Inconsistency, Irrelevance, Insufficiency, and Inappropriate Presumption

Site: Saylor Academy
Course: PHIL102: Introduction to Critical Thinking and Logic
Book: Inconsistency, Irrelevance, Insufficiency, and Inappropriate Presumption
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Date: Wednesday, October 20, 2021, 12:31 PM


Read these four tutorials, which introduce four major classifications of fallacies. Although there are many possible ways of categorizing fallacies, the four major groups discussed in these tutorials are fairly standard.


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 cannot be the case that nothing is true or false.

    • "Morality is relative and it 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 true, it must also have an exception itself. This implies that not all general claims have exceptions. 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 near enough in that it is obviously false when being asserted. Consider these examples:

    • Young children are fond of saying "I am not here" when they are playing hide-and-seek. The statement itself is not logically inconsistent, since it is 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!

Source: Joe Lau and Jonathan Chan,
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.


Fallacies of relevance are of two kinds:

§1. Taking Irrelevant Considerations into Account

This includes defending a conclusion by appealing to irrelevant reasons, such as 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 somone 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 into making snappy decisions thinking that our decisions 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. 


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

Limited Sampling

    • Momofuku Ando, the inventor of instant noodles, died at the age of 96. He said he ate instant noodles everyday. 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.

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 lack of evidence is not enough to prove guilt.

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.

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.

Here are some examples: 

    • 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.