Stephen Downe's Guide to the Logical Fallacies

Irving M. Copi, Carl Cohen. Introduction to Logic, 9th ed. New York : Maxwell Macmillan International. 1994.

Cederblom, J. B. and David W. Paulsen. Critical Reasoning : Understanding and Criticizing Arguments and Theories, 3rd ed. Belmont, Calif. : Wadsworth Pub. Co. 1991.

Stephen F. Barker. The Elements of Logic, 2d ed. New York, McGraw-Hill. 1974.

Davis, J. W. Philosophical Logic. Edited by J. W. Davis, D. J. Hockney and W. K. Wilson. Dordrecht, D. Reidel. 1969.

The point of an argument is to give reasons in support of a conclusion. An argument commits a fallacy when the reasons do not support the conclusion.

This guide follows the following format for each fallacy:

1. Name
2. Definition
3. Examples
4. Proof

The name and definition appear in this document.

We will discuss each fallacy, create examples, analyze these examples and show how we may prove that the fallacy has been committed.

A) Fallacies of Distraction

Each of these fallacies has an illegitimate use of a logical operator in order to distract the reader from the falsity of a certain proposition.

False Dilemma

Definition: A limited number of options (usually two) is given, while in reality there are more options. A false dilemma is an illegitimate use of the "or" operator.

Examples:

Proof:

Argument From Ignorance (argumentum ad ignorantiam)

Definition: Arguments of this form assume that since something has not been proven false, it is therefore true. Such an argument may assume that since something has not been proven true, it is false.

(This is a special case of a false dilemma, since it assumes that all propositions must ether be known to be true or known to be false.)

Example:

Proof:

Slippery Slope

Definition: In order to show that a proposition is unacceptable, a sequence of increasingly unacceptable events is shown to follow. A slippery slope is an illegitimate use of the"if-then" operator.

Example:

Proof:

Complex Question

Definition: Two unrelated points are put together and treated as a single proposition. We are expected to accept or reject both, when in reality one is acceptable while the other is not. A complex question is an illegitimate use of the "and" operator.

Example:

Proof:

B) Appeals to Motives instead of Support

The fallacies in this section appeal to emotions or other psychological factors. In this way, they do not provide legitamate reasons for belief.

Appeal to Force (argumentum ad baculum)

Definition: We are told that unpleasant consequences will follow if they do not agree with the author.

Example:

Proof:

Appeal to Pity (argumentum ad misercordiam)

Definition: We are told to agree to the proposition because of the pitiful state of the author.

Example:

Proof:

Appeal to Consequences (argumentum ad consequentiam)

Definition: We are told there are disagreeable consequences of holding a particular belief in order to show that this belief is false.

Example:

Proof:

Prejudicial Language

Definition: Loaded or emotive terms are used to lead us to think at believing a proposition is valueable or has some kind of moral goodness.

Example:

Proof:

Appeal to Popularity (argumentum ad populum)

Definition: We are told a proposition is true because it is widely held to be true or is held to be true by some (usually upper crust) part of the population. This fallacy is sometimes also called the "Appeal to Emotion" because emotional appeals often sway the population as a whole.

Example:

Proof:

C) Changing the Subject

The fallacies in this section change the subject by discussing the person making the argument instead of discussing reasons to believe or disbelieve the conclusion. While occasionalty it is useful to cite authorities, it is almost never appropriate to discuss the person instead of the argument.

Attacking the Person (argumentum ad hominem)

Definition: The person presenting an argument is attacked instead of the argument itself. This may take many forms. For example, the person's character, nationality or religion may be attacked. It may be pointed out we stand to gain a favorable outcome if we believe the argument. Or, finally, a person may be attacked by association, or by his company. There are three major forms of Attacking the Person:

(1) ad hominem (abusive): instead of attacking an assertion, the argument attacks the person who made the assertion.
(2) ad hominem (circumstantial): instead of attacking an assertion the author points to the relationship between the person making the assertion and the person's circumstances.
(3) ad hominem (tu quoque): this form of attack on the person notes that a person does not practice what he preaches.

Example:

Proof:

Appeal to Authority (argumentum ad verecundiam)

Definition: While occassionaly it may be appropriate to cite an authority to support a point, often it is not. An appeal to authority is inappropriate if:

(i) the person is not qualified to have an expert opinion on the subject,
(ii) experts in the field disagree on this issue.
(iii) the authority was making a joke, drunk, or otherwise not being serious

Hearsay is a variation of the fallacious appeal to authority. An argument from hearsay depends on second or third hand sources.

Example:

Proof:

Anonymous Authorities

Definition: The authority in question is not named. This is a type of appeal to authority because when an authority is not named it is impossible to confirm that the authority is an expert.

A variation on this fallacy is the appeal to rumor. Because the source of a rumor is typically not known, it is not possible to determine whether to believe the rumor. Very often false and harmful rumors are deliberately started in order to discredit an opponent.

Example:

Proof:

Style Over Substance

Definition: The manner in which an argument (or arguer) is presented is used to affect the likelihood that the conclusion is true.

Example:

Proof:

D) Inductive Fallacies

Inductive reasoning consists on inferring from the properties of a sample (a small portion) to the properties of a whole (a large portion).

For example, we may have a barrel of 1,000 stones. Some of the stones are black, some are white. If we take a sample of 100 stones from the barrel and find that 50 of them are white and 50 of them are black, we can infer inductively that half the stones in the barrel (500 of them) are black and half are white.

All inductive reasoning depends on the similarity of the sample and the whole. The more similar the sample is to the whole, the more reliable will be the inductive conclusion. If the sample is relevantly dissimilar to the whole, then the inductive conclusion will not be reliable.

No inductive inference is perfect. Inductive inferences can sometimes fail. Even though the premises are true, the conclusion might be false. A good inductive inference gives us a reason to believe that the conclusion is true.

Hasty Generalization

Definition: The size of the sample is too small to support the conclusion.

Example:

Proof:

Unrepresentative Sample

Definition: The sample in an inductive inference is relevantly different from the whole.

Example:

Proof:

False Analogy

Definition: In an analogy, two objects (or events), A and B are shown to be similar. If it is argued that since A has property X, so also B must have property X, the analogy will fail when the two objects, A and B, are different in a way which affects whether they both have property X.

Example:

Proof:

Slothful Induction

Definition: The proper conclusion of an inductive argument is denied despite the evidence to the contrary.

Example:

Proof:

Fallacy of Exclusion

Definition: Important evidence which would contradict an inductive argument is excluded from consideration. The requirement that all relevant information be included is called the"principle of total evidence."

Example:

Proof:

E) Fallacies Involving Statistical Syllogisms
(Syllogism: an argument or form of reasoning in which two statements or premises are made and a logical conclusion is drawn from them Ex.: All mammals are warmblooded (major premise); whales are mammals (minor premise); therefore, whales are warmblooded (conclusion). A form of deductive logical, where reasoning occurs from the general to the specific.)

A statistical generalization is a statement which is usually true, but not always true. Very often these are expressed using the word "most", as in "Most conservatives favor low taxes." Sometimes the word "generally" is used, as in "Conservatives generally favor low taxes." Or, sometimes, no specific word is used at all, as in: "Conservatives favor low taxes." Fallacies involving statistical generalizations occur because the generalization is not always true. If an author treats a statistical generalization as though it were always true, the author commits a fallacy.

Accident

Definition: A general rule is applied when circumstances suggest that an exception to the rule should apply.

Example:

Proof:

Converse Accident

Definition: An exception to a generalization is applied when circumstances suggest that a generalization should apply.

Example:

Proof:

F) Causal Fallacies

It is common for arguments to conclude that one thing causes another. The relation between cause and effect is a complex one. In general, we say that a cause C is the cause of an effect E if and only if:

(i) Generally, if C occurs, then E will occur, and
(ii) Generally, if C does not occur, then E will not occur ether.

There are always exceptions. For example:

We say that striking the match causes the match to light, because:

(i) Generally, when the match is struck, it lights (except when the match is dunked in water), and
(ii) Generally, when the match is not struck, it does not light (except when it is lit with a blowtorch).

Many writers also require that a causal statement be supported with a natural law. For example, the statement that "striking the match causes it to light" is supported by the principle that "friction produces heat, and heat produces fire".

Coincidental Correlation ( post hoc ergo prompter hoc )

Definition: The name in Latin means "after this therefore because of this".

We commit the fallacy when it is assumed that because one thing follows another that the one thing was caused by the other.

Example:

Proof:

Joint Effect

Definition: One thing is held to cause another when in fact both are the effect of a single underlying cause. This fallacy is often understood as a special case of post hoc ergo prompter hoc.

Example:

Proof:

Genuine but Insignificant Cause

Definition: The object or event which is identified as the cause of an effect is a genuine cause, but it is insignificant cause when compared to the other causes of that event. Note that this fallacy does not apply when all other contributing causes are equally insignificant. Thus, it is not a fallacy to say that you helped cause defeat the Conservative government because you voted Liberal, for your vote had as much weight as any other vote, and hence is equally a part of the cause.

Example:

Proof:

Wrong Direction

Definition: The relation between cause and effect is reversed.

Example:

Proof:

Complex Cause

Definition: The effect is caused by a number of objects or events, of which the cause identified is only a part. A variation of this is the feedback loop where the effect is itself a part of the cause.

Example:

Proof:

G) Missing the Point

These fallacies have in common a general failure to prove that the conclusion is true.

Begging the Question (petitio principii)

Definition: The truth of the conclusion is assumed by the premises. Often, the conclusion is simply restated in the premises in a slightly different form. In more difficult cases, the premise is a consequence of the conclusion.

Example:

Proof:

Irrelevant Conclusion (ignoratio elenchi)

Definition: An argument which tries to prove one thing instead
proves a different conclusion.

Example:

Proof:

Straw Man

Definition: The author attacks an argument which is different from, and usually weaker than, the opposition's best argument.

Example:

Proof:

H) Fallacies of Ambiguity

The fallacies in this section are all cases where a word or phrase is used unclearly. There are two ways this can happen.

(i) The word or phrase may be ambiguous (more than one distinct meaning).

(ii) The word or phrase may be vague(no distinct meaning).

Equivocation

Definition: The same word is used with two meanings.

Example:

Proof:

Amphiboly

Definition: An amphiboly occurs when the construction of a sentence allows it to have two different meanings.

Example:

Proof:

Accent Definition

Emphasis is used to suggest a meaning different from the actual content of the proposition.

Example:

Proof:

I) Category Errors

These fallacies occur because the author assumes that the whole is nothing more than the sum of its parts. However, when things are joined together they may have different properties than when they exist separately.

Composition Definition

Because the parts of a whole have a certain property, we are told that the whole has that property. That whole may be either an object composed of different parts, or it may be a collection or set of individual members.

Example:

Proof:

Division Definition

Because the whole has a certain property, we are told that the parts have that property. The whole in question may be either a whole object or a collection or set of individual members.

Example:

Proof:

J) Non-Sequitur

The term non sequitur literally means "it does not follow". These fallacies occur as a consequence of invalid arguments.

Affirming the Consequent

Definition: Any argument of the following form is invalid:
If A then B
B Therefore, A

Example:

Proof:

Denying the Antecedent

Definition: Any argument of the following form is invalid:

If A then B
Not A Therefore, Not B

Example:

Proof:

Inconsistency Definition

We are presented with more than one proposition such that the propositions cannot all be true. In such a case, there may be a contradiction or a contrary point of view between the propositions.

Example:

Proof: