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3. 2 Day 1Intro Day 2Chapter 1 Day 3Chapter 2 Day 4Chapter 3 Day 5Chapter 4 Day 6Chapter 4 Day 7Chapter 4 Day 8EXAM #1 40% of Exam 60% of Exam 10 arguments 4 pts each 12 translations 5 pts each

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5. 4 In order to uncover logical forms, paraphrase we paraphrase English sentences so that they contain only standard connectives. We also use special abbreviations and special punctuation.

6. 5 Roman 1.atomic sentences are abbreviated by upper case letters (of the Roman alphabet). 2.standard connectives are abbreviated by special symbols (logograms). 3.compound sentences are abbreviated by algebraic combinations of 1 and 2.

7. 6 symbolconnective  if – then  not  or &and

8. 7 … but … … although … … or … but not both neither … nor … … if … … only if … … if and only if … … unless … … is necessary for … … is sufficient for … … if … otherwise … …unless…in which case

9. 8 Some simple sentences are straightforwardly equivalent to compound sentences. Jay is a studentand Kay is a student Kay is a rich student J& K R& S and Jay and Kay are students Kay is richand Kay is a student

10. 9 Kay is formerand Kay is a student F& S ? Kay is a former student

11. 10 and Jay and Kay are marriedambiguous other words containing ‘ambi’ and ‘amphi’ [‘ambi’ (also ‘amphi’) means “both” and “around”] ambidextrousambivalent ambience (ambiance)ambitious amphibianamphitheater

12. 11 Jay is married (to someone)and Kay is married (to someone) J& K and Jay and Kay are married

13. 12 Jay and Kay are married-to-each-other later, in predicate logic, further parts are revealed M Mjk and Jay and Kay are married

14. 13 Odd use of ‘and’ Sometimes ‘and’ is used as follows. and 1)keep trying, and you will succeed and 2)keep it up buster, and I will clobber you and 3)give him an inch, and he will take a mile and 4)give me the money, and I’ll give you the product and 5)you do that, and I’ll kill ya

15. 14 Other Toughies

16. 15 What happens if we symbolize keep trying and you will succeed as: & K & S??? Kyou will keep trying you will succeedand you will keep trying S&K Syou will succeed

17. 16 if then (1)if you keep trying, then you will succeed if then (2)if you keep it up buster, then I will clobber you if then (3)if you give him an inch, then he will take a mile if then (4)if you give me the money, then I’ll give you the product if then (5)if you do that, then I’ll kill ya  K  S  K  C  G  T  M  P  D  K

18. 17 Ram xor Sam will win (the election) Ram will win, or Sam will win, but not both at least one of them win ( R  S ) also both of them will win…not!  ( R & S ) & Ram will win, and Sam will not win,( R &  S ) or Sam will win, and Ram will not win.( S &  R )  alternatively,

19. 18 neithernor it is neither raining nor sleeting notandnot it is not raining, and it is not sleeting  R &  S neithernor neither Jay nor Kay is sleeping notandnot Jay is not sleeping, and Kay is not sleeping  J &  K

20. 19 neithernor it is neither raining nor sleeting notor it is not raining or sleeting not or it is not true that ( it is raining or it is sleeting )  ( R  S )   R &  S

21. 20 standard expression: ifthen if A then C which is symbolized: A  C antecedent A is the antecedent consequent C is the consequent

22. 21  if A, then C  if A, C  C if A ‘ if ’ always introduces the antecedent all of these are symbolized the same: ‘ then ’ always introduces the consequent A  C

23. 22 provided C provided A in case C in case A supposing C supposing A all symbolized the same way A  C provided provided A, C in case in case A, C supposing supposing A, C

24. 23 ‘ only if ’ is not equivalent to ‘ if ’ only if I will get an A only if I take all the exams vs. if I will get an A if I take all the exams if I will get an A if I get a hundred vs. only if I will get an A only if I get a hundred TF TF

25. 24 only dual-negative ‘only’ operates as a dual-negative modifier. for example, (1) means to exclude exclude anyone who is not not an employee. only 1.employees only only 2.authorized personnel only only 3.cars only only 4.right turn only

26. 25 “I only have eyes for you” The Flamingos 1959 lyrics by Al Dubin music by Harry Warren 1934

27. 26 I only have eyes for you

28. 27

29. 28 I only have eyes for you

30. 29 Sam, world’s ugliest dog

31. 30 I only have eyes for you

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33. 32 ifnot if not B onlyif ‘only’ modifies ‘if’ two negations by introducing two negations     B   A then not not A only if A only if B notif not A if not B

34. 33 onlyif I will get an A only if I take all the exams only if A only if E notif not I will not get an A if I do not take all the exams notif not A if not E ifnot thennot if I do not take all the exams then I will not get an A if notthen not if not E then not A  E   A

35. 34 Two approaches to ‘if and only if’ 1.treat it as a simple connective (  ) 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.onlyif 3.only if each of which we already know how to paraphrase.

36. 35 (  A   P )&( A  P ) if not A then not P not P if not Aif A, then P P only if AandP if A Aif and only ifP I average 50if and only ifI will pass

37. 36 The following are all equivalent. I will pass only if I studyP only if S I will not pass unless I studynot P unless S I will not pass if I do not studynot P if not S only ifhas twobuilt-in negations unlesshasonebuilt-in negation ifhasnobuilt-in negation unlessif not unless = if not

38. 37 Sif not not not P Sunless not not P not I will not pass unless I study not Sif not not P thenif not S  P  P   S S

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