The document discusses translating natural language statements into propositional logic by identifying logical structures like negation, conjunction, disjunction, etc. It provides examples of translating statements involving negation (e.g. "Bill does not own a car"), conjunction (e.g. "Jenny went to the park and Bill went to the park"), disjunction (e.g. "Either my roommate will bring the textbook or my lab partner will let me borrow hers"), and discusses how to properly capture meaning and logical relationships. Key concepts covered are using variables to represent propositions, appropriate use of logical operators, and handling collective subjects, temporal sequences, and additive comparisons.

1. Propositional Logic Phil 57 section 3 San Jose State University Fall 2010

2. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. Bill does not own a car.

3. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. Bill does not own a car. P=Bill owns a car.

4. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. Bill does not own a car. ~P P=Bill owns a car.

5. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. Bill does not own a car. ~P P=Bill owns a car. It’s not the case that Mary is short.

6. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. Bill does not own a car. ~P P=Bill owns a car. It’s not the case that Mary is short. Q = Mary is short.

7. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. Bill does not own a car. ~P P=Bill owns a car. It’s not the case that Mary is short. ~Q Q = Mary is short.

8. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. It’s not true that watching TV rots the brain.

9. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. It’s not true that watching TV rots the brain. NOT: P= It’s not true that watching TV rots the brain.

10. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. It’s not true that watching TV rots the brain. NOT: P= It’s not true that watching TV rots the brain. P= Watching TV rots the brain.

11. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. It’s not true that watching TV rots the brain. ~P NOT: P= It’s not true that watching TV rots the brain. P= Watching TV rots the brain.

12. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. It is immoral to torture cats.

13. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. It is immoral to torture cats. NOT: It’s not true it is moral to torture cats.

14. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. It is immoral to torture cats. NOT: It’s not true it is moral to torture cats. P=It’s wrong to torture cats.

15. Using PL to translate natural language claims. Negation : translate to reveal the logical structure of the negation in the statement. It is immoral to torture cats. P NOT: It’s not true it is moral to torture cats. P=It’s wrong to torture cats. ( Some things are neither moral nor amoral )

16. Conjunction: Jenny went to the park and Bill went to the park.

17. Conjunction: Jenny went to the park and Bill went to the park. P=Jenny went to the park. Q=Bill went to the park.

18. Conjunction: Jenny went to the park and Bill went to the park. P=Jenny went to the park. Q=Bill went to the park. P  Q

19. Conjunction: Jenny went to the park and Bill went to the park. P=Jenny went to the park. Q=Bill went to the park. P  Q Jenny went to the park but Bill stayed home.

20. Conjunction: Jenny went to the park and Bill went to the park. P=Jenny went to the park. Q=Bill went to the park. P  Q Jenny went to the park but Bill stayed home. P=Jenny went to the park. R=Bill stayed home.

21. Some claims that look like conjunctions aren’t: The power was out for three days and the food in the fridge spoiled.

22. Some claims that look like conjunctions aren’t: The power was out for three days and the food in the fridge spoiled. P=The power was out for three days. Q=The food in the fridge spoiled.

23. Some claims that look like conjunctions aren’t: The power was out for three days and the food in the fridge spoiled. P=The power was out for three days. Q=The food in the fridge spoiled. P  Q

24. Some claims that look like conjunctions aren’t: The power was out for three days and the food in the fridge spoiled. P=The power was out for three days. Q=The food in the fridge spoiled. P  Q Loses the temporal flow of the claim.

25. Some claims that look like conjunctions aren’t: The power was out for three days and the food in the fridge spoiled. P=The power was out for three days. Q=The food in the fridge spoiled. P  Q Loses the temporal flow of the claim. Not the same as: The food in the fridge spoiled and the power was out for three days.

26. Some claims that look like conjunctions aren’t: Fred and Jane made the soup.

27. Some claims that look like conjunctions aren’t: Fred and Jane made the soup. P=Fred made the soup. Q=Jane made the soup. P  Q

28. Some claims that look like conjunctions aren’t: Fred and Jane made the soup. P=Fred made the soup. Q=Jane made the soup. P  Q Misses the collective subject.

29. Some claims that look like conjunctions aren’t: Fred and Jane made the soup. P=Fred made the soup. Q=Jane made the soup. P  Q Misses the collective subject. Better: Fred and Jane made the salad together.

30. Some claims that look like conjunctions aren’t: Lentils have more protein than peanut butter and jelly.

31. Some claims that look like conjunctions aren’t: Lentils have more protein than peanut butter and jelly. P=Lentils have more protein than peanut butter. Q=Lentils have more protein than jelly. P  Q

32. Some claims that look like conjunctions aren’t: Lentils have more protein than peanut butter and jelly. P=Lentils have more protein than peanut butter. Q=Lentils have more protein than jelly. P  Q Misses the additive comparison.

33. Some claims that look like conjunctions aren’t: Lentils have more protein than peanut butter and jelly. P=Lentils have more protein than peanut butter. Q=Lentils have more protein than jelly. P  Q Misses the additive comparison. Better: Lentils have more protein than peanut butter and jelly combined.

34. Disjunction: Either my roommate will bring the textbook or my lab partner will let me borrow hers.

35. Disjunction: Either my roommate will bring the textbook or my lab partner will let me borrow hers. P=My roommate will bring the textbook. Q=My lab partner will let me borrow her textbook.

36. Disjunction: Either my roommate will bring the textbook or my lab partner will let me borrow hers. P=My roommate will bring the textbook. Q=My lab partner will let me borrow her textbook. P  Q

37. Disjunction: Either my roommate will bring the textbook or my lab partner will let me borrow hers. P=My roommate will bring the textbook. Q=My lab partner will let me borrow her textbook. P  Q “ Inclusive or” – true if either P or Q (or both) is true.

38. Disjunction: Either Meg Whitman or Jerry Brown will be the next Governor of California.

39. Disjunction: Either Meg Whitman or Jerry Brown will be the next Governor of California. P=Meg Whitman will be the next Governor of California. Q=Jerry Brown will be the next Governor of California.

40. Disjunction: Either Meg Whitman or Jerry Brown will be the next Governor of California. P=Meg Whitman will be the next Governor of California. Q=Jerry Brown will be the next Governor of California. P  Q

41. Disjunction: Either Meg Whitman or Jerry Brown will be the next Governor of California. P=Meg Whitman will be the next Governor of California. Q=Jerry Brown will be the next Governor of California. P  Q ( but note that only one of P and Q will actually be true! )

42. Disjunction: You can have either the soup or the salad with dinner.

43. Disjunction: You can have either the soup or the salad with dinner. P=You can have the soup with dinner. Q=You can have the salad with dinner.

44. Disjunction: You can have either the soup or the salad with dinner. P=You can have the soup with dinner. Q=You can have the salad with dinner. “ Excusive or” – can’t have both!

45. Disjunction: You can have either the soup or the salad with dinner. P=You can have the soup with dinner. Q=You can have the salad with dinner. “ Excusive or” – can’t have both! (P  Q)  ~(P  Q)

46. Disjunction: Julie will be on time unless she sleeps through her alarm.

47. Disjunction: Julie will be on time unless she sleeps through her alarm. P=Julie will be on time. Q=Julie will sleep through her alarm.

48. Disjunction: Julie will be on time unless she sleeps through her alarm. P=Julie will be on time. Q=Julie will sleep through her alarm. P  Q

49. What’s on the quiz Tuesday? Informal fallacies (identifying them, explaining what the problem is with them). HW #5 (Informal fallacies workbook) Informal fallacies: a list. Propositional Logic (truth-table definitions of logical operators, recognizing wffs and main connectives, basic translation) HW #6