Category: Informal Fallacies

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Informal Fallacies: Fallacy of Division

The fallacy of division, also known as “false deduction”, is a type of informal fallacy which occurs when the arguer mistakenly concludes that something is true to one or some of the parts of the whole simply because it is true of the whole. 

As we can see, the fallacy of division is the opposite of the fallacy of composition; as we may already know, the fallacy of composition is committed when the arguer erroneously assumes that something is true to the whole simply because it is true to some of the parts of the whole.

Let us consider the example below.

Example 1

One of the causes of poverty is laziness. Since 80 percent of the Filipino people are poor, then it can be logically argued that the Filipino people are lazy.

As we can see in the example above, the specific characteristic of the group as a whole (that is, the laziness of the Filipino people) is mistakenly attributed to all the members of the group (that is, the Filipino people are lazy). As the example illustrates, many Filipinos may have the characteristic of being lazy, which may be one of the causes of poverty. However, it is not safe to assume that the characteristic of being lazy is possessed by all the Filipino people taken individually. Thus, again, what is true of the whole is not necessarily true of the parts.

The examples below will further illustrate the nature and dynamics of the fallacy of division.

Example 2

The union voted to strike. Thus, every member of the union voted to strike.

Example 3

Humans are the only animals capable of philosophical thinking. Thus, every person is capable of philosophical thinking.

Example 4

Tomatoes are common in California. Therefore, since Los Angeles is in California, tomatoes are common in Los Angeles.

Example 5

The average beginning salary of college graduates with a major in nursing is USD 90, 000 per annum. Therefore, if I major in nursing, I can expect to begin at USD 90, 000.

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Either/Or Fallacy (or False Dichotomy)

An either/or fallacy, sometimes called false dichotomy, occurs when the arguer mistakenly reason from two alternatives, one claimed to be bad (that is, to be avoided) so that we ought to choose the other alternative. Put differently, an either/or fallacy consists of mistakenly assuming that there are only two possible solutions to some problem or that solving some problem consists of choosing between only two alternatives. 

Thus, in either/or fallacy or false dichotomy, the argument develops by showing that one of the alternatives is false or unacceptable and then concludes that the other must be true. 

Let us consider the example below.

Example 1

As I see it, either we enforce the death penalty or we eventually find the convicted murderer out on parole. We cannot have murderers going free, so we had better start enforcing the death penalty.

The example above has this from:

Either we enforce the death penalty or we eventually find the convicted murderer out on parole.


We cannot have murderers going free.
Therefore, we must enforce the death penalty.

The form of the argument is as follows:

Either P or Q
Not Q
Therefore, P

If one is familiar with a disjunctive proposition in symbolic logic, one may notice that the argument above is a valid argument form. Hence, the either/or fallacy or false dichotomy does not consist in the use of an invalid argument form. Rather, it consists in a false premise, that is, the premise that says that there are only two alternatives available in addressing the problem or, as in the case of the example above, the death penalty or parole for murderers.

Let us consider another example.

Example 2

President George W. Bush: If you are not with us, then you are against us.

We heard this famous line of the former president of the United State George W. Bush during his war against the Al Qaida. In his attempt to force the governments in the world to support him, he argued that if they are not with him, they are against him. Of course, it does not always follow that if one is not in favor of a particular idea, then he is against it. For sure, if one nation is not on the side of President George W. Bush in his war against the Al Qaida, it does not necessarily follow that it is against Bush.

The following examples below will further illustrate the either/or fallacy or false dichotomy.

Example 3

Either we give in to these terrorists’ demands and jeopardize the lives of thousands of Americans or we refuse and risk the lives of the hostages. Well, I for one will not risk the lives of the Americans all over the world. So, we must not give in to these terrorists.

Example 4

The idea of deliberately causing trauma, deliberately injuring the head of a living baboon, is extremely distasteful. But if we are not allowed to continue this research, then we will simply not learn how to treat human beings with head injuries. It is unfortunate, but it must be done.

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Notes in Informal Fallacies

Ignoratio Elenchi: ignorance of what is required to refute or establish a conclusion.

Kinds of Fallacies (Ignoratio Elenchi):

1) Argumentum Ad Hominem (Argument against the man): one which ignores the real claims or issues in the argument so that what is emphasized is the character, personality, or belief of the opponent.

Example:  Your honor, it is impossible for us not to believe that the accused of this murder case in not guilty, because the father and grandfather of the accused had been convicted of murder several years ago.  And besides, the accused is of bad moral reputation.

2) Argumentum Ad Ignorantiam (Appeal to Ignorance): arises when an argument is taken as true wherein it has not yet proven to be false, or an argument is false because this has not been proven as true.

Example: The existence of heaven must be true since nobody has ever successfully defended that it is just a product of imagination.

3) Argumentum Ad Verecundiam (Appeal to Authority): arise when one who has the difficulty in confronting or understanding complicated questions will seek refuge to the ideas, concepts, principles, or judgments of a person who enjoys a reputation as an expert  or an authority of the matter at issue.

Example: Anybody who does not go to church will not be saved according to St. Augustine.

4) Argumentum Ad Populum (Appeal to People): arises when one who, instead of concentrating on the relevant facts of the argument, gives more emphasis to the emotions and opinions of the people as basis of his conclusion.

Example: Budweisser is better than any other beer in the world because 90% of the Americans drink it.

5) Argumentum Ad Misericordiam (Appeal to Pity): arises when an appeal to evidence is replaced by an appeal to pity, mercy, or sympathy.

Example: Marco should not be given a failing mark in symbolic logic since he has taken the subject 3 times.

6) Argumentum Ad Baculum (Appeal to Force): arises when one appeals to intimidation, or use force in order to gain acceptance of his propositions or arguments.

Example: Parent to his son/daughter: You should study nursing; otherwise, I will not send you to College.

7) Accident : in this fallacy, general rules are applied to particular cases wherein such rule are applicable.

Example: The mark one gets in symbolic logic measures the kind of intelligence one has.  Chiara failed in symbolic logic.  Ergo, Chiara has low intelligence.

8) Converse Accident : just he opposite of the fallacy of accident

Example: Takyo is rich.  But Takyo is from the America.  So, all Americans are rich.

9) Tu Quoque : arises when one answers a charge of wrongdoing by a similar charge to his oppoent.

Example: If (the) father smokes, therefore, there is nothing wrong if (the) son smokes too.

10) False Cause: arises when one assigns as the cause those facts that merely preceded or accompanied the effect

Example: Satanas cuts the acacia tree near the Silliman AS building.  The following day, he died. Therefore, the cutting of the acacia tree is the cause of Satanas’ death.

11) Non Sequitor: arises when an argument, the conclusion categorically lacks connection with the proposition. 

Example: Jelo is a Sillimanian, therefore, he is a good debater.

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Logic: Informal Fallacies

In these notes, I will discuss some of the most common types of informal fallacies. These include: 

1) Appeal to Authority (Argumentum ad Verecundiam)

2) Appeal to People (Argumentum ad Populum).  

3) Appeal to Force (Argumentum ad Baculum)

4) Appeal to Pity (Argumentum ad Misericordiam)

5) Appeal to Ignorance (Argumentum ad Ignorantiam)

6) Argument against the Man (Argumentum ad Hominem)

7) False Cause

8) Slippery Slope

9) Either/Or Fallacy or False Dichotomy

10) Fallacy of Equivocation

11) Hasty Generalization

12) Fallacy of Composition

13) Fallacy of Division

14) We will update this page for more types of informal fallacies.

But before we discuss these common types of fallacious arguments, let us first briefly define the term fallacy.

A fallacy is generally understood as a kind of error in reasoning. Both deductive and inductive arguments can be fallacious. Some fallacious arguments are detectable by an examination of the form of the argument. Hence, they are called formal fallacies.

The techniques that logicians used in determining the validity of arguments in traditional and symbolic (or advanced) logic, such as the 8 rules of syllogism, and the truth table and partial truth table methods, enable them to recognize inconsistencies or errors in reasoning. These are called formal fallacies. All other types of fallacies are called informal fallacies, and they can be detected by an examination of the content of the argument itself.

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Appeal to Authority

An appeal to authority is a common type of fallacy that arises when one who has the difficulty in confronting or understanding complicated questions will seek refuge to the ideas, concepts, principles or judgments of a person who enjoys a reputation as an expert or an authority of the matter at issue. In other words, an appeal to authority is a fallacious argument in which the testimony of someone believed to be an authority is cited in support of a conclusion. It must be noted that the person being cited here is not, in fact, an expert or an authority on the matter or for some reason should not be relied upon. Thus, the fallacy of appeal to authority occurs when the authority cited is not qualified in the relevant matters or, less typically, is not free from adverse influences. Thus, the arguer is relying upon the assertions of someone who is not truly in a position to know.

Let us consider the following examples:

  1. I know your doctor says you need your appendix removed, but according to the famous herbalist Mar Lopez, people with your symptoms just need a change in their diet, plus a daily intake of MX3 capsule. So, forget about having your appendix removed.
  2. Augustine said there is no salvation outside the Catholic Church. That’s reasonable enough for me.

The underlying idea of such arguments is that some statement p is true because some authority q has said it is true. The argument’s basic structure is this:

Authority p asserts that q.
Therefore, q.

Here, we see immediately that such an argument is neither valid nor inductively strong, since the mere fact that someone asserts q neither makes it so nor makes it probable. Typically, however, the arguer believes more than the mere fact that p asserts that q. The arguer very likely is assuming such things as that p is someone who knows what he or she is talking about regarding q, or that p is speaking without bias, or that p is telling the truth. If those or similar assumptions are well founded, then the appeal to authority p may constitute a good argument, that is, non-fallacious reasoning. It must be noted that not all appeals to authority are fallacious. In fact, some appeal to authority may be inductively strong. After all, we should accept the testimony of qualified and unbiased experts, for there are indeed experts in their own right.

Now, to identify an appeal to authority fallacy, we ask two questions:  1) Is the authority, in fact, a qualified authority about matters related to q? and 2) Is there any good reason to believe that the authority may be biased in matters related to q?

Regarding Example #1 above, we should ask whether Mar Lopez is qualified to claim that proper diet and daily intake of MX3 capsule will render the removal of someone’s appendix unnecessary. So, is Mar Lopez an expert in human anatomy? Can he provide a scientific proof that proper diet and daily intake of MX3 capsule will render the removal of someone’s appendix unnecessary?

Regarding Example #2, we should ask whether St. Augustine, although he was a famous Catholic theologian, has proofs that heaven and hell really exist. As a matter of fact, issues about heaven and hell are very complicated ones. In fact, nobody has proven that indeed heaven and hell exist. If this is the case, how can we meaningfully talk about salvation?

A common variation on the appeal to authority is an appeal to a magazine or newspaper article or a radio or TV program. Consider this example:

“They have found a cure for cancer. I read about it in The New York Times.”

In such case, we ought to ask the same question: Is the source cited a reliable one in this matter? Ordinarily, we should be very suspicious of medical breakthroughs reported in The New York Times, though not of such breakthroughs reported in, say, the Journal of the American Medical Association. On the other hand, we would not expect to get reliable advice on the news or current events in a medical journal. Hence, the appeal to authority fallacy occurs when an argument is supported by reference to a publication or program not known for specialization on the subject.

In summary, not all appeals to authority are fallacious. The appeal to authority fallacy only occurs when an arguer appeals to someone who is not an expert in the field for which he or she is cited as support or who is not unbiased.

To recognize the appeal to authority fallacy, we need only look for an argument based primarily on the premises that some person (or some publication) reports that q is true. The fallacy occurs when the person (or publication) is not relevantly qualified or is not speaking without bias.

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