Chapter 10 Part 2: Deduction and Induction: A Closer Look

Modus Ponens

A valid rule of inference assuming that if an antecedent is true, and the conditional statement is true, then the consequence is true; If P then Q → P is true → Therefore, Q must be true

Modus Tollens

A valid rule of inference that allows you to deduce the negation of an antecedent by denying the consequent; If P then Q → Q is false → Therefore, P is certainly false

Fallacy of Affirming the Consequent

Assuming that if a consequence is true, its original cause or condition must also be true; If P then Q → Q → Therefore, P

Fallacy of Denying the Antecedent

A formal logical error that happens when an if-then statement assumes that a false first part automatically means the second part is also false; If P then Q → P is false → Therefore, Q is false

Disjunctive Syllogism

An argument pattern that has been known as a valid form of reasoning since ancient times; P or Q → It is false that P → Therefore, certainly Q

Hypothetical Syllogism

An argument pattern that has been known as a valid form of reasoning since the Middle Ages; If P then Q → If Q then R → Therefore, if P then R

Sentential Arguments

Arguments broken down into whole sentences that are linked together by logical operator words such as and, or, and if, then.

Valid

If its premises are true, then its conclusion must be true

Invalid

It is possible for the premises to be true and the conclusion false

Sound Deductive Argument

Has two properties; it is deductively valid, and its premises are all true