If . . . then? An Introduction to Logic.
Part 1. Section 4a

Part 1. Section 4a

[click here for Part 1. Section 3]

4. Logical Fallacies

 

So far we have concentrated on types of arguments which can either guarantee the truth of the conclusions given all true premises (valid arguments) or can provide good reasons to accept the truth of their conclusions (strong arguments based on induction). We now turn to a set of loosely connected types of bad reasoning which have occurred throughout the ages in public debates and arguments which are collectively known as logical fallacies.

 

Logical Fallacy

Definition: A logical fallacy is an an error in reasoning which has been particularly persuasive or common historically.

 

In other words, logical fallacies are not good arguments from a logical standpoint but turn out to still be persuasive for one reason or another. Here we do not consider fallacies which occur by virtue of the form of the argument, which are known as formal fallacies in other treatments, but rather only discuss fallacies based on certain characteristics which have 'psychological' appeal. To illustrate this, let's consider some actual examples of one particular fallacy type.

 

90% of the people in several independent polls report accepting the claim that O.J. Simpson was indeed guilty of the murder of his wife and Ron Goldman, so he must be guilty.

 

No one believes that Kara is telling the truth, hence she is lying.

 

In 1720 almost no one thought that slavery based on race was wrong, hence it wasn't in 1720.

 

In early Spring of 1912, everyone believed that the ocean liner RMS Titanic was impossible to sink, hence anyone travelling on the Titanic will arrive safely at their destination.

 

Notice that all of these arguments make a conclusion based only on what people believe or believed, but long experience tells us that belief alone is not sufficient to establish the truth or probability of a claim - one needs evidence or reasons for one's belief. Arguments that make inferences based on the beliefs of many people alone are a type of fallacy known as ad populum arguments (or 'appeal to the populace' arguments). The fact that popular belief alone is not sufficient to establish the truth of a claim is well known and readily agreed on by almost anyone pressed with the question and given time to consider several examples. Why then do ad populum fallacies exist? The answer to this question takes us beyond the study of logic, but we venture to make two observations which may help explain the continued popularity of so many fallacies.

  1. People mentally 'add' premises to fallacious arguments which make them stronger.
  2. There is an emotional appeal to such arguments which is strong enough to override critical thinking.

To give some motivation for 1, when hearing the first argument above it may be the case that there is an unspoken assumption by those who hear this argument that the people polled know about the evidence given in the 'trial of the century' and those polled were basing their conclusions on that evidence. Notice if this fact is indeed true, then the argument is modified to something of the form, "Most people polled knew the arguments in the OJ Simpson case and in several independent polls report … ". However, the argument given does not make this claim, and in evaluating it, one should be careful not to add information not given in the original argument.

For reason 2 we just note that there is often an observed conflict between one's emotions and logic. As a matter of fact, the ancient Greek Sophists were accused of exploiting this very difference in teaching the art of rhetoric rather than logic.

Whatever the reason for the continued use of fallacies, they are still very much with us and one's reasoning skills are greatly improved by having some familiarity with the most common fallacies. For the purposes of argument classification, all of the fallacies which follow, with the exception of circular reasoning, should be classified as weak arguments. Circular reasoning is an example of a valid argument which is valid by virtue of the fact that one of its premises is equivalent to the conclusion.

Below we present some common fallacies arranged in no particular order with a test yourself quiz at the end of each group. In the Section Review, there is also a Flashcard activity where you can review the fallacy names and definitions.

4.1 Accident, two ad hominems, all or nothing, equivocation and amphiboly

 

Accident

Consider the following argument:

Most homicides of females in their 20's are committed by someone they know or with whom they are in a current relationship, or a person with whom they have had a relationship in the recent past.

Susie Gordan, a 24 year old female, was found dead and the evidence clearly points to homicide but the evidence also indicates it was done by a local homeless man who has schizophrenia.

But that is probably wrong, since most homicides of females in their 20's are committed by people who have been in a relationship with the victim or are known to the victim, and the homeless person was unknown to the victim

Notice that the conclusion that the homicide was committed by a homeless man with schizophrenia is dismissed in favor of a general rule which is true of most homicides. When this happens we say that the argument has committed the fallacy known as accident. Why this name? Since the time at least of the ancient Greek philosophers, to understand the nature of a thing was to understand its essential properties. Non-essential properties were known as accidental properties which can vary or change without changing the essential nature of the thing. For example, the nature of a circle is the set of all points the same distance from a distinguished point known as the center of the circle. An accidental property of a circle is that distance (known as the radius), hence one can change the radius and still have a circle, so the actual value of the radius is an accidental property. With this in mind, the accidental fallacy ignores important known accidental properties in favor of general properties of something. This fallacy is sometimes known as 'destroying the exception' since it ignores important exceptions to a rule in favor of a general rule.

accidental fallacy

Definition: When an inference is made based on a general rule applied to a particular case where it does not apply, the resulting error in reasoning is known as an accidental fallacy (or a fallacy of accident).

 


Ad hominem abusive and circumstantial

Two closely related types of logical fallacies occur when some aspect of a person is attacked, rather than the claim or subject under debate.

(a) Don't expect my opponent to be tough on crime, his parents were Quakers and pacifists.

 

(b) Mr. Smith is a convicted criminal, hence his stance on education reform can't be trusted.

The first argument presented attacks the circumstances of the opponent being born of Quaker parents, rather than the opponent's actual views on crime - while the second attacks in a negative or abusive way a person's past rather than the person's stance on educational reform. Both types of arguments are forms of a fallacy known as an ad hominem (Latin for 'against the person'), the first being an ad hominem circumstantial and the second being an ad hominem abusive. It seems almost too obvious for words that such arguments hold little relevancy to the subject matter under debate, but their proliferation in political ads is but one indication of their persistent use and effectiveness.

Dilbert comic

In the above Dilbert cartoon, the secretary attacks the newspaper columnist instead of disputing the argument that the use of the word 'dongle' was indeed correct. The newspaper columnist also commits an ad hominem abusive by accusing the secretary of being a nutbag, but at least gives an additional justification for the use of the word 'dongle'.

 

ad hominem (against the person) abusive and circumstantial

Definition: An argument which negatively attacks some aspect of a person making a claim rather than the claim itself is known as an ad hominem abusive fallacy. When some circumstance pertaining to a person's life is attacked rather than the claim the person is making the resulting fallacy is known as an ad hominem circumstantial.

 


All or nothing fallacy

Recall that one way we can show that an inference is not valid is to show it is possible for all premises to be true and at the same time the conclusion could be false. When considering such possibilities it turns out that not all possibilities work, and part of the informal way of showing an inference is invalid is to explore many until one works. This means that the exploration of other possibilities is an integral part of logical reasoning. Our next fallacy stems from a failure to consider other possibilities. Consider what is wrong with the following inference about car crashes

Since the cause of the car crash was not careless driving, it must be due to the driver being extremely intoxicated.

 

Edward Snowden is a traitor or a hero, hence any judicial decision must take into account the consequences of dropping all charges against a traitor or criminally indicting a hero.

 

Notice in the first case when one possibility is rejected another extreme possibility is taken to be the conclusion, but there are many other possible causes of car crashes, and hence other possible conclusions. In the second Edward Snowden is classified as either a traitor or a hero, when other options also exist (a person with good intentions that went beyond what was needed to expose illegal data collection, for example).

Dilbert presents his boss with a false dichotomy

The type of fallacy which makes inferences based on only two possibilities, as if they were the only ones, is known as the all or nothing fallacy, which is sometimes called the black-white fallacy or the false dichotomy fallacy.

all or nothing fallacy

Definition: When an inference is made based on two options (many times extreme) are given as if they were the only ones when other options exist (which are many times more probable than the two presented), then the resulting error in reasoning is known as the all or nothing fallacy.

 


Equivocation and ambiguity

In July of 2008 the Phoenix Mars Lander successfully landed on the planet Mars and began the start of a mission of sending data back to earth, which included the composition of some icy soil on the surface of Mars. William Boynton of the University of Arizona, lead scientist for the the Thermal and Evolved Gas Analyzer (TEGA) was then quoted as saying,

"We have water. We've now finally touched it and tasted it—and from my standpoint it tastes very fine1."

Upon hearing this on the news an acquaintance of mine quipped, "Who would ever put something in their mouth that has been on another planet, much less taste it?"

1. Handwerk, Brian. "Mars Water Discovered, "Tasted" by Lander -- A First." National Geographic. National Geographic Society, 1 Aug. 2008. Web. 06 Aug. 2016.

The acquaintance made an error in reasoning by misunderstanding the meaning of 'taste' in the original quote, and concluded that it is unwise to put any Martian substance in one's mouth. As funny as this example is, it denotes another class of fallacies based on misunderstanding the meanings of terms, which can happen by ambiguity in words or phrases or ambiguity in grammar. When the ambiguity results in words or phrases the fallacy is called equivocation, on the other hand when the fallacy rests on an ambiguity in grammar the fallacy is known as amphiboly, two examples of which are given below. In the first case, the word 'unsweet' is confused with 'sugar-free', in the second 'face-lift' is confused with a literal lifting of one's face.

Tim requested a coffee without sugar, but the employee prepared a coffee with the sugar-free substitute Stevia instead.

dilberts co-worker checks the wrong meaning of facelift

 

These two fallacies have the following characteristic properties.

the fallacy of equivocation / amphiboly

Definition: When an inference is made based on an ambiguous word or phrase, the resulting fallacy is called equivocation. If the error in reasoning is based on a grammatical ambiguity the fallacy is known as amphiboly.

 


Test your ability to recognize the above fallacies by taking the following quiz:

quiz: fallacies 1

 Show quiz group

 

4.2 The anachronistic fallacy, appeals to inappropriate authority, the populace, nature, force, tradition and vanity and the tu quoque fallacy

 

The anachronistic fallacy

Everyone will readily agree that we live in a rapidly changing world, especially in terms of technological advances. The devices we use to view and access the web today almost certainly will not be the same devices we will use 10 years from now. Moreover, the changes are taking place so rapidly that at this writing facebook (will it exist in 10 years?) has many popular postings initiated by an older generation asking, "Who remembers this?", and indeed, who among those reading this now remembers a time when watching television was impossible if someone in the family wanted to use the vacuum cleaner or blow dry their hair (since both vacuums and blow driers produced strong radio waves that interfered with television reception)? These changes in time (Greek chronos) can cause errors in reasoning, and when that occurs the resulting fallacy is called an anachronistic fallacy. Consider the following erroneous inferences:

It has been stated that Theodore Roosevelt (October 27, 1858 – January 6, 1919) overcame his serious health issues as a child by embracing a strenuous lifestyle, however this statement is probably propaganda, since modern science has advanced leaps and bounds since the time when evil spirits were thought to be a cause of illness and leeches were given as treatment for disease. In particular, Roosevelt probably benefited greatly from penicillin which certainly saved him from more than one serious case of pneumonia.

 

My father who finished his PhD in 1978 in Mathematics is always telling me how hard it was to write up his dissertation, especially since he was a terrible speller and was always having to re-write entire pages to correct one error. But this is just an exaggeration, since spell checkers can be programmed to include even advanced mathematical vocabulary and when used, fix the errors in just a few seconds.

When Mary's grandmother heard that she needed a new mouse for her computer, she wondered why such a pesty rodent as that was required for Mary's computer.

The anachronism in the first example results from the fact that penicillin was not discovered for almost a decade after Roosevelt's death, and not put into mass production until the late 1940's. Similarly for the second argument, word processors which use spell checkers were not commonly used until after 1983. Dissertations were typed up using typewriters before that time. The last example might be considered an equivocation fallacy, and indeed it is not uncommon that the same error in reasoning can be classified as being more than one type of fallacy. We include it here since the conceptual error deals with a change in the meanings of the word 'mouse' over time.

anachronistic fallacy

Definition: When an inference is made resulting from the misappropriation of concepts and ideas in time, the resulting fallacy is known as an anachronistic fallacy.

Furthermore, the misplaced idea or object is called an anachronism.

 


Appeal to inappropriate authority

As noted above the world is rapidly changing. Such changes require further specializations of research areas which were once quite general. The general subject of biology has evolved to include several specializations, including molecular, micro, environmental and human, to name just a few. Even if we ignore such changes, the total number of skills and trades acquired by humans over their long history is so vast it is impossible for a single person to know all humankind's amassed knowledge. Who, for example, knows how to make paper, produce and manufacture antibiotics, send a spaceship into orbit or even weave a carpet? It is simply a matter of fact that we must appeal to authorities in various fields when we wish to learn more about certain subjects. Such appeals are appropriate and necessary - however when one bases an inference on an appeal to someone who does not have an expertise in a given field one commits the fallacy known as an inappropriate appeal to authority. Here are two examples: 

 

Our local weather man says the recent lull in tropical storms is not due to global warming and that he is doubtful such warming is real, hence global warming is a scam.

 

Usain Bolt, world record breaker in the 100 meter race said on television that Gatorade is the best drink for an active life-style, hence Gatorade is better than other sports drinks or even water.

People who study the effects of climate and climatic changes over time are known a climatologists - weather is not the same as climate (and arguments that equate them commit the fallacy of equivocation), hence the first example is an appeal to an inappropriate authority.

The Philosopher Arthur Shopenhauer's (1788 - 1860) view on the appeal to inappropriate authority fallacy:

When we come to look into the matter, so-called universal opinion is the opinion of two or three persons;…

We should find that it is two or three persons who, in the first instance, accepted it, or advanced and maintained it; and of whom people were so good as to believe that they had thoroughly tested it. Then a few other persons, … also accepted the opinion. These, again, were trusted by many others, whose laziness suggested to them that it was better to believe at once, than to go through the troublesome task of testing the matter for themselves. Thus the number of these lazy and credulous adherents grew from day to day; for the opinion had no sooner obtained a fair measure of support than its further supporters attributed this to the fact that the opinion could only have obtained it by the cogency of its arguments. The remainder were then compelled to grant what was universally granted, so as not to pass for unruly persons who resisted opinions which every one accepted, or pert fellows who thought themselves cleverer than any one else.

Shopenhauer, Arthur. The Art of Controversy and other Posthumous Papers. trans. T. Bailey Saunders. Swan, Sonnenschein and Co. New York. 1896, p. 38-39.

While it is true that Usain Bolt is a world recording holding sprinter, he is not someone who studies the nutritional needs of the human body or which liquids are best for different human activities, so this too is an appeal to inappropriate authority.

Here we should note that in new areas of study, sometimes the evidence does not clearly point one way or another - in such cases appropriate authorities will often disagree and appeal to appropriate authorities will often result in inconsistent claims. In these cases we just have to wait until the evidence points clearly in one direction or another and allow those who are authorities in the field to come to agreement. However, when appeals to people outside their area of expertise should always be treated with caution.

In some cases, even after the data is in and points to one direction, sometimes appeals to appropriate authority are combined with other fallacies to produce seemingly good inferences. For example, Profesor of Molecular and Cell Biology, Peter Deusberg of U C Berkeley claims that the HIV virus is not the cause of AIDS. His views are in sharp disagreement with a much larger percentage of experts in the field who dispute Dr. Duesberg's views. Since we are not experts in the field, which authorities do we believe? This is a hard question, but induction gives a good rule of thumb. Once sufficient evidence on a scientific phenomena has been collected and numerous papers and experiments conducted, a scientific consensus about the meaning of the evidence usually begins to emerge, at which point we should ask whether it is more probable than not that the majority census is incorrect and the minority is correct, especially when the minority is a very small percentage of those qualified in the field (here we assume all parties have access to the same set of experimental data and arguments about the data). Induction shows that usually the consensus view stands the test of time. This is not to say that new experimental evidence could not prove the majority wrong - it is not hard to find cases in the history of science where this has occurred. But that is not the context of this examination, where we assumed that all parties have access to all available experiments and all arguments on both sides. Also this is not to say that the consensus view, even under these stated conditions could not be wrong - it is however a statement about the strength of the conclusions drawn. At any rate, clearly examining arguments from both sides is never a bad idea before coming to a conclusion when considering appropriate appeals to authorities which disagree.

appeal to inappropriate authority

Definition: When an inference is made by appealing to someone in a celebrated or respected position on a topic which is not in the expertise of the person appealed to, the resulting fallacy is known as an appeal to inappropriate authority.

 


Ad populum

For our next fallacy, we revisit the fallacies we introduced in the beginning of this section, namely fallacies which appeal to the people as a means for establishing a conclusion. Below we repeat these examples and and then define these fallacies.

 

90% of the people in several independent polls report accepting the claim that O.J. Simpson was indeed guilty of the murder of his wife and Ron Goldman, so he must be guilty.

 

No one believes that Kara is telling the truth, hence she must be lying.

 

In 1720 almost no one thought that slavery based on race was wrong, hence it must not have been back in 1720.

 

In early Spring of 1912, everyone believed that the ocean liner RMS Titanic was impossible to sink, hence one could purchase a transatlantic ticket without fear of the ship sinking.

 

ad populum /appeal to the people fallacy

Definition: When an inference is made on the sole basis of what the majority of people believe or do not believe, then the resulting error in reasoning is known as the ad populum / appeal to the people fallacy.

 


Naturalistic fallacy

Consider the the following three arguments:

Allowing someone to take lethal medications to end their life prematurely is immoral because such drugs are not natural and one should only die a natural death.

Mammal populations reproduce by sexual intercourse between males and females. Such intercourse is natural and part of how nature made mammals, hence sexual intercourse between people of the same sex is not natural and therefore immoral.

Don't drink anything with artificial colors or sweeteners, they are unnatural and hence unhealthy.

 

In each case an inference is made based on whether something is natural or not in such a way as to imply that what is natural is good and what is unnatural is bad. This is bad reasoning. Many medicines used to cure or prevent diseases are not natural in the sense that they are man-made, and moreover neither is driving a car or taking a train for that matter – if one assumes that natural means something which is not man-made and could be found in nature without humans. Clearly the second argument does not depend on that definition but it is implied there that what non-human animals do is natural and we should not depart from any such practice. But non-human animals do many things that humans feel we should not do including abandoning their offspring when attacked , eating their offspring's placenta at birth, drinking from rivers or ponds without boiling or filtration and having sex with siblings, to list but a few differences.

While it is true that there are instances where food companies, for example, have added unnatural = artificial ingredients to foods to make them taste better and such additions have been the cause of cancer and other serious health issues, the reason was not that the additions are unnatural but rather the ingredients added have properties which turned out to cause cancer or other health problems in humans.

In any case, inferences made which claim that what is natural is good and what is unnatural is bad are called naturalistic fallacies.

 

naturalistic fallacy

Definition: Any inference which makes the claim that what is natural is good and what is unnatural is bad is called a naturalistic fallacy.


Appeal to force 

For our last fallacy in this group we consider inferences based on threats or force rather than reason. Consider the following examples:

 

If you don't believe that placing an amulet against the evil eye (mal de ojo) on your door protects against the spirits of ill will and bad health, then you will suffer terrible consequences.

You have to accept our position on immigration, otherwise not only you but the nation as a whole will pay a heavy price.

Relevant reasons, rather than force or an appeal to dire consequences should be given to support any claims. To appeal to bad consequences or force the conclusion on someone is to commit the logical fallacy known as appeal to force.

appeal to force

Definition: When force or bad consequences are used to support the truth of a claim the resulting error in reasoning is known as an appeal to force fallacy.


Appeal to tradition

As a species humans have a long history which is replete with traditions and customs. Think about how modern stores prepare for festive holidays like Christmas and Easter or how we have traditionally viewed the value of freedom of speech in the United States. With this is mind it is not surprising that these traditions can be used as justifications for claims even when such facts about tradition are irrelevant to the case. Consider for example the following arguments:

 

Females have traditionally never been allowed combat roles in the army, but instead have been given roles related to the care of the wounded, hence the proposed policy change to allow females a combat role in the army should be rejected.

For thousands of years, males were traditionally allowed to have more than one wife, hence males should continue this practice in current times.

In the Shamara society sick children were traditionally treated using native herbal medicines and ointments, so modern medicine should be rejected as it was never needed in the past.

When an argument's claim is supported by an appeal to what has always been the case, or traditions and customs, the resulting error in reasoning is known as an appeal to tradition fallacy.

appeal to tradition

Definition: When an inference is based on an appeal to tradition, custom or what has been the case in the past, the resulting error in reasoning is known as an appeal to tradition fallacy.

 


Appeal to pity

It is simply a known fact that humans do not make decisions based on logic alone. Indeed some decisions we make are entirely illogical. One reason for this is that emotions guide our actions sometimes as much or more than reason itself. A powerful human emotion is that of pity, and many arguments are made by appealing to pity rather than to relevant facts related to the claim at hand. Here is an example:

Homeless people everywhere face the end of each day without a shelter over their heads or a pace to call home. Imagine what that would be like! Hence, if you have any feelings at all of pity or compassion, you should support the Homeless Shelter Organization of America by sending a check or money order to the address you see at the end of this advertisement.

Notice that the claim that you should sent money to a specific organization is supposed to be supported on the sole basis of an emotional appeal. However, that appeal alone is insufficient to support the claim that you should send money. If reasons were given as to how your money helps alleviate the homeless situation and assurances that your money will be used almost exclusively to that end, then the claim that you should send money is made much stronger. When appeals to pity alone are made to support a claim, then the resulting fallacy is known as an appeal to pity.

appeal to pity

Definition: When an inference is made based on an appeal to pity alone the resulting fallacy is called an appeal to pity fallacy.

The appeal to pity fallacy gives a blueprint for many other similar types of fallacies which include appeals to vanity and snobbery, to name a few.

 


tu quoque

For our last fallacy in this section, consider the following argument:

The speaker of the house just voted for legislation restricting the use of marijuana, but just last week he was cited for using marijuana himself, hence his views against marijuana use is incorrect

Notice that the conclusion that marijuana use is bad is considered to be erroneous because the person coming to the conclusion himself uses marijuana - this type of reasoning is fallacious and is known as the tu quoque fallacy (lat. but you too!). To see this consider the following argument which is very similar in nature:

The speaker of the house just voted for legislation requiring children under a certain age or size to be required to use car seats. However just last week the speaker of the house was photographed with his two-year-old son in his car without a car seat, hence the conclusion that children under a certain age should be required to use car seats is wrong.

 

The nature of such fallacies rests in observing a certain inconsistency between a claim a person holds and a characteristic or public view possessed by the person holding the claim. In this sense the tu quoque fallacy is a type of ad hominem fallacy, but occurs so often we treat it as a distinct fallacy.

tu quoque fallacy

Definition: When an inference about a claim is rejected because some trait held by the person making the claim is inconsistent with the claim itself, the resulting error in reasoning is known as a tu quoque fallacy.

 


Now it is time to test your ability to recognize the above fallacies by taking the following quiz:

quiz: fallacies 2

   

 

Summary Section 4a

A logical fallacy is an an error in reasoning which has been particularly persuasive or common historically.

When an inference is made based on a general rule applied to a particular case where it does not apply, the resulting error in reasoning is known as an accidental fallacy (or a fallacy of accident).

An argument which negatively attacks some aspect of a person making a claim rather than the claim itself is known as an ad hominem abusive fallacy. When some circumstance pertaining to a person's life is attacked rather than the claim the person is making the resulting fallacy is known as an ad hominem circumstantial.

When an inference is made based on two options (many times extreme) are given as if they were the only ones when other options exist (which are many times more probable than the two presented), then the resulting error in reasoning is known as the all or nothing fallacy.

When an inference is made based on an ambiguous word or phrase, the resulting fallacy is called equivocation. If the error in reasoning is based on a grammatical ambiguity the fallacy is known as amphiboly.

When an inference is made resulting from the misappropriation of concepts and ideas in time, the resulting fallacy is known as an anachronistic fallacy. Furthermore, the misplaced idea or object is called an anachronism.

When an inference is made by appealing to someone in a celebrated or respected position on a topic which is not in the expertise of the person appealed to, the resulting fallacy is known as an appeal to inappropriate authority.

When an inference is made on the sole basis of what the majority of people believe or do not believe, then the resulting error in reasoning is known as the ad populum / appeal to the people fallacy.

Any inference which makes the claim that what is natural is good and what is unnatural is bad is called a naturalistic fallacy.

When force or bad consequences are used to support the truth of a claim the resulting error in reasoning is known as an appeal to force fallacy.

When an inference is based on an appeal to tradition, custom or what has been the case in the past, the resulting error in reasoning is known as an appeal to tradition fallacy.

When an inference is made based on an appeal to pity alone the resulting fallacy is called an appeal to pity fallacy.

When an inference about a claim is rejected because some trait held by the person making the claim is inconsistent with the claim itself, the resulting error in reasoning is known as a tu quoque fallacy.

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