Class Note for PHIL 110 at UMass(3)
Class Note for PHIL 110 at UMass(3)
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This 17 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 12 views.
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Date Created: 02/06/15
INTRO LOGIC Schedule for Unit 1 Day 1 Intro Day 2 Chapter 1 Day 3 Chapter 2 40 of 8 arguments Day 4 Chapter 3 Exam 5 pts each Day 5 Chapter 4 60 of 12 translations D 6 Ch t 4 ay ap er Exam 5 pts each Day 7 Chapter 4 I Day 8 EXAM 1 CHAPTER 4 TRANSLATIONS IN SENTENTIAL LOGIC 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 standard connectives are abbreviated by special symbols Iogograms compound sentences are abbreviated by algebraic combinations of 1 and 2 Standard Connectives connective symbol and amp or v not if then a NonStandard Connectives a few examples but although or butnotboth neither nor if onlyif ifand only if unless is necessary for is sufficientfor if othenNise unessin which case Simple Transformations Some simple sentences are straightfonNardly equivalent to compound sentences Jay and Kay are students Jay is a student J and amp Kay is a student K Kay is a rich student Kay is rich R and amp Kay is a student S Pitfall 1 Kay is a former student Kay is a former F and amp Kay is a student S 9 Pitfall 2 Jay and Kay are married ambiguous two or more meanings ambi also amphi means both and around otherwords containing ambi and amphi ambidextrous ambience ambiance amphibian ambivalent ambitious amphitheater 10 First Reading Jay and Kay are married Jay is married to someone and Kay is married to someone 11 Second Reading Jay and Kay are married Jay and Kay are marriedtoeachother later in predicate logic further parts are revealed Mjk 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 Pitfall 3 continued What happens if we symbolize keep trying and you will succeed as KampS X you will keep trying 8 you will succeed K amp S you will keep trying and you will succeed 17 appropriate paraphrase 1 iLizuyEie i rysiggeeed K gt 3 lt2 iL 5v i lf2Ee f S K c 3 iliiuhgvvjnmginaip r G T 4 531 i fvgiggihrgop i uct 39V39 gt P mm o a K 18 Exclusive Or Ram amp Sam will win the election Ram will win or Sam will win but not both at least one of them win R v S also amp both of them will win not R amp S alternatively Ram will win and Sam will not win R amp S or v Sam will win and Ram will not win S amp NR 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 20 Alternative Formulation 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 21 Conditionals standard expression if A then C which is symbolized A gtC A is the antecedent C is the consequent 22 Simple Variants of ifthen if A then C all of these are if A C symbolized the C ifA same A gt C if always introduces the antecedent then always introduces the consequent 23 1O Other Variants of if C provided A provided A C C in case A in case A C C supposing A supposing A C all symbolized the same way A gtC 24 Only If only if is not equivalent to if lwill get an A only if I take all the exams vs lwill get an A if I take all the exams lwill get an A if I get a hundred vs lwill get an A only if I get a hundred 25 11 How does only work 1 employees only 2 authorized personnel only 3 cars only 4 right turn only only operates as a dualnegative modifier for example 1 means to exclude anyone who is not an employee 26 a more lyrical example of only I only have eyes for youquot The Flamingos 1959 lyrics by Al Dubin music by Harry Warren 1934 27 12 only is focussensitive only have eyes for you 28 alternative focus for only only have eyes for you 30 13 alternative focus for only only have eyes for you 33 How does only modify if only modifies if by introducing two negations A only if B A El not A if not B if not B then not A B A 36 14 Example lwill get an A only if I take all the exams A ony If E K lwill not get an A if I do not take all the exams 391 A If 391 E K if I do not take all the exams then I will not get an A If not E then not A E gtA 37 If And Only If Two approaches to if and only if 1 treat it as a simple connective H 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 38 15 Example of if and only if Iwill pass if and only if I average 50 P if and only if A P if A and P only if A if A then P not P if not A if not A then not P A gt P amp A gt P 39 Unless The following are all equivalent Iwill pass only if I study P only if S I will not pass unless I study not P unless S I will not pass if I do not study not P if not S only if has two builtin negations unless has one builtin negation if has no builtin negation unless if not 40 16 Example of unless wi 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 41 THE END 42 17