I. What Are Fallacies?¹

Fallacies are mistakes of reasoning, as opposed to making mistakes that are of a factual nature. If I counted twenty people in the room when there were in fact twenty-one, then I made a factual mistake. On the other hand, if I believe that there are round squares I believe something that is contradictory. A belief in “round squares” is a mistake of reasoning and contains a fallacy because, if my reasoning were good, I would not believe something that is logically inconsistent with reality.

In some discussions, a fallacy is taken to be an undesirable kind of argument or inference. In our view, this definition of fallacy is rather narrow, since we might want to count certain mistakes of reasoning as fallacious even though they are not presented as arguments. For example, making a contradictory claim seems to be a case of fallacy, but a single claim is not an argument. Similarly, putting forward a question with an inappropriate presupposition might also be regarded as a fallacy, but a question is also not an argument. In both of these situations though, the person is making a mistake of reasoning since they are doing something that goes against one or more principles of correct reasoning. This is why we would like to define fallacies more broadly as violations of the principles of critical thinking, whether or not the mistakes take the form of an argument.

The study of fallacies is an application of the principles of critical thinking. Being familiar with typical fallacies can help us avoid them and help explain other people’s mistakes.

There are different ways of classifying fallacies. Broadly speaking, we might divide fallacies into four kinds:

• Fallacies of inconsistency: cases where something inconsistent or self-defeating has been proposed or accepted.
• Fallacies of relevance: cases where irrelevant reasons are being invoked or relevant reasons being ignored.
• Fallacies of insufficiency: cases where the evidence supporting a conclusion is insufficient or weak.
• Fallacies of inappropriate presumption: cases where we have an assumption or a question presupposing something that is not reasonable to accept in the relevant conversational context.

II. Fallacies of Inconsistency

Fallacies of inconsistency are cases where something inconsistent, self-contradictory or self-defeating is presented.

1. Inconsistency

Here are some examples:

• “One thing that we know for certain is that nothing is ever true or false.” – If there is something we know for certain, then there is at least one truth that we know. So it can’t be the case that nothing is true or false.
• “Morality is relative and is just a matter of opinion, and so it is always wrong to impose our opinions on other people.” – But if morality is relative, it is also a relative matter whether we should impose our opinions on other people. If we should not do that, there is at least one thing that is objectively wrong.
• “All general claims have exceptions.” – This claim itself is a general claim, and so if it is to be regarded as true we must presuppose that there is an exception to it, which would imply that there exists at least one general claim that does not have an exception. So the claim itself is inconsistent.

2. Self-Defeating Claims

A self-defeating statement is a statement that, strictly speaking, is not logically inconsistent but is instead obviously false. Consider these examples:

• Very young children are fond of saying “I am not here” when they are playing hide-and-seek. The statement itself is not logically consistent, since it is not logically possible for the child not to be where she is. What is impossible is to utter the sentence as a true sentence (unless it is used for example in a telephone recorded message.)
• Someone who says, “I cannot speak any English.”
• Here is an actual example: A TV program in Hong Kong was critical of the Government. When the Hong Kong Chief Executive Mr. Tung was asked about it, he replied, “I shall not comment on such distasteful programs.” Mr. Tung’s remark was not logically inconsistent, because what it describes is a possible state of affairs. But it is nonetheless self-defeating because calling the program “distasteful” is to pass a comment!

III. Fallacies of Relevance

1. Taking irrelevant considerations into account

This includes defending a conclusion by appealing to irrelevant reasons, e.g., inappropriate appeal to pity, popular opinion, tradition, authority, etc. An example would be when a student failed a course and asked the teacher to give him a pass instead, because “his parents will be upset.” Since grades should be given on the basis of performance, the reason being given is quite irrelevant.

Similarly, suppose someone criticizes the Democratic Party’s call for direct elections in Hong Kong as follows: “These arguments supporting direct elections have no merit because they are advanced by Democrats who naturally stand to gain from it.” This is again fallacious because whether the person advancing the argument has something to gain from direct elections is a completely different issue from whether there ought to be direct elections.

2. Failing to Take Relevant Considerations into Account

For example, it is not unusual for us to ignore or downplay criticisms because we do not like them, even when those criticisms are justified. Or sometimes we might be tempted to make a snap decision, believing knee-jerk reactions are the best when, in fact, we should be investigating the situation more carefully and doing more research.

Of course, if we fail to consider a relevant fact simply because we are ignorant of it, then this lack of knowledge does not constitute a fallacy.

IV. Fallacies of Insufficiency

Fallacies of insufficiency are cases where insufficient evidence is provided in support of a claim. Most common fallacies fall within this category. Here are a few popular types:

1. Limited Sampling

• Momofuku Ando, the inventor of instant noodles, died at the age of 96. He said he ate instant noodles every day. So instant noodles cannot be bad for your health.
• A black cat crossed my path this morning, and I got into a traffic accident this afternoon. Black cats are really unlucky.

In both cases the observations are relevant to the conclusion, but a lot more data is needed to support the conclusion, e.g., studies show that many other people who eat instant noodles live longer, and those who encounter black cats are more likely to suffer from accidents.

2. Appeal to Ignorance

• We have no evidence showing that he is innocent. So he must be guilty.

If someone is guilty, it would indeed be hard to find evidence showing that he is innocent. But perhaps there is no evidence to point either way, so a lack of evidence is not enough to prove guilt.

3. Naturalistic Fallacy

• Many children enjoy playing video games, so we should not stop them from playing.

Many naturalistic fallacies are examples of fallacy of insufficiency. Empirical facts by themselves are not sufficient for normative conclusions, even if they are relevant.

There are many other kinds of fallacy of insufficiency. See if you can identify some of them.

V. Fallacies of Inappropriate Presumption

Fallacies of inappropriate presumption are cases where we have explicitly or implicitly made an assumption that is not reasonable to accept in the relevant context. Some examples include:

• Many people like to ask whether human nature is good or evil. This presupposes that there is such a thing as human nature and that it must be either good or bad. But why should these assumptions be accepted, and are they the only options available? What if human nature is neither good nor bad? Or what if good or bad nature applies only to individual human beings?
• Consider the question “Have you stopped being an idiot?” Whether you answer “yes” or “no,” you admit that you are, or have been, an idiot. Presumably you do not want to make any such admission. We can point out that this question has a false assumption.
• “Same-sex marriage should not be allowed because by definition a marriage should be between a man and a woman.” This argument assumes that only a heterosexual conception of marriage is correct. But this begs the question against those who defend same-sex marriages and is not an appropriate assumption to make when debating this issue.

VI. List of Common Fallacies

ad hominem

A theory is discarded not because of any evidence against it or lack of evidence for it, but because of the person who argues for it. Example:

A: The Government should enact minimum-wage legislation so that workers are not exploited.
B: Nonsense. You say that only because you cannot find a good job.

ad ignorantiam (appeal to ignorance)

The truth of a claim is established only on the basis of lack of evidence against it. A simple obvious example of such fallacy is to argue that unicorns exist because there is no evidence against their existence. At first sight it seems that many theories that we describe as “scientific” involve such a fallacy. For example, the first law of thermodynamics holds because so far there has not been any negative instance that would serve as evidence against it. But notice, as in cases like this, there is evidence for the law, namely positive instances. Notice also that this fallacy does not apply to situations where there are only two rival claims and one has already been falsified. In situations such as this, we may justly establish the truth of the other even if we cannot find evidence for or against it.

ad misericordiam (appeal to pity)

In offering an argument, pity is appealed to. Usually this happens when people argue for special treatment on the basis of their need, e.g., a student argues that the teacher should let them pass the examination because they need it in order to graduate. Of course, pity might be a relevant consideration in certain conditions, as in contexts involving charity.

ad populum (appeal to popularity)

The truth of a claim is established only on the basis of its popularity and familiarity. This is the fallacy committed by many commercials. Surely you have heard of commercials implying that we should buy a certain product because it has made to the top of a sales rank, or because the brand is the city’s “favorite.”

Affirming the consequent

Inferring that P is true solely because Q is true and it is also true that if P is true, Q is true.

The problem with this type of reasoning is that it ignores the possibility that there are other conditions apart from P that might lead to Q. For example, if there is a traffic jam, a colleague may be late for work. But if we argue from his being late to there being a traffic jam, we are guilty of this fallacy – the colleague may be late due to a faulty alarm clock.

Of course, if we have evidence showing that P is the only or most likely condition that leads to Q, then we can infer that P is likely to be true without committing a fallacy.

Begging the question (petito principii)

In arguing for a claim, the claim itself is already assumed in the premise. Example: “God exists because this is what the Bible says, and the Bible is reliable because it is the word of God.”

Complex question or loaded question

A question is posed in such a way that a person, no matter what answer they give to the question, will inevitably commit themselves to some other claim, which should not be presupposed in the context in question.

A common tactic is to ask a yes-no question that tricks people into agreeing to something they never intended to say. For example, if you are asked, “Are you still as self-centered as you used to be?”, no matter whether you answer “yes” or ”no,” you are bound to admit that you were self-centered in the past. Of course, the same question would not count as a fallacy if the presupposition of the question were indeed accepted in the conversational context, i.e., that the person being asked the question had been verifiably self-centered in the past.

Composition (opposite of division)

The whole is assumed to have the same properties as its parts. Anne might be humorous and fun-loving and an excellent person to invite to the party. The same might be true of Ben, Chris and David, considered individually. But it does not follow that it will be a good idea to invite all of them to the party. Perhaps they hate each other and the party will be ruined.

Denying the antecedent

Inferring that Q is false just because if P is true, Q is also true, but P is false.

This fallacy is similar to the fallacy of affirming the consequent. Again the problem is that some alternative explanation or cause might be overlooked. Although P is false, some other condition might be sufficient to make Q true.

Example: If there is a traffic jam, a colleague may be late for work. But it is not right to argue in the light of smooth traffic that the colleague will not be late. Again, his alarm clock may have stopped working.

Division (opposite of composition)

The parts of a whole are assumed to have the same properties as the whole. It is possible that, on a whole, a company is very effective, while some of its departments are not. It would be inappropriate to assume they all are.

Equivocation

Putting forward an argument where a word changes meaning without having it pointed out. For example, some philosophers argue that all acts are selfish. Even if you strive to serve others, you are still acting selfishly because your act is just to satisfy your desire to serve others. But surely the word “selfish” has different meanings in the premise and the conclusion – when we say a person is selfish we usually mean that he does not strive to serve others. To say that a person is selfish because he is doing something he wants, even when what he wants is to help others, is to use the term “selfish” with a different meaning.

False dilemma

Presenting a limited set of alternatives when there are others that are worth considering in the context. Example: “Every person is either my enemy or my friend. If they are my enemy, I should hate them. If they’re my friend, I should love them. So I should either love them or hate them.” Obviously, the conclusion is too extreme because most people are neither your enemy nor your friend.

Gambler’s fallacy

Assumption is made to take some independent statistics as dependent. The untrained mind tends to think that, for example, if a fair coin is tossed five times and the results are all heads, then the next toss will more likely be a tail. It will not be, however. If the coin is fair, the result for each toss is completely independent of the others. Notice the fallacy hinges on the fact that the final result is not known. Had the final result been known already, the statistics would have been dependent.

Genetic fallacy

Thinking that because X derives from Y, and because Y has a certain property, that X must also possess that same property. Example: “His father is a criminal, so he must also be up to no good.”

Non sequitur

A conclusion is drawn that does not follow from the premise. This is not a specific fallacy but a very general term for a bad argument. So a lot of the examples above and below can be said to be non sequitur.

Post hoc, ergo propter hoc (literally, “after this, therefore because of this”)

Inferring that X must be the cause of Y just because X is followed by Y.

For example, having visited a graveyard, I fell ill and infer that graveyards are spooky places that cause illnesses. Of course, this inference is not warranted since this might just be a coincidence. However, a lot of superstitious beliefs commit this fallacy.

Red herring

Within an argument some irrelevant issue is raised that diverts attention from the main subject. The function of the red herring is sometimes to help express a strong, biased opinion. The red herring (the irrelevant issue) serves to increase the force of the argument in a very misleading manner.

For example, in a debate as to whether God exists, someone might argue that believing in God gives peace and meaning to many people’s lives. This would be an example of a red herring since whether religions can have a positive effect on people is irrelevant to the question of the existence of God. The positive psychological effect of a belief is not a reason for thinking that the belief is true.

Slippery slope

Arguing that if an opponent were to accept some claim C₁, then they have to accept some other closely related claim C₂, which in turn commits the opponent to a still further claim C₃, eventually leading to the conclusion that the opponent is committed to something absurd or obviously unacceptable.

This style of argumentation constitutes a fallacy only when it is inappropriate to think if one were to accept the initial claim, one must accept all the other claims.

An example: “The government should not prohibit drugs. Otherwise the government should also ban alcohol or cigarettes. And then fatty food and junk food would have to be regulated too. The next thing you know, the government would force us to brush our teeth and do exercises every day.”

Straw man

Attacking an opponent while falsely attributing to them an implausible position that is easily defeated.

Example: When many people argue for more democracy in Hong Kong, a typical “straw man” reply is to say that more democracy is not warranted because it is wrong to believe that democracy is the solution to all of Hong Kong’s problems. But those who support more democracy in Hong Kong never suggest that democracy can solve all problems (e.g., pollution), and those who support more democracy in Hong Kong might even agree that blindly accepting anything is rarely the correct course of action, whether it is democracy or not. Theses criticisms attack implausible “straw man” positions and do not address the real arguments for democracy.

Suppressed evidence

Where there is contradicting evidence, only confirming evidence is presented.