LOGIC & CRITICAL THNKG
LOGIC & CRITICAL THNKG PHIL 1313
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Dr. Alisha Osinski
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This 0 page Class Notes was uploaded by Dr. Alisha Osinski on Sunday November 1, 2015. The Class Notes belongs to PHIL 1313 at Oklahoma State University taught by Barbara Taylor in Fall. Since its upload, it has received 21 views. For similar materials see /class/232940/phil-1313-oklahoma-state-university in PHIL-Philosophy at Oklahoma State University.
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Date Created: 11/01/15
Exercise 8 5 The 3 Operations Equivalent or Non Equivalent Obversion Change from Contrary to Contrary if start with A or E at top of Square All or Subcontrary to Subcontrary if start with I or O at bottom of Square AND Only negate the predicate class if predicate class results in a double negative then turn into a positive WFCs Eg E No students of mine are unregistered students See note below A All students of mine are nonunregistered students becomes A All students of mine are registered students Remember Within a class 7 a doublenegative becomes a positive Obversion will produce an equivalent on all four claims WFFS See note below KEY E N 2 E No P are A A students admitted to the program A All P are Non A P students who wrote poor essays E N 6 E No M are NonR M students ofmine A All M are R R registered students Contraposition Reverse Subject and Predicate positions AND negate BOTH classes Only A amp O Contraposition will produce an equivalent only on A and 0 claims E N 3 0 Some A are not W W students who scored 0 Some Non W are not Non A well on the exam See 2 above for key E N 5 A All A are NonP See 2 above for key A All P are Non A E N 8 A All C are NonR C commuters persons who commute A All R are Non C R persons whose automobile ownership is restricted E N 9 I Some B are W B students who do badly in History I Some Non W are Non B W students with shortterm memory problems Note See Old Exam III 7 On this portion of the test you will use WFCs not WFF s Exercise 8 10 Making Noncorresponding Claims Correspond and then Testing for Validity on the Square of Opposition Bonus PIS on Exam I Claim 1 premise and Claim2 conclusion of a one premise argument Claim 1 Claim 2 2 0 Some S are not NonE E No E are S I Some S are E E No S are E obvert convert T 2 Step Combo F 4 I Some R are NonV E No V are R O SomeR are not V E NOR are V obvert convert F 2 Step Combo F 0 Some 0 are not V already correspond 6 I Some 0 are V T UF 0 Some G are not K already correspond 7 I Some G are K Key af rmative E eligible candidates S students Sound Unsound Invalid R residents V voters 2 Step Combo Sound Unsound Invalid O opera singers V people who take voice lessons their whole lives Sound Unsound Invalid G Gary BrodnaX novels K novels in which the hero gets killed Sound Unsound Invalid 8 E No B are NonO 0 Some 0 are not B B boxes in the last A All B are 0 shipment O opened boxes cannot do 2quot 1 Step so cannot make correspond legitimately T UF Sound Unsound Invalid Note It s logically impossible to make an A and 0 claim correspond by conversion Why N on equivalents So if claim 1 premise is T then we assume claim 2 the conclusion is UF so we assume the argument is Invalid even though it may not be at all It may actually be validsound A real limit to this old logic 10 below 10 A All NonR are A 0 Some R are not A A astringent persimmons E No Non R are Non A R ripened persimmons obvert E No Non A are Non R 0 Some Non A are not Non R convert contraposit 3 Step Combo T T Sound Unsound Invalid Note A sound argument is the best argument in deductive logic De nition of a sound argument A sound argument is a valid argument with all true premises In other words provided the premise is T the conclusion is guaranteed to be T Put differently in a sound argument it would be logically impossible for the conclusion to be F provided the premise is T Exercise 8 8 Making NonCorresponding Claims Correspond 2 6 8 9 Translate the homework s WFCS Well formed Categorical Claims Quanti er subject class noun or noun phrase plural copula verb predicate class noun or noun phrase plural into WFFS Well Formed Formulas Quantifier subject variable letter copula verb predicate variable letter and use the following affirmative key Then follow the instructions for making noncorresponding claims correspond by using only operations that produce equivalents on bottom of page 23b in the CO Claim 1 Claim 2 All E are W Some NonW are NonE All NonW are NonE contraposition only A amp 0 All G are E Some NonE are G No G are NonE Some G are NonE COMBO obversion conversion Any only E amp I All NonM are T Some NonT are M All NonT are M contraposition only A amp 0 Some C are not H No C are NonH Some C are NonH obversion Any No NonP are N Some N are P No N are NonP conversion 7 only E amp I COMBO All N are P obversion Any Some P are T Some NonT are P Some P are not NonT obversion Any Some P are NonT COMBO Conversion 7 only E amp 1 Key affirmative E Europeans W Westerners E Europeans G Greeks M club members T exam takers C cheeses H high cholesterol products N people with name tags P participants P perennials T tuber growing plants Exercises 8 1 and 8 2 Translations into WFCs A wellformed categorical claim has a quanti er a nounnoun phrase plural subject class a copula verb and a nounnoun phrase plural predicate class Notice that each WFC is present tense plural Note Only 4 WFC exist an A E I or 0 And only the 0 claim has are not as it s copula verb Warning Only Converted E and 1 claims are equivalent maintain the same truth value CONVERSION is the logical operation whereby the subject and predicate are switched or reversed So this means a converted A or 0 claim will not be equivalent Exercise 8 1 2 0 Claim Some lizards are not salamanders 3 A Claim All lizards are reptiles 5 A Claim All members of the suborder Ophidia are snakes 6 E Claim No burrowing snakes are poisonous snakes No poisonous snakes are burrowing snakes 8 A Claim All frogs are amphibians 9 A Claim All snake places are frog places 11 A Claim All times the frog population decreases are times the snake population decreases 12 A Claim All arrivals are cheerleaders 14 A Claim All seat getters are early arrivals 1 7 E Claim No persons identical to the bank robber are persons identical to Jane 39s fiance No persons identical to Jane s fiance are person identical to the bank robber 18 A Claim All automobiles built before 1950 are antiques 20 0 Claim Some examples of corn are not examples of good popcorn Exercise 8 2 2 E Claim No students ofmine arefailing students No failing students are students of mine 3 E Claim No alorm students are students who can own a car car owning students No students who can own a car car owning students are dorm students 5 A Claim All times Joan sings are times people make faces Logical Deductive Meaning Joan singing is a sufficient condition for people to make faces but not a necessary condition for people to make faces People make faces for all kinds of reasons other than Joan singing For example my sister makes faces every time she hears the conservative Sarah Palin speak but this isn39t the only time she makes faces She also makes faces whenever Keith Oberman goes off on one of his liberal tirades 6 A Claim All tests George fails are tests George takes Converting an A claim does not guarantee equivalence The above claim is saying that taking a test is anecessary condition for George to fail the test but not sufficient If you convert the claim to All tests George takes are tests George fails then you are saying that George has never taken a test he has not failed or George has failed every test he has ever taken Big difference One could be true but the other necessarily false 8 A Claim All members are persons over 50 years old Notice that both 8 and 9 have double negative words in English Can t and without in 8 and nobody and without in 9 The terms only unless except and without introduce the predicate class which is the necessary condition in an A claim and when combined with a negative term in one of the classes become a negative term itself thereby forming a double negative which creates a positive See note bottom of p 3 9 A Claim All students who catch on are students who study This is claiming that studying is a necessary condition for catching on and if this claim is true then catching on is sufficient evidence for the truth of the student studying Notice this doesn t tell us how much studying or for how long etc Some students can catch on studying for only 20 minutes a week whereas others must study 3 to 6 hours a day in order to catch on 7 especially in logic 1 E Claim No roofers are millionaires No millionaires are roofers True or False All you need to do to prove this claim false is to find at least one roofer who is a millionaire and visa versa find one millionaire who is a roofer Which WF C would this be I Claim Some roofers are millionaires or Some millionaires are roofers 12 E Claim No parts ofMichael Jackson s face are examples of original equipment No examples of original equipment are parts of M ichael Jackson s face 14 A Claim All gun owners are outlaws True or False False My brother owns a gun and he is not an outlaw in any way shape or form So Some gun owners are not outlaws is true 15 A Claim All things you have to lose are chains Notice that but takes the place of only in this particular sentence Notice also that deductive logic does not capture the symbolic or metaphoric meaning of this English sentence at all 17 A Claim All cheating times are times your professor will make you sorry 18 A Claim All cheating times are times your friends couldn t care less 20 A Claim All players are members who are in full uniform l7 and 18 above are asserting sufficient and necessary times 20 is asserting that being in full uniform is a necessary condition for being allowed to play and playing is sufficient evidence the member is in full uniform Nobody and isn t are two negatives that make this claim a universal affumative Question CAN it be a universal negative E Equivalents by OB VERSION Yes you CAN turn an A into an E universal negative claim but ONLY IF you keep the original two negatives from the English sentence How By performing the logical operation known as OB VERSION 20 A Claim A All players are members who are in full uniform E No players are members who are not in full uniform OBVERSION E No members who are not in full uniform are players CONVERSION Keep in mind the E claim is No are So the first negative is the quanti er but the second negative is in the predicate class or the subject class when converted and not as part ofthe copula or verb Why not No 7 are not is not a WFC Turning All players are members who are in full uniform into No members are members who are not in full uniform is a logical operation called OBVFRSION whereby a universal claim is changed to it s contrary or a particular claim is changed to its subcontrary 7 in this case it s contrary because this is originally an A claim 7 AND the predicate class is a negatedopposite class Translation Rule AnyAll 4 claims can be obverted and remain equivalent as long as it is obverted correctly that is universals changed to their contraries particulars changed to their subcontraries AND the predicate classes negations opposites of one another Eg Some examples of corn are examples of BAD popcorn Exer 81 20 Exercise 08 03 Square of Opposition The rules of Logical PossibilityImpossibility and Necessity on the Square of Opposition l 0 Some anniversaries are not happy occasions T 2 E No drugs are completely harmless substances T 3 I Some wars are justi ed actions T 4 I Some allergies are killers T 5 A All woodpeckers are birds that can sing really well F 6 E No mockingbirds are birds that can sing F 7 I Some herbs are medicinal plants F 8 A All logic exercises are easy exercises F
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