Class Note for PHIL 110 at UMass(13)
Class Note for PHIL 110 at UMass(13)
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This 10 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Massachusetts taught by a professor in Fall. Since its upload, it has received 19 views.
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Date Created: 02/06/15
INTRO LOGIC DAY 05 CHAPTER 4 TRANSLATIONS IN SENTENTIAL LOGIC Schedule for Unit 1 Day 1 Intro Day 2 Chapter 1 Day 3 Chapter 2 Day 4 Chapter 3 Day 5 Chapter 4 Day 6 Chapter 4 Day 7 Chapter 4 Day 8 EXAM 1 40 of 10 arguments Exam 4 pts each 60 of 12 translations Exam 5 pts each T Basic Idea In order to uncover logical forms we paraphrase English sentences so that they contain only standard connectives We also use special abbreviations and special punctuation Abbreviation Scheme atomic sentences are abbreviated by upper case letters of the Roman alphabet NonStandard Connectives a few examples standard connectives are abbreviated by special symbols Iogograms compound sentences are abbreviated by algebraic combinations of 1 and 2 but ifandonyif although unless or but not both is necessary for neither nor is sufficientfor if ifotherwise onlyif unlessin which case Standard Connectives connective symbol and amp or v not if then Simple Transformations Some simple sentences are straightforwardly equivalent to compound sentences Jay and Kay are students Jay is a student and Kay is a student XWL Kay is a rich student Kay is rich and Kay is a student 09 30 Pitfall 1 Kay is a former student Kay is former F and amp Kay is a student I S 9 Pitfall 2 Jay and Kay are married ambiguous ambi also amphi means both and around other words containing ambi and amphi ambivalent ambitious amphitheater ambidextrous ambience ambiance amphibian First Reading Jay and Kay are married Jay is married to someone J and amp Kay is married to someone K 11 Second Reading Jay and Kay are married Jay and Kay are M marriedtoeachother t 39 d39 t 39 a er In pre Ica e ogic Mjk further parts are revealed 10 12 Pitfall 3 Odd use of and Sometimes and is used as follows 1 keep trying and you will succeed 2 keep it up buster and I will clobber you 3 give him an inch and he will take a mile 4 give me the money and I ll give you the W 777 5 you do that and I ll kill ya produc 13 Pitfall 3 continued What happens if we symbolize keep trying and you will succeed as K amp S K you will keep trying 8 you will succeed K amp S yo u will keep trying and you will succeed 15 Other T 1quot 1 quot i777 9 appropriate paraphrase 1 iii uyiievm g eed K a S lizmsamsn we 3 iLiiuhgeivinmgLinaii r G gt T 4 1121123 ii ethrZ Dprli hct 39V39 a P 5 if you do that D K then I ll kill ya 16 Exclusive Or Alternative Formulation Ram M Sam will win the election Ram will win or Sam will win but not both it is neither raining nor sleeting it is not raining or sleeting it is not true that it is raining or it is sleeting RVS RampS at least one of them win R v 8 also amp both of them will winnot N R amp S E alternatively Ram will win and Sam will not win R amp MS or v Sam will win and Ram will not win 8 amp NR 17 19 NeitherNor it is neither raining nor sleeting it is not raining and it is not sleeting RampS neither Jay nor Kay is sleeping Jay is not sleeping and Kay is not sleeping N J amp N K 18 Conditionals standard expression if A then C which is symbolized A gtC A is the antecedent C is the consequent 20 Simple Variants of ifthen Only If if A then C all of these are only if is notequivalent to if if A C symbolized the I C A same I will get an A only ifl take all the exams vs I will get an A if I take all the exams A gt C I will get an A if I get a hundred if always introduces the antecedent vs I will get an A only if I get a hundred then always introduces the consequent 21 Other Variants of if How does only work 1 employees only C provided A provided A C 2 authorized personnel only C in case A in case A C 3 Gal39s only C supposing A supposing A C 4 right turn only all symbolized only operates as a the same way dualnegative modifier A gt C for example 1 means to exclude anyone who is not an employee 22 a more lyrical example of only I only have eyes for youquot The Flamingos 1959 lyrics by Al Dubin music by Harry Warren 1934 25 only is focussensitive I only have eyes for you 26 alternative focus for only I only have eyes for you 28 alternative focus for only How does only modify if only modifies if by introducing two negations Aonly if B I only have eyes for you A I notA if notB if 1ch then not A B gtA 30 32 Example I will get an A only if I take all the exams A 0ny if E t a IWIII not get an A If not A if not E I do not take all the exams ifl do not take all the exams then I will not get an A I if not E then not A E gtA 33 Example of if and only if If And Only If Two approaches to if and only if 1 treat it as a simple connective lt gt 2 treat it as a complex connective We will concentrate on 2 according to which if and only if consists of 3 components 1 if 2 and 3 only if each of which we already know how to paraphrase s4 I will pass if and only if I average 50 P if and only if A P ifA and P only ifA if A then P not P if not A if not A then not P A a P amp A a N P 35 Unless The following are all equivalent I will pass only ifl study P only ifS I will not pass unless I study not P unless S I will not pass ifl do not study not P if not 8 only if unless if has two has one has no builtin negations builtin negation builtin negation unless if not 36 Example of unless I will not pass unless I study not P unless 8 not P if not 8 not P if not 8 if not 8 then not P 8 gt P 37 10
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