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Louisiana State University
PHIL 1021

PHIL 1021Intro To LogicMay 19DefinitionsStatementa sentence that is capable of being either true or false Other sentences ie Imperatives and Questions cannot be true or falseArgumentsa group of statements one of which the conclusion of the argument is supportedTruth ValueA true statement is said to have truth value True a false statement is said to have to truth value FalseDeductive ValidityAn argument is deductively valid iff it is impossible for all its premises to be true and its conclusion false This cannot happen Must be TFSoundAn argument is sound iff it is deductively valid and has all true premises Must be TTInductive ValidityAn argument is inductively valid iff its conclusion is probably true if all of its premises are trueCogent argumentAn argument is cogent iff it is inductively valid and has all true premises Tells how sound an inductively valid argument isSimple StatementSometimes called atomic statementsCompound StatementContains more than one simple or atomic statement Sometimes known as molecular statementsNatural LanguageLanguage learn prior to formal education ie your First LanguageFormal LanguageShorthand LanguageNecessary ConditionIn AB B is the necessary conditionSufficient ConditionIn AB A is the sufficient conditionStatement Variablea lower case letter typically p q r or s that can stand for any statement either simple or compoundStatement Forman arrangement of statement variables and operators such that uniform substitution of statements for statement variables creates statementsTruth TableA truth table is an arrangement of truth values that shows the truth value of a compound statement in every possible case as determined by the truth of its components simple statementsMain Operatorthe operator that governs the largest components in the statementNotes and ExamplesChapter 1Ex of proving a statement of being deductively validAll humans are mortalBarack Obama is a humanBarack Obama is mortal TTDeductive validity states that it is impossible if the premises are true and the conclusion is false Barack Obama is mortal so it is deductively validAll humans are mortalBarack Obama is immortalTherefore Barack Obama is immortal FFBarack Obama is not immortalBarack Obama is President and Hilary Clinton is Secretary of DefenseTherefore Barack Obama is President FTWhile Barack Obama is President Hilary Clinton is the Secretary of State so the premise is FalseEx of proving a statement is inductively validZack plays Final Fantasies 79He likes Final Fantasies 79Zack believes that he likes the entire Final Fantasy seriesChapter 61We use uppercase letters to represent simple statements Normally the letter chosen to represent a statement is chosen to lead one to think about the statement it represents For example to represent the statementsBrahms was a great composer We might choose the letter BHere B is called the statement letter Statement letter may only stand for simple statementsPropositional logic uses five operators to form compound statements from simple statements and generally form more complex statements from less complex one The operators aretilde express negationdot expresses conjunctionvwedge expresses disjunctionhorseshoe expresses implicationtriple bar expresses equivalenceANegation of AabA and BAvB A or BABif A then B and A only if B and B if AABA iff BAB and AB are not the same thingA statement is of the form AB is known as a conditional statement remember proofs in geometry A is the antecedent and B is consequentEx Having fuel in my car is a necessary condition on my car startingWould be translated as If my car starts then there is fuel in my carTranslated again to CFMy car starting is sufficient condition for having fuel in my carTranslated to CFParenthesis ad BracketsCommasBothEitherOrAAtlanta is BeautifulBBoston is interestingCChicago is Windy
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