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# PHIL 200 EXAM ONE STUDY GUIDE PHIL 200

BSU

GPA 3.2

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This 9 page Study Guide was uploaded by Alejandra Paz on Sunday January 24, 2016. The Study Guide belongs to PHIL 200 at Ball State University taught by Dr. Thorson in Spring 2016. Since its upload, it has received 46 views. For similar materials see Symbolic Logic in PHIL-Philosophy at Ball State University.

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Date Created: 01/24/16

EXAM ONE STUDY GUIDE gt VOCABULARY O Premises gt Reasons for thinking the conclusion is true 0 Conclusion gt Follows the premises 9 Deductive Arguments gt The goal of deductive arguments is to have true premises that guarantee conclusions 0 Deductive Arguments are used in logic 9 Inductive Arguments gt Premises JUSTIFY a conclusion as PROBABLE 0 We DO NOT use Inductive Arguments in logic Q Declarative Sentences gt Are either TRUE or FALSE but they CANNOT be BOTH O The true or false of a declarative sentence is called the Truth Value 9 Propositions gt Statements 0 Example If I go to Trader Joe s then I ll get salmon O Propositional Logic gt Uppercase letters represent propositions 0 Example If I go to Trader Joe s then I ll get Salmon 0 This is a statement 0 In Propositional Logic we would write this statement as o If T then S O Operators gt the symbols used in logic to stand for if then and or if and only if and or Q Conditional Statements gt if then statements 0 If T then S 0 Where If T is the ANTECEDENT and then S is the CONSEQUENT Q Conjunction Statements gt and statements 0 R amp M 0 Also used for but statements Q Disjunction Statements gt or statements 0 Either A or B Q Biconditional Statements gt if and only if statements 0 A if and only if B Q Negation Statements gt not statements 0 I will not buy the Salmon 0 It is false that I ll buy the salmon O WellFormed Formula WFF gt a well formed sentence propositional logic operators that follows all the rules of symbolic logic Q Syntax gt Rules for making well formed formulas WFFs O Semantics gt The meaning of sentences O In logic there are only TWO meanings TRUE or FALSE 9 Main connectives gt hold the entire WFF together Q Meta Variables gt lower case letters that can stand for any sentence conjunction whatsoever 0 Truth tables gt gives the truth value of a compound proposition for every possible truth value of its simple components 0 Each line of the truth table represents one possible arrangement of truth values 9 Valid gt If the premises are true then the conclusion must be true 0 An argument with a true conclusion that has one or more false premises would still be valid because the conclusion is true 9 Sound gt An argument is sound if it is valid AND has all true premises 9 Invalid gt An argument is invalid when it is possible for the premises to be true and the conclusion to be false 0 For an argument to be invalid the CONCLUSION must be FALSE and BOTH PREMISES must be TRUE Q Tautologous Statement gt A statement is a tautology if ALL of the truth values under the main connective are TRUE Q Selfcontradictory Statement gt A statement is a contradiction if ALL of the truth values under the main connective are FALSE 9 Contingent gt A statement is contingent if at least ONE truth value under the main connective is TRUE and ONE is FALSE gt SYMBOLS Memorize is short for therefore Operators symbols 3 9 if then amp or 9 and V 9 either or 9 if and only if 9 not gt RULES TO KNOW Memorize Q SYNTAX How to create WFFs O amp or anked by a WFF is a WFF O V anked by a WFF is a WFF O I anked by a WFF is a WFF O E anked by a WFF is a WFF 0 followed by a WFF is a WFF 0 Examples 0 AVBampCDTampZNOTWFF O ButAVBampC DTampZWFF o A V B WFF O C DTampGEZWFF O TRUTH TABLE KEY p q pampq qu p261 qu p q T T T T T T F F T F F T F F F T F T F T T F T F F F F F T T T T In a conjunction amp 9 It is only true when both variables are true 0 If any part of the conjunction is false then the whole thing is false I In a disjunction V 9 It is false only when both variables are false I In a conditional D 9 it is false only when the ANTECEDENT is TRUE and the CONSEQUENT is FALSE I In a biconditional E 9 It is only true when both variables match 0 ie Both variables are true or both variables are false then it is true I In a negation 9 The truth value is opposite of what the original says Q DIFFERENT WAYS PREMISES AND CONCLUSIONS ARE WRITTEN P E N gt Premise N v P gt Conclusion AVB BDCAgtC Ill Premise Premise Conclusion gt EXAMPLES G T T T T F F F F O Conditional Statements 0 IfA then B o If A Antecedent 0 Then B Consequent 0 If I go to Macy s then I ll buy perfume ADB o If M then P M I P 0 I ll buy perfume if I go to Macy s 0 If M then P M I P Q Conjunction Statements 0 It s hot in this room and it s Monday 0 R amp M o R M Q Disjunction Statements 0 Either A or B Q Biconditional Statements 0 You are a bachelor if and only if you are unmarried o B E U Q Negation Statements 0 Examples 0 I will not buy perfume 0 It s false that I ll buy perfume AVB P P Q Main Connectives 0 Examples 0 A I B o A v B I C o IAVBgtCEDgt GampZ Q gtkMain connective is bolded and highlighted in these examplesgt lt Q Truth Tables amp S CD TJ39TJH TJ39TJH H TJH39TJH TJH39 Hm 39TJ TJ TJ39TJH HH TJ39TJ39TJ H 0 Using Truth Tables to find if an argument is VALID or INVALID gtExamplel K L KEL LampK KDL T T TFF TTFF TTT T F TIT IFFF TF F T FTF FTTT FTT F F FFT TFFT FTT Example 1 INVALID gt Example 2 P Example 2 VALID gt TIPS Q Todd and Jim are cousinsgt lt O TampJ gtTToddisacousin JJisacousin O This is wrong sentence loses meaning 0 It would simply be T Why 0 Todd and Jim are cousins to each other cannot be made into two sentences without losing original meaning Q UNLESS statements 0 Mom will be mad at me unless I shove the walk 0 M V W and W D M are equivalent O M V W Either my mom will be mad at me or I shovel the walk Q W D M If I m t shovel the walk then my mom will be mad at me Q Whatever follows the IE is the ANTECEDENT Q gt If naked ANTECEDENT follows it Q gt If with only ie only if CONSEQUENT follows it Q gtkCommas can tell where the main connective is gt PROBLEMS Practice makes perfect gt WFF or not WFF 1 A 3 B 2 A V B amp C 3 AampBVCA 4 AEBV C ampD 5 AEB I CampD 6 A D B E C amp D V E amp F gt Truth Tables 0 Problem 7 A B C 0 Problem 8 A B C D gt Valid or Invalid 0 Problem 9 B A E B 0 Problem 10 D C E D FFFT FFFF FFTF FFTT FTTT FTTF FTFT FTFF TFTF TFFT TFFF TFTT A B CD TTTT TTTF TTFT TTFF T T T T F F F F F F F T T T T F F F F B T T T T D 3 A T C amp 8 6 WFF 5 WFF 3 Not WFF 4 WFF 2 Not WFF gt ANSWER KEY 1 WFF T I F T F T F T TTFF TFFF D amp C F T T F C 10 VALID 9 INVALID

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