Fallacies are arguments which make use of a mistake in reasoning. They do count as arguments, but are faulty arguments. There is an inappropriate connection between premises an conclusion. Formal fallacies are fallacies where there is an inappropriate logical connection. Substantive (informal) fallacies involve reliance or unjustified assumptions or inferences. Substantive fallacies are different from unsound arguments in the sense that the false premise is of general nature and has nothing to do specifically with the subject.

There are several formal fallacies:

1. Affirming the consequent
   This is affirming the consequent and using this to reason that the antecedent must be true because of this.
   --------------
   If A, then B
   B
   --------------
   A
2. Denying the antecedent
   This is denying the antecedent and using this to reason that the consequent must be false because of this.
   -----------------
   If A, then B
   Not A
   -----------------
   Not B
3. Deriving ought from is
   A prescriptive conclusion cannot be validly derived from purely descriptive premises.
4. Base rate fallacy
   This is neglecting the base rate to make a conclusion.

There are several informal fallacies:

1. Majority belief
   This is concluding that the proposition is true on the basis that the majority beliefs that the proposition is true.
2. Common practice
   This is concluding that the proposition is true on the basis that ‘everyone does it’.
3. Gambler’s fallacy
   This is concluding that the probability of winning something is increased because of previous events (e.g. roulette ball falls on red twice in a row, so it must be black now).
4. Ad hominem
   This is responding to a claim by making an attack upon the person or by rejecting a claim because of dislike for the person making the claim.
5. Ad hominem circumstantial
   This is believing an argument is discounted because the person making the argument would allegedly benefit from people believing the argument (e.g. academic want more students because they will have more jobs).
6. Tu quoque (you too)
   This is making unwarranted connections between a person’s alleged lack of credibility and the strength of their argument. It assumes that whenever a person’s behaviour is inconsistent with their advice, we should not take it seriously or it is false.
7. Appeal to authority
   This is an unjustified appeal to authority.
8. The perfectionist fallacy
   This is placing excessive demands on an idea or a proposal and reject the idea or proposal solely because it will not completely solve a problem.
9. Conflation of morality with legality
   This is assuming that anything that is legal must be moral or that anything that is illegal must be immoral. It is summarised in: ‘there’s no law against it, so it’s acceptable’.
10. Weak analogy
    This is assuming that if one thing is similar to another in one aspect, it is similar in all aspects. It also assumes that things that are similar to each other in every way should be treated the same. Analogies can be effective, if the analogy is argued for.

There are several causal fallacies:

1. Post hoc ergo propter hoc (after that, this, therefore this because of that)
   This is inferring that an event caused another event merely on the basis that one event occurred after the other.
2. Mistaking correlation for cause
   This is assuming that correlation is equal to the cause of an event. Correlation does not imply causation.
3. Inversion of cause and effect
   This is assuming that if A causes B, then an absence of A will prevent B. It is not necessarily true that there is only one cause to every effect.

There are several epistemic fallacies:

1. Appeal to ignorance
   This is assuming that if something has not been proven, it must be false or that if something has not been disproven, it must be true. The fact that a proposition hasn’t been proven is no reason to think it is false.
2. Epistemic fallacy
   It is assuming that if someone believes A that they must also believe B on the grounds that A and B are about the same thing or person, even though the way in which they refer to that thing or person is different. It includes the assumption that someone has knowledge of specific things.

Propositional attitude verbs are verbs such as ‘knows’, ‘believes’ and ‘wants’ that are used to undermine the credibility of and support for a position.

FAULTY ARGUMENT TECHNIQUES
These fallacies are poor techniques of argument, but can nonetheless be useful in non-rational persuasion. These fallacies have persuasive power, but not rational persuasive power.

1. Equivocation
   This is accepting a conclusion even though you shouldn’t as vagueness or ambiguity have intentionally been used.
2. Red herring
   This is distracting someone from the argument by giving an irrelevant premise. The ability to recognize red herring arguments varies depending on our knowledge of the subject matter of the argument.
3. Slippery slope
   This is wrongly assuming that to permit or forbid a course of action will inevitably lead to the occurrence of further related and undesirable events without providing good reasons to suppose that the events will actually occur (e.g. decriminalization of marihuana will lead to more abuse of cocaine).
4. Straw man
   This is ignoring an opponent’s real position and setting up a weaker version of that position by misrepresentation, exaggeration, distortion or simplification.
5. Begging the question (circular reasoning)
   This occurs when the truth of its conclusion is assumed by one or more of its premises. The truth of the premises depend on their justification of the truth of the conclusion.
6. False dilemma
   This is limiting consideration of positions on an issue to fewer alternatives than are actually available to be considered.

STATISTICAL REASONING
There are two forms of faulty reasoning as a result of misinterpretation of statistics:

1. Confusing absolute and relative difference
   This is misinterpreting the difference between absolute and relative (e.g. reduces the risk with 24% may sound a lot, but if the risk already is only 1%, it is not really a lot).
2. Margin of error
   This is misinterpreting the margin of error (typically of a confidence interval) when arguing a point.