lecture9(2)

# lecture9(2) - StatementLogic Recall the distinction between...

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Statement Logic Recall the distinction between categorical logic and statement logic . 1) All A are B 1) if P then Q 2) No B are C 2) if Q then R 3) No A are C 3) if P then R In categorical logic we use letters to stand for terms; the logical vocabulary is ‘all’, ‘no’, ‘some’, ‘not’. In statement logic we use letters to stand for statements; the logical vocabulary is ‘not’, ‘and’, ‘or’, ‘if…then’, ‘if and only if’. For the next four weeks we are going to be focusing on statement logic. We’re going to develop a simple language which will allow us to make explicit the way in which the logical vocabulary determines whether or not an argument is valid, and which will allow us to use more precise methods for determining validity.

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Statements: Atomic and Compound Atomic statements do not contain any other statement as a component. Ex. Manny hit two homers The Red Sox won Compound statements contain at least one atomic statement as a component. Ex. Manny hit two homers and the Red Sox won If Manny hit two homers, then the Red Sox won It’s not the case that Manny hit two homers Manny hit two homers or the Red Sox won We will use capital letters to stand for atomic statements.
Logical Operators Compound statements can be formed by connecting atomic sentences using ‘or’, ‘not’, ‘and’, ‘if…then’, ‘if and only if’. These words are called logical operators , and we have symbols for each of them: Operator Name Translates Type of Compound ~ tilde not negation dot and conjunction v vee or disjunction arrow if…then conditional double-arrow if and only if biconditional

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The Language L So we have a language, L. It has: Capital letters, which stand for sentence letters ~, v, ●, →, ↔, which stand for the operators Parentheses, which function as punctuation marks.
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