Affirming the consequent — An invalid argument form: “If p then q / q // p’
Argument – a series of declarative statements, one of which (the conclusion), is intended to be supported by the others (the premises).
Biconditional statement (biconditional) — A statement having a triple bar as its main operator (read, if and only if)
Commutativity — A valid rule of inference that provides for the rearrangement of conjunctions and disjunctions
Compound statement — A statement that contains at least one simple statement as a component
Conclusion – (1) the statement in an argument that the premises are claimed to support or imply; (2) a statement in an argument supported by premises.
Conjunct — The component in a conjunctive statement on either side of the main operator
Conjunction — (1) A statement having a dot as its main operator (2) a valid rule of inference: “p / q // p and q’
Conjunctive statement (conjunction) — A statement having a dot as its main operator
Connectives Symbols — used to connect or negate propositions in propositional logic
Consistent statements — Statements for which there is at least one line on their truth tables in which all of them are true
Constructive dilemma — A valid argument form/rule of inference: “If p then q, and if r then s / p or r // q or s’
Contingent statement — A statement that is neither necessarily true nor necessarily false
Corresponding conditional — The conditional statement having the conjunction of an argument’s premises as its antecedent and the conclusion as its consequent
Denying the antecedent — An invalid argument form: “If p then q / not p // not q’
Destructive dilemma — A valid argument form/rule of inference: “If p then q, and if r then s / not q or not s // not p or not r’
Disjunct — The component in a disjunctive statement on either side of the main operator
Disjunctive statement (disjunction) — A statement having a wedge as its main operator
Disjunctive syllogism (1) — A syllogism having a disjunctive statement for one or both of its premises (2) a valid argument form/rule of inference: “p or q / not p // q’
Enthymeme – an argument with hidden premises
Fallacy – an argument that appears to be deductive or inductive, but which is based on mistaken rules of inference. (These may, of course, be widely accepted.)
False – a sentence that incorrectly describes the way things are is false.
Inconsistent statements — Statements such that there is no line on their truth tables in which all of them are true
Logical Form (of a proposition) – the basic structure of a statement in which only the operators are prominent.
Logical Form (of an argument) – the basic structure of an argument in which only the operators are prominent.
Logically equivalent statements — (1) Statements that necessarily have the same truth value (2) statements having the same truth value on each line under their main operators
Logically false statement — A statement that is necessarily false, a self-contradictory statement
Main operator — The operator (connective) in a compound statement that governs the largest component(s) in the statement
Material equivalence — (1) The relation expressed by a truth-functional biconditional (2) a valid rule of inference that allows an equivalence statement to be replaced by a conjunctive statement or a disjunctive statement
Material implication — (1) The relation expressed by a truth-functional conditional (2) a valid rule of inference that allows an implication sign to be replaced by a disjunction sign if and only if the antecedent is negated
Necessary condition — The condition represented by the consequent in a conditional statement
Negation — A statement having a tilde as its main operator
Non-sequitur – a statement , intended as a conclusion, that does not actually follow logically from the statements that are alleged to support it.
Operators – (1) symbols used to connect simple propositions in propositional logic; (2) the truth-functional parts of a proposition.
Premise – a statement in an argument offered as a reason supporting a conclusion.
Proposition – a statement represented in its logical form.
Propositional logic — A kind of logic in which the fundamental components are whole statements or propositions
Self-contradictory statement — A statement that is necessarily false, a logically false statement
Simple statement — A statement that does not contain any other statement as a component
Sound Argument – an argument that is valid and has all true premises.
Standard Form (of an argument) – an argument, laid out as a series of steps, in which the supporting reasons (premises) occur first and the defended statement (conclusion) last.
Statement – a sentence capable of being either true or false.
Statement form — An arrangement of statement variables and operators such that the uniform substitution of statements in place of the variables results in a statement
Statement variable — A lowercase letter, such as p or q, that can represent any statement
Substitution instance — An argument or statement that has the same form as a given argument form or statement form of an argument form
Sufficient condition — The condition represented by the antecedent in a conditional statement
Tautologous statement — A statement that is necessarily true a logically true statement
True – a sentence that correctly describes the way things are is true.
Truth function — A compound proposition whose truth value is completely determined by the truth values of its components
Truth table — An arrangement of truth values that shows in every possible case how the truth value of a compound proposition is determined by the truth values of its simple components
Valid Argument – an argument in which the conclusion cannot be false when its premises are true.
Well-formed formula (WFF) — A syntactically correct arrangement of symbols