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Basic Logical Concepts


Affirming the consequent   An invalid form of argument: "If A, then B; B; so, A," 64-65, 508
Analogy   A comparison of things that are claimed to be similar in some respect, 70, 175, 323, 423
Argument   A claim defended with reasons. More precisely, an argument is a set of statements, one of which (called the conclusion) is claimed or intended to be supported by the others (called the premises), 25, 50; cogent, 82--83, 222--223, 310, 312; complex, 32--33; deductive, 52--67, 83; explanation and, 42--43; inductive, 52--62, 67, 71, 83, 305--350; invalid, 74--78, 83; not a fight, 407--409; simple, 32--33; sound, 78, 83, 222--223, 310; strong, 78, 83, 222, 305, 312; uncogent, 82--83, 312; unsound, 78, 83; valid, 74--78, 83, 222, 276, 286; weak, 79-83, 305, 312
Argument based on mathematics   An argument in which the conclusion is claimed to depend largely or entirely on some mathematical calculation or measurement, 66
Argument by elimination   An argument that seeks to logically rule out various possibilities until only a single possibility remains, 65--66
Argument from analogy   An argument in which the conclusion is claimed to depend on an analogy (i.e., a comparison or similarity) between two or more things, 70-71, 323-333; constructing, 332-333; evaluating, 325-329; in law, 330; in ethics, 330
Argument from definition   An argument in which the conclusion is presented as being true by definition, 66--67
Categorical syllogism   A three-line argument in which all three statements are categorical statements, 65, 256--257, 269
Causal argument   An argument that asserts or denies that something causes, has caused, or will cause something else, 69, 334--340
Chain argument   A deductive argument of the form "If A, then B; if B, then C, so, if A, then C," 63
Cogent argument   An inductive argument that is strong and has all true premises, 82--83, 310, 312
Common pattern test   A test in which characteristic patterns of deductive or inductive reasoning are used to determine whether an argument is deductive or inductive, 56, 58--59
Counterexample method of proving invalidity   A method for proving invalidity that consists in constructing a formally identical argument having true premises and an obviously false conclusion, 89--93
Deductive argument   An argument in which the conclusion is claimed or intended to follow necessarily from the premises, 52--67, 83; common patterns of, 62--67
Denying the antecedent   An invalid form of argument: "If A, then B; not A; so, not B," 64--65
Disjunctive syllogism   A three-line deductive argument having a disjunctive statement (i.e., an "either/or" statement) for one or both of its premises, 543 n. 13
Generalization   A statement that asserts that all or most things of a certain kind have a certain property or characteristic. Also, in statistics, a statement of the form "A certain percentage of all A's are B's," 67, 172
General statement   A statement of the form "All A's are B's" or "Most A's are B's," 543 n. 5. See also Generalization
Hypothetical syllogism   A three-line argument in which at least one of the premises is an "if . . . then" statement, 62--65
Indicator word test   A test in which indicator words (words such as "therefore," "hence," and "because") are used to determine whether an argument is deductive or inductive, 56-57
Inductive argument   An argument in which the conclusion is claimed or intended to follow probably from the premises, 52-62, 67-71, 83, 94, 305; common patterns of, 67-71
Inductive generalization   An argument that uses evidence about a limited number of people or things of a certain type to make a claim about a larger group of people or things of that type, 67--68, 71, 306--317; evaluating, 309--312; and opinion polls, 313--317
Invalid argument   A deductive argument in which the conclusion does not follow necessarily from the premises, 76--78, 83
Modus ponens   A valid argument form: "If A then B; A; therefore, B," 59, 63--65
Modus tollens   A valid argument form: "If A then B; not B; therefore, not A," 63--65, 507
Particular statement   A statement that refers to a particular person, place, or thing, 543 n. 5
Prediction   A statement about what may or will happen in the future, 68
Predictive argument   An argument in which a prediction is defended with reasons, 68
Principle of charity   A principle of interpretation that requires that unclear passages or arguments be interpreted in the way most favorable the speaker or writer, 41--42, 59-60, 203--204, 206, 291
Principle of charity test   A test for determining whether an argument is deductive or inductive. According to the principle of charity test, if it is unclear whether an argument is deductive or inductive, the argument should be interpreted in whatever way is most favorable to the arguer, 56, 59--60
Sound argument   A deductive argument that is valid and has all true premises, 78, 83, 95, 310
Statistical argument   An argument that argues from premises regarding a percentage of a population to a conclusion about an individual member of that population or some part of that population, 67, 70--71, 317--321
Strict necessity test   A test for determining whether an argument is deductive or inductive. According to the strict necessity test, if the conclusion of an argument follows from the premises with strict logical necessity, then the argument should be regarded as deductive, 56--58, 305; exceptions to, 61, 94
Strong argument   An inductive argument in which the conclusion follows probably from the premises, 78--83, 95, 305
Syllogism   A three-line argument that consists of two premises and a conclusion, 62. More narrowly, a three-line deductive argument, 256
Uncogent argument   An inductive argument that is weak or has at least one false premise, or both, 82-83, 310, 312
Unsound argument   A deductive argument that is invalid or has at least one false premise, or both, 78, 83, 310, 312
Valid argument   A deductive argument in which the conclusion follows necessarily from the premises, 74--78, 83, 276
Weak argument   An inductive argument in which the conclusion does not follow probably from the premises, 79, 83, 305, 312