Logic · College

Logic: Common Formal Fallacies

Formal fallacies that break a valid argument structure, such as affirming the consequent, with a symbolic example of each.

30 cards · basic cards · AI-written, checked twice. Edit anything.

Affirming the Consequent

Inferring the antecedent from the consequent in a conditional. Invalid form: If P then Q; Q is true; therefore P is true. Example: If it rains, the grass is wet; the grass is wet; therefore it rained.

Denying the Antecedent

Inferring the negation of the consequent from the negation of the antecedent. Invalid form: If P then Q; P is false; therefore Q is false. Example: If you study, you will pass; you did not study; therefore you will not pass.

False Biconditional

Treating a conditional as a biconditional, assuming the converse is also true. Invalid form: If P then Q; therefore P if and only if Q. Example: If you have a fever, you are sick; therefore you are sick if and only if you have a fever.

Converse Fallacy

Inferring the converse of a conditional from the original conditional. Invalid form: If P then Q; therefore If Q then P. Example: If it is a dog, then it is an animal; therefore if it is an animal, it is a dog.

Inverse Fallacy

Inferring the inverse of a conditional from the original conditional. Invalid form: If P then Q; therefore If not P then not Q. Example: If it is sunny, then it is daytime; therefore if it is not sunny, then it is not daytime.

Disjunctive Fallacy

Inferring the negation of one disjunct from an inclusive disjunction and one true disjunct. Invalid form: P or Q; P is true; therefore Q is false. Example: You may have tea or coffee; you chose tea; therefore you cannot have coffee.

Conjunction Fallacy

Inferring a consequent from a conditional with conjunctive antecedent when only one conjunct is true. Invalid form: If (P and Q) then R; P is true; therefore R. Example: If you study and sleep well, you will pass; you studied; therefore you will pass.

Undistributed Middle

Syllogism where the middle term is undistributed in both premises. Invalid form: All A are B; All C are B; therefore All A are C. Example: All cats are animals; All dogs are animals; therefore all cats are dogs.

Illicit Major

Syllogism where the major term is distributed in the conclusion but not in the major premise. Invalid form: All A are B; All A are C; therefore All C are B. Example: All roses are flowers; All roses are fragrant; therefore all fragrant things are flowers.

Illicit Minor

Syllogism where the minor term is distributed in the conclusion but not in the minor premise. Invalid form: All A are B; All C are A; therefore All B are C. Example: All poodles are dogs; All poodles are animals; therefore all animals are dogs.

Exclusive Premises

Categorical syllogism with both premises negative, violating the rule that at least one premise must be affirmative. Invalid form: No A are B; No C are A; therefore No C are B. Example: No fish are mammals; No mammals are plants; therefore no plants are fish.

Negative Conclusion from Affirmative Premises

Deriving a negative conclusion from two affirmative premises, violating premise-conclusion polarity matching. Invalid form: All A are B; All C are A; therefore No C are B. Example: All students are learners; All teachers are learners; therefore no teachers are students.

Affirmative Conclusion from Negative Premise

Deriving an affirmative conclusion from one or more negative premises. Invalid form: No A are B; All C are A; therefore All C are B. Example: No fish are mammals; All dolphins are fish; therefore all dolphins are mammals.

Existential Fallacy

Assuming existential import where there is none, treating universal statements as having existential force. Invalid form: All A are B; therefore Some A are B. Example: All unicorns are magical; therefore some unicorns are magical (when no unicorns exist).

Four Terms (Quaternio Terminorum)

Syllogism containing four or more distinct terms instead of exactly three. Invalid form: A is B; C is D; therefore A is C. Example: Roses are beautiful; Dogs are loyal; therefore roses are dogs.

15 more cards in the app