# Lecture 003

Arguments: statement collection (supported by the truth of other statement) - deductive arguments: conclusion is (we want valid deductive argument) TODO: why has no predictive value - valid: iff follow directly from premises - sound: valid argument whose premises are all true (good) - circular: useless - invalid: conclusion don't follow premise - inductive arguments (invalid deductive arguments): conclusion goes beyond premise, not directly from premises (denying the antecedent, but might have predictive value)

Premise: assumption (often inductive, that is sad) Conclusion: what we are trying to prove

Propositional Statement: statement can be true of false (anything that could be true or false) - Positive Statement: stating a claim

Modus ponens: good - P1: If A, then B (A -> B) - P2: A (A) - C: Therefore, B

Modus tallens: good - P1: If A, then B (A -> B = !B -> !A) - P2: Not B (!B) - C: Therefore, not A

Affirming the consequence: bad - P1: If A, then B (A -> B) - P2: B - C: Therefore, A

Denying the antecedent: bad - P1: If A, then B (A -> B = !B -> !A) - P2: Not A - C: Therefore, not B

sound deductive: E=mc^2 -> E/m=c^2 valid-unsound deductive: E=mc -> E/m=c invalid deductive: E=mc^2 -> E/m=c good inductive = invalid deductive: E=mc^2 -> E/m=c

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