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PHIL 140 (7)
Chapter 7

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University of Saskatchewan
PHIL 140
Eric Dayton

Chapter 7 Text NotesMarch26121150 PMCompound SentencesTruth functional compound sentencesentences that are formed out of other simpler sentences and whose truth values are related to those simpler sentencesJohn likes Mary or Steven can be broken into John likes Mary OR John likes StevenJohn likes Mary and Bill can be broken into John likes Mary AND John likes BillThe truth of the compound sentence is a function of its parts hence the phrase truthfunctional logicIn this chapter we will use capital letters as abbreviations of sentencesMdef John likes MaryBdef John likes BillSdef John likes StevenOur original sentences can now be written asM and BM or STruth FunctionsSentence functiona string of English words and one or more sentence variables If the sentence variables are replaced by English sentences the whole string becomes a sentence in EnglishEXIt is true that B1Either B or Eric is tired2B or B and H3Bill hopes that B4When a variable is repeatedit must be replaced by the same sentence at each occurrenceTruth functiona sentence function that has an additional feature truth functionality The truth or falsity of the whole sentence is a function of the truth or falsity of the sentences replacing the variables in itFor example if BIt is raining then1 says that It is true that it is raining which is true if it is raining and false if it is not2 says Either it is raining or Eric is tired This is not a truth function because if it is raining then the sentence is true but if it not raining the truth of the sentence is not determined because it depends on whether or not Eric is tired1 and 3 are truth functional because they only contain sentence variables and truth functional words like and or or ifthenHowever 4 is not truth functional because it says Bill hopes that it is raining and the truth or falsity of the sentence is entirely a function of what Bill hopes and not whether or not it is rainingThe Five Standard Truth FunctionsQNot Qnegationit is false that Bill is sadQWQ and WconjunctionBill is late and Mary is tiredQ v WQ or WdisjunctionBill is late or Mary is tiredQWIf Q then Wimplicationif Bill is late then Mary is tiredQWQ if and only if WequivalenceBill is late if and only if Mary is tiredTruth TablesNegation1QQQTFTFTFConjunction2Q WQWT TTT FFF TFF FFDisjunction3Q WQ v WT TTT FTF TTF FFImplication4Q WQWT TTT FF Ch7 Text Notes Page 1
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