Chapter 10 Glossary

This alphabetical glossary contains short definitions for all the important terms and concepts from the chapter. You will also find hyperlinks to Websites relevant to the study of these terms and concepts. You should employ good critical thinking when evaluating the merit of any information you find on the World Wide Web, including what you find by following these links.

Annotation:  In a deduction, a short note to the right of a line produced from the premises.  The annotation consists of the numbers of the lines used in producing this new line, and the abbreviation for the rule used.

Antecedent:  In a conditional claim, the subsidiary claim before the arrow, or immediately after the word "if."

Claim variable:  A capital letter standing for a claim.

Conditional:  A truth-functional relation, symbolized by the truth-functional "-->" and usually translated "if-then."  A conditional claim is false if and only if its antecedent is true and its consequent is false.

Conditional proof:  A deductive method for deriving the truth of a conditional claim.  If you can begin with a hypothetical claim and show that (given other lines of the deduction), another claim follows, you may state the conditional that has the hypothetical claim as its antecedent and the claim's implication as its consequent.

Conjunction:  A truth-functional relation, symbolized by the truth-functional symbol "&" and usually translated "and."  The conjunction of two claims is true if and only if both the claims are true.

Consequent:  In a conditional claim, the subsidiary claim after the arrow, or immediately after the word "then," or after the phrase "only if."

Deduction:  The method of proving an argument to be valid by means of logical rules.  A deduction applies rules of Group I and Group II to the argument's premises, until it arrives at the conclusion.

Disjunction:  A truth-functional relation, symbolized by the truth-functional symbol "v" and usually translated "or."  The disjunction of two claims is true if and only if at least one of the claims is true; it is false if and only if both are false.

Elementary valid argument pattern:  In a deduction, a simple type of argument to be used as a rule in elucidating the steps of more complex arguments; a rule from Group I.  These rules apply only to complete lines of deduction, not to smaller parts of lines.

Necessary condition:  A condition that must be the case in order for something else to follow.  Oxygen is a necessary condition for human respiration (though you may have plenty of oxygen around and still not be able to breathe, as when being throttled).  Necessary conditions become the consequents of conditionals.

Negation:  A truth-functional operation, symbolized by the truth-functional symbol "~" and usually translated "not."  The negation of a claim is true if and only if the claim is false.

Short truth-table method:  A kind of indirect proof of an argument's validity or invalidity.  In using this method, we assume the conclusion to be false, and then try to assign truth values to the argument's premises to make them all come out true.  If that is possible, the argument is invalid; if not, it is valid.

Sufficient condition:  A condition that is enough (suffices) for something else to follow.  Being born in the United States is a sufficient condition for citizenship (thought you may also acquire citizenship through other means).  Sufficient conditions become the antecedents of conditionals.

Truth-functional equivalence (1):  The state or condition of having the same truth values under the same circumstances.  Two or more claims are equivalent if and only if their columns in a truth table are identical.

Truth-functional equivalence (2):  In a deduction, a statement of the identity of two forms of claims, which can be substituted for one another in carrying out a derivation; a rule from Group II.  These rules can be applied to any part of a deduction's line.

Truth-functional logic:  The branch of symbolic logic treating complete sentences and the relations among them; also called propositional or sentential logic.

Truth-functional symbol:  A symbol for one of the operations that affect the truth value of expressions: "~," "&," "v," and "-->."

Truth table:  A table indicating all combinations of truth values of the component claims in a more complex expression of in an argument.  It is used to test an argument for validity.  We look for rows in which all the premises of the argument are true; then we check the truth values of the conclusion in those rows.  If it is always true, the argument  is valid; if false even once, invalid.

• Statements, truth values and truth tables:  A discussion of the topic.
• Working with Truth Tables:  Short description that includes actual tables as examples.
• Argument Forms:  Discussion of forms of Argument that uses truth tables located at the Philosophy Pages of Garth Kemerling.