1. 1

2. 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 1 60% of Exam 1 warm-up

3. 3

4. 4 An argument is valid or invalid purely in virtue of its form. Form is a function of the arrangement of the terms in the argument, where the LOGICAL TERMS play a primary role.

5. 5 Logical terms Example Arguments all some no are not all X are Y all Y are Z / all X are Z all X are Y no Y are Z / no X are Z all X are Y some X are not Z / some Y are not Z

6. 6 In sentential logic the logical terms are statement connectives

7. 7 statement connective connective A statement connective (or simply, a connective) is an "incomplete" expression – i.e., an expression with one or more blanks – such that, whenever the blanks are filled by statements, the resulting expression is also a statement. connective statement 2 statement 1 statement 3

8. 8 S1S1 ANDS2S2 snow is whiteANDgrass is green it is rainingANDit is sleeting 2+2 = 4AND3+3 = 6

9. 9 1-place connective a 1-place connective has 1 blank 2-place connective a 2-place connective has 2 blanks 3-place connective a 3-place connective has 3 blanks etc.

10. 10 IT IS FALSE THAT S IT IS POSSIBLE THAT S Jay BELIEVES THAT S Kay HOPES THAT S

11. 11 S1S1 AND S2S2 S1S1 OR S2S2 S1S1 IF S2S2 S1S1 ONLY IF S2S2 IF S1S1 THEN S2S2 S1S1 UNLESS S2S2

12. 12 S1S1 IF S2S2 OTHERWISE S3S3 S1S1 UNLESS S2S2 IN WHICH CASE S3S3

13. 13 compoundmolecular A compound (molecular) statement is one that is constructed from one or more smaller statements by the application of a statement connective. simpleatomic A simple (atomic) statement is one that is not constructed out of smaller statements by the application of a statement connective.

14. 14 Intro Logic is not concerned with all connectives, but only special ones – namely… truth-functional connectives

15. 15 the truth-value of a true statement is T the truth-value of a false statement is F

16. 16 truth-functional To say that a connective is truth-functional is to say that the truth-value of any compound statement produced by that connective is a function of the truth-values of its immediate parts. the whole is merely the sum of its parts

17. 17 1.atomic sentences are abbreviated by upper-case letters (of the Roman alphabet) 2.connectives are abbreviated by special symbols (logograms) 3.compound sentences are abbreviated by algebraic-combinations of 1 and 2

18. 18 ( R & S ) it is raining and it is sleeting & and S it is sleeting R it is raining abbreviation expression

19. 19 ampersand The symbol ‘&’ is called ampersand, which is a stylized way of writing et the Latin word ‘et’, which means “and”. & & &

20. 20 conjunction R&S is called the conjunction of R and S. conjuncts R and S are individually called conjuncts. ampersand the word ‘ampersand’ is a children’s pronunciation of the original word and per se and

21. 21 F F T T R F T F T S case 4 case 3 case 2 case 1 &R&S&R&S F F F T

22. 22 A conjunction  &  is true if and only if both conjuncts  and  are true. A conjunction  &  is true if both conjuncts  and  are true; otherwise, it is false.

23. 23  ( R  S ) or it is raining or it is sleeting or S it is sleeting R it is raining abbreviationexpression

24. 24 wedge The symbol ‘  ’ is called wedge, which is a stylized way of writing the letter ‘v’, which initializes the Latin word ‘vel’, which means “or”. disjunction R  S is called the disjunction of R and S. disjuncts R and S are individually called disjuncts.

25. 25 would you like soup, OR salad? would you like coffee or dessert? would you like a baked potato, OR French fries? would you like cream or sugar?

26. 26 exclusive ‘or’soup OR salad inclusive ‘or’cream or sugar Logic concentrates on inclusive ‘or’. Latin has two words: ‘aut’is exclusive ‘or’ ‘vel’is inclusive ‘or’ Legalistic English has the word ‘and/or’

27. 27 F F T T R F T F T S case 4 case 3 case 2 case 1 RSRS F T T T inclusive ‘or’

28. 28 A disjunction    is true if and only if at least one disjunct  or  is true. A disjunction    is false if both disjuncts  and  are false; otherwise, it is true.

29. 29 R because S F F T T R F T F T SS because R F F F ??? F F F merely knowing that R and S are both true tells us nothing about whether one is responsible for the other

30. 30 RR it is not raining  not R it is raining abbreviationexpression

31. 31 The symbol ‘  ’ is called “tilde” (as in ‘matilda’); which is a highly stylized way of writing the letter ‘N’, which is short for ‘not’.

32. 32 ifR is true, then  R is false ifR is false, then  R is true R and  R have opposite truth-values

33. 33 ( R  S ) if then if my car runs out of gas, then my car stops ( S  R ) if then if my car stops, then my car runs out of gas  if… then… Smy car stops Rmy car runs out of gas R  S is not equivalent to S  R.

34. 34 conditional A  C is called a conditional (of A and C). antecedent A is called the antecedent. ifantecedentthenconsequent if antecedent, then consequent consequent C is called the consequent.

35. 35 the prefix ‘ante’ means ‘before’ other words that contain ‘ante’ ante antechamber antediluvian antebellum ante meridian (a.m.) antipasto (Italian form)

36. 36 I live in Los AngelesL I live in New York CityN I live in CaliforniaC would if I lived in L.A., then I would live in CAL  L  C would if I lived in NYC, then I would live in CAL  N  C

37. 37 I live in LAI live in Cal LCLC FF T I live in NYCI live in Cal NCNC FF F in one case "adding" F and F produces T in one case "adding" F and F produces F

38. 38 it rains R I shut the windows S if it rains, then I (will) shut the windows R  S

39. 39 F F T T R F T F T S case 4 case 3 case 2 case 1 RSRS T T F T true by “default”

40. 40 If you promise to shut the windows IF it rains, then only one scenario (case) constitutes breaking your promise – the scenario in which it rains but you don’t shut the windows. In case 3 and case 4, you keep your promise "by default".

41. 41