Logic and Conditional Reasoning: When Things Are Iffy

Vocabulary flashcards covering the logical definitions, components, equivalences, and cognitive biases associated with conditional reasoning.

Conditional proposition

A complex proposition formed by connecting simple propositions with the connective words "if… then…", often referred to as "the heart of logic."

Antecedent

The first or premise proposition ($p$) in a conditional statement of the form "$\text{If } p \text{ then } q$".

Consequent

The second or concluding proposition ($q$) in a conditional statement of the form "$\text{If } p \text{ then } q$", which necessarily follows when the antecedent is true.

Sufficient condition

A condition ($p$) whose occurrence or truth guarantees the occurrence or truth of another proposition ($q$).

Necessary condition

A condition ($q$) that must hold in order for another proposition ($p$) to occur, meaning $p$ cannot occur in the absence of $q$.

Cryptologic methods

A bidding and signaling system in the game of bridge developed by mathematician Peter Winkler that uses conditionals to prevent opponents from knowing which antecedent is true.

Wason selection task

A four-card deductive reasoning problem devised in 1966 by Peter C. Wason to evaluate hypothesis-testing and reasoning with conditional rules.

Matching bias

A cognitive bias wherein people judge the information explicitly named in a conditional rule as relevant while ignoring important unmentioned alternatives.

Logically equivalent

The relationship between two or more logical statements that always share the exact same truth value under all circumstances.

Converse

A proposition formed by transposing the antecedent and consequent of a conditional, turning "$\text{If } p \text{ then } q$" into "$\text{If } q \text{ then } p$".

Sensitivity

In medical testing, the conditional probability that a screening test will be positive given that the patient has contracted the disease.

Specificity

In medical testing, the conditional probability that a screening test will be negative given that the patient does not have the disease.

Conditional probability

A probability evaluated and presented within the context of a logical conditional, expressing the likelihood of an outcome given a specific preceding condition.

Biconditional

A compound statement that asserts both a conditional statement and its converse simultaneously ("$\text{If } p \text{ then } q$ and $\text{if } q \text{ then } p$").

Contrapositive

A statement formed by negating and swapping both the antecedent and consequent ("$\text{If not } q \text{ then not } p$"), which is always logically equivalent to the original conditional "$\text{If } p \text{ then } q$".

Inverse

The contrapositive of the converse, formed by negating both the antecedent and consequent without swapping them ("$\text{If not } p \text{ then not } q$").