Abbreviated Dictionary of Philosophical Terminology

Argument: a sequence of two or more statements of which one is designated as the conclusion and all the others of which are premises.

Biconditional: a “p if and only if q” compound statement (ex. This ball will fall from the window if and only if it is dropped from the window); a biconditional is true when the truth value of the statements on both sides is the same, and false otherwise.

Compound statement: a statement which contains another statement as a component part.

Conclusion: that statement which is affirmed on the basis of the other propositions (the premises) of the argument.

Conditional statement: an “if p, then q” compound statement (ex. If I throw this ball into the air, it will come down); p is called the antecedent, and q is the consequent.  A conditional asserts that if its antecedent is true, its consequent is also true; any conditional with a true antecedent and a false consequent must be false.  For any other combination of true and false antecedents and consequents, the conditional statement is true.

Conjunction: a compound statement formed by inserting the word ‘and’ between two statements (note: other conjunction words besides ‘and” can also be used, such as 'but', 'yet', 'still', 'howeve'r, 'moreover', 'although','furthermore', 'also', etc.).

Conjuncts: the statements that are combined in a conjunction (ex. Mary has blue hair and Tom has purple hair); a conjunction is true only if both its conjuncts are true, but false otherwise.

Counterexample: an example which contradicts some statement or argument (ex. a counterexample to the statement “All fifteen year-olds have blue hair” would be a fifteen-year-old without blue hair); for an argument, a counterexample would be a situation in which the premises of the argument are true and the conclusion is false; counterexamples show statements to be false and arguments to be invalid.

Deductive argument: involves the claim that the truth of its premises guarantees the truth of its conclusion; the terms valid and invalid are used to characterize deductive arguments.  A deductive argument succeeds when, if you accept the evidence as true (the premises), you must accept the conclusion.

Disjunction: a compound statement made by inserting the word ‘or’ between two statements.

Disjuncts: the statements that are combined in a disjunction (ex. Mark has a dog or Lisa has a cat); a disjunction is true unless both disjuncts are false.

Inductive argument: involves the claim that the truth of its premises provides some grounds for its conclusion or makes the conclusion more probable; the terms valid and invalid cannot be applied.

Invalid: an argument that is not valid.  We can test for invalidity by assuming that all the premises are true and seeing whether it is still possible for the conclusion to be false.  If this is possible, the argument is invalid.

Necessary condition: where p and q are statements, p is a necessary condition for q if q cannot be true unless p is true; it is impossible for q to be true and p to be false; if p is a necessary condition for q, then the conditional “ig q, then p” is true.

Premises:  the statements which are affirmed as providing grounds for accepting the conclusion.

Sound: an argument is sound if and only if it is valid and contains only true premises.

Statement/proposition: a declarative sentence that must either be true or false. Simple statement: a statement which does not contain another statement as a component part.

Statement variable: a letter used to represent a simple statement, most commonly from the middle of the alphabet (ex. p, q, r).

Sufficient condition: where p and q are statements, p is a sufficient condition for q if p’s truth guarantees the truth of q; it is impossible for p to be true and q to be false; if p is a sufficient condition for q, then the conditional “if p, then q” is true.

Truth value: the truth value of a true statement is true and that of a false statement is false.

Unsound: an argument that is not sound.

Valid: an argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true; if all the premises are true, then the conclusion must be true; it is impossible that all the premises are true and the conclusion is false.