The possibility of being wrong is the price we pay for the possibility of being right.
When someone said, "Convince me that logic is necessary," Epictetus asked: "Do you wish me to demonstrate this to you?" "Yes." "Then must I use a demonstrative form of argument?" And when this was admitted: "Then how will you know whether I argue fallaciously?" And as the man was silent: "Don't you see," said Epictetus, "how even you yourself acknowledge that logic is necessary, since without its assistance you cannot as much as know whether it is necessary or not.
The Illogic Primer Index
- Truths: A proposition is true if and only if what it says about the world is in fact the way it is.
- Propositions: A logical operator joins two propositions to form a new, complex, proposition.
A logical operator joins two propositions to form a new, complex, proposition. The truth value of the new proposition is determined by the truth values of the two propositions being joined and by the operator that joins them.
- Conjunction (and): The proposition P and Q is true if and only if both P and Q are true. It is false otherwise.
- Disjunction (or): The proposition P and Q is true if and only if either P or Q are true. It is false only if both P and Q are false.
- Conditional (if-then): The proposition If P then Q is true if and only if either P is false or Q is true. It is false only when P is true and Q is false.
- Negation (not): The proposition Not P is true if and only if P is false. It is false only if P is true..
- Biconditional (if-and-only-if): The proposition P if and only if Q is true if and only if both P and Q are true, or if both P and Q are false. It is false only when one of them is true and the other false.
Each of these fallacies is characterized by the illegitimate use of a logical operator in order to distract the reader from the apparent falsity of a certain proposition.
- False Dilemma: Two choices are given when in fact there are three options.
- From Ignorance: Because something is not known to be true, it is assumed to be false.
- Slippery Slope: A series of increasingly unacceptable consequences is drawn.
- Complex Question: Two unrelated points are conjoined as a single proposition.
The fallacies in this section have in common the practise of appealing to emotions or other psychological factors. In this way, they do not provide reasons for belief.
- Appeal to Force: The reader is persuaded to agree by force.
- Appeal to Pity: The reader is persuaded to agree by sympathy.
- Consequences: The reader is warned of unacceptable consequences.
- Prejudicial Language: Value or moral goodness is attached to believing the author.
- Popularity: A proposition argued to be true because it is widely held to be so.
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.
- Attacking the Person: (1) The person's character is attacked. (2) the person's circumstances are noted. (3) the person does not practise what is preached.
- Appeal to Authority: (1) The authority is not an expert in the field. (2) experts in the field disagree. (3) the authority was joking, drunk, or in some other way not being serious
- Anonymous Authority: The authority in question is not named.
- Style Over Substance: The manner in which an argument (or arguer) is presented is felt to affect the truth of the conclusion.
Inductive reasoning consists of inferring from the properties of a sample to the properties of a population as a whole.
- Hasty Generalization: The sample is too small to support an inductive generalization about a population.
- False Analogy: The two objects or events being compared are relevantly dissimilar.
- Unrepresentative: The sample is unrepresentative of the sample as a whole.
- Slothful Induction: The conclusion of a strong inductive argument is denied despite the evidence to the contrary.
- Fallacy of Exclusion: Evidence which would change the outcome of an inductive argument is excluded from consideration.
A statistical generalization is a statement which is usually true, but not always true.
- Accident: A generalization is applied when circumstances suggest there should be an exception.
- Converse Accident: An exception is applied in circumstances where a generalization should apply.
It is common for arguments to conclude that one thing causes another. But the relation between cause and effect is a complex one. It is easy to make a mistake
- Post Hoc: Because one follows another, it is held to be caused by the other.
- Joint Effect: One thing is held to cause another when in fact they are both the joint effects of an underlying cause.
- Insignificant: One thing is held to cause another, and it does, but it is insignificant compared to other causes of the effect.
- Wrong Direction: The direction between cause and effect is reversed.
- Complex Cause: The cause identified is only a part of the entire cause of the effect.
These fallacies have in common a general failure to prove that the conclusion is true.
- Begging the Question: The truth of the conclusion is assumed by the premises.
- Irrelevant Conclusion: An argument in defense of one conclusion proves a different conclusion.
- Straw Man: Attacking an argument different and weaker than the opposition's best argument.
The fallacies in this section are all cases where a word or phrase is used unclearly.
- Equivocation: The same term is used with two different meanings.
- Amphiboly: The structure of a sentence allows two different interpretations.
- Accent: The emphasis on a word or phrase suggests a meaning contrary to what the sentence actually says.
These fallacies occur because the author mistakenly assumes that the whole is nothing more than the sum of its parts.
- Composition: Because the attributes of the parts of a whole have a certain property, it is argued that the whole has that property.
- Division: Because the whole has a certain property, it is argued that the parts have that property.
The term non sequitur literally means "it does not follow". In this section we describe fallacies which occur as a consequence of invalid arguments.-
- Affirming the Consequent: Any argument of the form: If A then B, B, therefore A.
- Denying the Antecedent: Any argument of the form: If A then B, Not A, thus Not B.
- Inconsistency: Asserting that contrary or contradictory statements are both true.
A categorical syllogism is an argument consisting of exactly three categorical propositions (two premises and a conclusion) in which there appear a total of exactly three categorical terms, each of which is used exactly twice.
- Four Terms: A syllogism has four terms.
- Undistributed Middle: Two separate categories are said to be connected because they share a common property.
- Illicit Major: The predicate of the conclusion talks about all of something, but the premises only mention some cases of the term in the predicate.
- Illicit Minor: The subject of the conclusion talks about all of something, but the premises only mention some cases of the term in the subject .
- Exclusive Premises: A syllogism has two negative premises.
- Drawing Affirmative: Drawing an Affirmative Conclusion From a Negative Premise.
- Existential Fallacy: A particular conclusion is drawn from universal premises.
An explanation is a form of reasoning which attempts to answer the question "why?" For example, it is with an explanation that we answer questions such as, "Why is the sky blue?"
- Subverted Support: The phenomenon being explained doesn't exist.
- Non-support: Evidence for the phenomenon being explained is biased.
- Untestability: The theory which explains cannot be tested.
- Limited Scope: The theory which explains can only explain one thing.
- Limited Depth: The theory which explains does not appeal to underlying causes.
The purpose of a definition is to state exactly what a word means. A good definition should enable a reader to 'pick out' instances of the word or concept with no outside help.
- Too Broad: The definition includes items which should not be included.
- Too Narrow: The definition does not include all the necessary items.
- Failure to Elucidate: The definition is more obscure than the concept being defined.
- Circular Definition: Definition includes the term being defined as part of the definition.
- Conflicting Conditions: The definition is self-contradictory.