Chapter 9- Deduction

Deductive reasoning - Reasoning that aims to guarantee the conclusion if the premises are true.

Inductive reasoning - Reasoning that makes a conclusion likely without guaranteeing it.

Premise - A statement offered as a reason to support a conclusion.

Conclusion - The statement an argument tries to establish.

Logical strength - How well the premises, if true, support the conclusion.

Logical form - The pattern of an argument, separate from its specific topic or content.

Simple statement - A statement that does not contain another statement as a component.

Complex statement - A statement that contains another statement as a component.

Truth value - Whether a statement is true or false.

Truth-functional statement - A complex statement whose truth depends entirely on the truth values of its component statements.

Component statement - A statement that forms part of a larger complex statement.

Logical operator - A word or phrase, such as “not,” “and,” “or,” or “if…then,” that determines how component truth values affect the whole statement.

Negation - A statement that denies another statement; not-p is true when p is false and false when p is true.

Conjunction - A statement in the form “p and q”; it is true only when both parts are true.

Conjunct - Either component statement in a conjunction.

Disjunction - A statement in the form “p or q”; it is true when at least one part is true and false only when both are false.

Disjunct - Either component statement in a disjunction.

Inclusive or - The logical meaning of “or” that allows either statement or both statements to be true.

Implication - A statement in the form “if p, then q”; it is false only when p is true and q is false.

Antecedent - The “if” part of an implication; p in “if p, then q.”

Consequent - The “then” part of an implication; q in “if p, then q.”

Formal validity - The property of an argument whose conclusion must be true if all its premises are true.

Sound deductive argument - A deductive argument that is valid and has true premises.

Formal invalidity - The property of an argument whose premises could all be true while its conclusion is false.

Valid argument form - A reasoning pattern that guarantees a true conclusion whenever its premises are true.

Affirming the antecedent - A valid form: If p, then q. p. Therefore, q.

Denying the consequent - A valid form: If p, then q. Not-q. Therefore, not-p.

Chain argument - A valid form: If p, then q. If q, then r. Therefore, if p, then r.

Disjunctive syllogism - A valid form: p or q. Not-p. Therefore, q.

Fallacy of denying the antecedent - An invalid form: If p, then q. Not-p. Therefore, not-q. It fails because q could occur without p.

Fallacy of affirming the consequent - An invalid form: If p, then q. q. Therefore, p. It fails because something other than p could explain q.

Symbolization - Using letters such as p, q, and r to represent statements and reveal an argument’s logical form.