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Unformatted text preview: Definition Monday, February 25, 2008 2:36 AM Tautology A single statement form that is true for every substitution instance; that is, it comes out under the major operator for every row in the truth table. Contradiction A single statement form that is false for every substitution instance; that is, it comes out false under the major operator for every row in the truth table. Contingency A single statement form that is false for some substitution instances and true for other; that is, it has both T's and F's in its truth table under the major operators Logically Equivalent • Two or more statements forms are this if and only if they logically imply each other • Two or more statements forms are this if and only if the result of joining them with a Biconditional is a tautology Inconsistent A set of statement forms is this, if and only if there is no row in their joint truth table in which they all come out true at once. Consistent A set of statements forms is this, if and only if there is a row in their joint truth table in which they all come out true at once. Tautologies, Contradictions, and Contingencies Tuesday, February 26, 2008 3:45 PM Contradictio n A statement form that is false (under its major operator) for every substitution instance or, equivalently, one that turns out false for every row in the truth table. Negation of a tautology Tautologies A statement form that is true (under its major operator) for every substitution instance. To determine the kind of statement form 1. Symbolize 2. Extract the form 3. Apply the truth table method • Since tautologies are always true under any circumstance, they don’t make any definite claim about the way things actually are. They are an "empty" claim. • They are axioms and theorems of formal logical systems, the "truths" of the system. They are useful in logic precisely because they do not make any claim about the empirical world, but are true no matter what the worldly facts • They are formulas whose truth we can absolutely depend on, and whatever is limited...
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 Spring '08
 Wausch
 Philosophy, Logic, Biconditional

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