuli. If the predicted event fails to occur, then this is evidence against the theory.

A theory cannot be tested when it makes no predictions. It is also untestable when it predicts events which would occur whether or not the theory were true.

Examples
(i) Every property of every thing or organism found in nature is the result of evolution.
(A property or thing that we could not trace to something from which it clearly or probably evolved, would be not be admitted as evidence against evolution. Rather, it would be said to have evolved from as yet unknown, possibly extinct predecessors.)
(ii) A man's actions are already predetermined long before his birth by the physical condition of the universe.
(However, it is impossible for any man to fully describe the physical condition of the universe at any time; therefore, our inability to predict how a man will act does not count as evidence against the theory. For the theory implies that a man's actions are predetermined, if not by known or knowable then by unknown and possibly unknowable elements or forces in the physical universe.) 
(iii) All natural things are what they are because God created them that way. 
(A refutation would require us to find some natural thing that is different from the way God created it. However, the theory holds that God's ways are inscrutable: we cannot find out God's intentions concerning any thing except by noting what the thing is, how it behaves or evolves, etc.)
(iv) The world we live in is the best of all possible worlds.
(v) The world we live in is the worst of all possible worlds.
(Obviously, we can observe only the world that exists. Therefore, we cannot compare empirically this world with another non-existing world to find out which of the two is better than the other.)

Proof
Identify the theory. Show that it makes no predictions, or that the predictions it does make cannot ever be proved wrong, even if the theory is false.


Limited Scope
Definition
The theory doesn't explain anything other than the phenomenon it explains.

Examples
(i) Germany lost the war because by 1918 it was exhausted. 
(ii) The rich can buy more and better things than the poor because they have more money. 

Proof
Identify the theory and the phenomenon it explains. Show that the theory does not explain anything else. Argue that theories which explain only one phenomenon are likely to be incomplete, at best.

Limited depth
Definition
Theories explain phenomena by appealing to some underlying cause or phenomena. Theories which do not appeal to an underlying cause, and instead simply appeal to membership in a category, commit the fallacy of limited depth.

Examples
(i) My cat likes tuna because she's a cat.
(Why do cats like tuna?)
(ii) Ronald Reagan was militaristic because he was American.
(What is it about being American that makes one militaristic?)
(iii) You're just saying that because you belong to the union.
(Why would union members say that?)

Proof
Theories of this sort attempt to explain a phenomenon by showing that it is part of a category of similar phenomenon. Accept this, then press for an explanation of the wider category of phenomenon. Argue that a theory refers to a cause, not a classification.


Fallacy of Exclusion
Definition:
Important evidence which would undermine an inductive argument is excluded from consideration. The requirement that all relevant information be included is called the
"principle of total evidence".

Examples:
(i) I'm good at chess because I never lost a game.
(The information left out is that the speaker never played a game of chess or only played against pre-school children.)
(ii) He had a motive for killing Xyz, he has confessed to having had the desire to kill Xyz; therefore, he is the most likely killer of Xyz.
(However, the information that the person referred to by the speaker was abroad at the time of the killing, is left out.) 

Proof:
Give the missing evidence and show that it changes the outcome of the inductive argument. Note that it is not sufficient simply to show that not all of the evidence was included; it must be shown that the missing evidence will change the conclusion.


Fallacies of Definition

In order to make our words or concepts clear, we use a definition. The purpose of a definition is to state exactly what a word means. A good definition should enable a reader to 'pick out' instances of the word or concept with no outside help.

For example, suppose we wanted to define the word "apple". If the definition is successful, then the reader should be able go out into the world and select every apple which exists, and only apples. If the reader misses some apples, or includes some other items (such as pears), or can't tell whether something is an apple or not, then the definition fails.

Definition is too broad
Definition
The definition includes items which should not be included.

Examples
(i) The definition of 'Man' is 'a two-legged featherless animal'.
(Is a chicken after its feathers have been removed a man? Is a kangaroo?) 
(ii) The definition of 'Apple' is 'something which is red and round'.
(Is the planet Mars, which is red and round, an apple?)
(ii) A figure is square if and only if it has four sides of equal length.
(Is a trapezoid with four equal sides a square?)

Proof
Identify the term being defined. Identify the conditions in the definition. Find an item which meets the condition but is obviously not an instance of the term.

Definition is too narrow
Definition
The definition does not include items which should be included.

Examples
(i) An apple is something which is red and round.
(Aren't Golden Delicious, which are green or yellow, apples?)
(ii) A book is pornographic if and only if it contains explicit pictures of people engaged in sexual activity. 
(Aren't the books written by the Marquis de Sade, which do not contain pictures, pornographic?)
(iii) Something is music if and only if it can be played on a flute.
(Aren't symphonic orchestrations, which cannot be played on a flute, music?)

Proof
Identify the term being defined. Identify the conditions in the definition. Find an item which is an instance of the term but does not meet the conditions.


Obfuscation or Failure to elucidate

Definition
The definition is no easier to understand than the term being defined.

Examples
(i) Someone is lascivious if and only if he is wanton.
("Wanton" is just as obscure as "lascivious".)
(ii) An object is more beautiful than another if and only if its aesthetic content is more complex.
("Complex aesthetical content" is harder to understand than "beautiful".)

Proof
Identify the term being defined. Identify the conditions in the definition. Show that the conditions are no more clearly defined than the term being defined.


Circular definition
Definition
The definition includes the term being defined as a part of the definition. A circular definition is a special case of a Failure to Elucidate.

Examples
(i) An animal is human if and only if it belongs to the human species. 
(ii) A book is pornographic if and only if it contains pornography.

Proof
Identify the term being defined. Identify the conditions in the definition. Show that at least one term used in the conditions is the same as the term being defined.

Conflicting conditions
Definition
The definition is self-contradictory.

Examples
(i) People are eligible to apply for a learner's permit (to drive) if they have (a) no previous driving experience, (b) access to a vehicle, and (c) experience operating a motor vehicle.
(A person cannot have experience operating a motor vehicle if they have no previous driving experience.)

Proof
Identify the conditions in the definition. Show that they cannot all be true at the same time (in particular, assume that one of the conditions is true, then show from this that another of the conditions must be false).