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# Propositional logic

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### Propositional logic

1. 1. Propositional Logic Phil 57 section 3 San Jose State University Fall 2010
2. 2. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>Bill does not own a car. </li></ul>
3. 3. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>Bill does not own a car. </li></ul><ul><li>P=Bill owns a car. </li></ul>
4. 4. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>Bill does not own a car. ~P </li></ul><ul><li>P=Bill owns a car. </li></ul>
5. 5. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>Bill does not own a car. ~P </li></ul><ul><li>P=Bill owns a car. </li></ul><ul><li>It’s not the case that Mary is short. </li></ul>
6. 6. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>Bill does not own a car. ~P </li></ul><ul><li>P=Bill owns a car. </li></ul><ul><li>It’s not the case that Mary is short. </li></ul><ul><li>Q = Mary is short. </li></ul>
7. 7. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>Bill does not own a car. ~P </li></ul><ul><li>P=Bill owns a car. </li></ul><ul><li>It’s not the case that Mary is short. ~Q </li></ul><ul><li>Q = Mary is short. </li></ul>
8. 8. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>It’s not true that watching TV rots the brain. </li></ul>
9. 9. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>It’s not true that watching TV rots the brain. </li></ul><ul><li>NOT: </li></ul><ul><li>P= It’s not true that watching TV rots the brain. </li></ul>
10. 10. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>It’s not true that watching TV rots the brain. </li></ul><ul><li>NOT: </li></ul><ul><li>P= It’s not true that watching TV rots the brain. </li></ul><ul><li>P= Watching TV rots the brain. </li></ul>
11. 11. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>It’s not true that watching TV rots the brain. ~P </li></ul><ul><li>NOT: </li></ul><ul><li>P= It’s not true that watching TV rots the brain. </li></ul><ul><li>P= Watching TV rots the brain. </li></ul>
12. 12. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>It is immoral to torture cats. </li></ul>
13. 13. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>It is immoral to torture cats. </li></ul><ul><li>NOT: </li></ul><ul><li>It’s not true it is moral to torture cats. </li></ul>
14. 14. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>It is immoral to torture cats. </li></ul><ul><li>NOT: </li></ul><ul><li>It’s not true it is moral to torture cats. </li></ul><ul><li>P=It’s wrong to torture cats. </li></ul>
15. 15. Using PL to translate natural language claims. <ul><li>Negation : translate to reveal the logical structure of the negation in the statement. </li></ul><ul><li>It is immoral to torture cats. P </li></ul><ul><li>NOT: </li></ul><ul><li>It’s not true it is moral to torture cats. </li></ul><ul><li>P=It’s wrong to torture cats. ( Some things are neither moral nor amoral ) </li></ul>
16. 16. Conjunction: <ul><li>Jenny went to the park and Bill went to the park. </li></ul>
17. 17. Conjunction: <ul><li>Jenny went to the park and Bill went to the park. </li></ul><ul><li>P=Jenny went to the park. </li></ul><ul><li>Q=Bill went to the park. </li></ul>
18. 18. Conjunction: <ul><li>Jenny went to the park and Bill went to the park. </li></ul><ul><li>P=Jenny went to the park. </li></ul><ul><li>Q=Bill went to the park. P  Q </li></ul>
19. 19. Conjunction: <ul><li>Jenny went to the park and Bill went to the park. </li></ul><ul><li>P=Jenny went to the park. </li></ul><ul><li>Q=Bill went to the park. P  Q </li></ul><ul><li>Jenny went to the park but Bill stayed home. </li></ul>
20. 20. Conjunction: <ul><li>Jenny went to the park and Bill went to the park. </li></ul><ul><li>P=Jenny went to the park. </li></ul><ul><li>Q=Bill went to the park. P  Q </li></ul><ul><li>Jenny went to the park but Bill stayed home. </li></ul><ul><li>P=Jenny went to the park. </li></ul><ul><li>R=Bill stayed home. </li></ul>
21. 21. Some claims that look like conjunctions aren’t: <ul><li>The power was out for three days and the food in the fridge spoiled. </li></ul>
22. 22. Some claims that look like conjunctions aren’t: <ul><li>The power was out for three days and the food in the fridge spoiled. </li></ul><ul><li>P=The power was out for three days. </li></ul><ul><li>Q=The food in the fridge spoiled. </li></ul>
23. 23. Some claims that look like conjunctions aren’t: <ul><li>The power was out for three days and the food in the fridge spoiled. </li></ul><ul><li>P=The power was out for three days. </li></ul><ul><li>Q=The food in the fridge spoiled. P  Q </li></ul>
24. 24. Some claims that look like conjunctions aren’t: <ul><li>The power was out for three days and the food in the fridge spoiled. </li></ul><ul><li>P=The power was out for three days. </li></ul><ul><li>Q=The food in the fridge spoiled. P  Q </li></ul><ul><li>Loses the temporal flow of the claim. </li></ul>
25. 25. Some claims that look like conjunctions aren’t: <ul><li>The power was out for three days and the food in the fridge spoiled. </li></ul><ul><li>P=The power was out for three days. </li></ul><ul><li>Q=The food in the fridge spoiled. P  Q </li></ul><ul><li>Loses the temporal flow of the claim. </li></ul><ul><li>Not the same as: The food in the fridge spoiled and the power was out for three days. </li></ul>
26. 26. Some claims that look like conjunctions aren’t: <ul><li>Fred and Jane made the soup. </li></ul>
27. 27. Some claims that look like conjunctions aren’t: <ul><li>Fred and Jane made the soup. </li></ul><ul><li>P=Fred made the soup. </li></ul><ul><li>Q=Jane made the soup. P  Q </li></ul>
28. 28. Some claims that look like conjunctions aren’t: <ul><li>Fred and Jane made the soup. </li></ul><ul><li>P=Fred made the soup. </li></ul><ul><li>Q=Jane made the soup. P  Q </li></ul><ul><li>Misses the collective subject. </li></ul>
29. 29. Some claims that look like conjunctions aren’t: <ul><li>Fred and Jane made the soup. </li></ul><ul><li>P=Fred made the soup. </li></ul><ul><li>Q=Jane made the soup. P  Q </li></ul><ul><li>Misses the collective subject. </li></ul><ul><li>Better: Fred and Jane made the salad together. </li></ul>
30. 30. Some claims that look like conjunctions aren’t: <ul><li>Lentils have more protein than peanut butter and jelly. </li></ul>
31. 31. Some claims that look like conjunctions aren’t: <ul><li>Lentils have more protein than peanut butter and jelly. </li></ul><ul><li>P=Lentils have more protein than peanut butter. </li></ul><ul><li>Q=Lentils have more protein than jelly. P  Q </li></ul>
32. 32. Some claims that look like conjunctions aren’t: <ul><li>Lentils have more protein than peanut butter and jelly. </li></ul><ul><li>P=Lentils have more protein than peanut butter. </li></ul><ul><li>Q=Lentils have more protein than jelly. P  Q </li></ul><ul><li>Misses the additive comparison. </li></ul>
33. 33. Some claims that look like conjunctions aren’t: <ul><li>Lentils have more protein than peanut butter and jelly. </li></ul><ul><li>P=Lentils have more protein than peanut butter. </li></ul><ul><li>Q=Lentils have more protein than jelly. P  Q </li></ul><ul><li>Misses the additive comparison. </li></ul><ul><li>Better: Lentils have more protein than peanut butter and jelly combined. </li></ul>
34. 34. Disjunction: <ul><li>Either my roommate will bring the textbook or my lab partner will let me borrow hers. </li></ul>
35. 35. Disjunction: <ul><li>Either my roommate will bring the textbook or my lab partner will let me borrow hers. </li></ul><ul><li>P=My roommate will bring the textbook. </li></ul><ul><li>Q=My lab partner will let me borrow her textbook. </li></ul>
36. 36. Disjunction: <ul><li>Either my roommate will bring the textbook or my lab partner will let me borrow hers. </li></ul><ul><li>P=My roommate will bring the textbook. </li></ul><ul><li>Q=My lab partner will let me borrow her textbook. </li></ul><ul><li>P  Q </li></ul>
37. 37. Disjunction: <ul><li>Either my roommate will bring the textbook or my lab partner will let me borrow hers. </li></ul><ul><li>P=My roommate will bring the textbook. </li></ul><ul><li>Q=My lab partner will let me borrow her textbook. </li></ul><ul><li>P  Q </li></ul><ul><li>“ Inclusive or” – true if either P or Q (or both) is true. </li></ul>
38. 38. Disjunction: <ul><li>Either Meg Whitman or Jerry Brown will be the next Governor of California. </li></ul>
39. 39. Disjunction: <ul><li>Either Meg Whitman or Jerry Brown will be the next Governor of California. </li></ul><ul><li>P=Meg Whitman will be the next Governor of California. </li></ul><ul><li>Q=Jerry Brown will be the next Governor of California. </li></ul>
40. 40. Disjunction: <ul><li>Either Meg Whitman or Jerry Brown will be the next Governor of California. </li></ul><ul><li>P=Meg Whitman will be the next Governor of California. </li></ul><ul><li>Q=Jerry Brown will be the next Governor of California. </li></ul><ul><li>P  Q </li></ul>
41. 41. Disjunction: <ul><li>Either Meg Whitman or Jerry Brown will be the next Governor of California. </li></ul><ul><li>P=Meg Whitman will be the next Governor of California. </li></ul><ul><li>Q=Jerry Brown will be the next Governor of California. </li></ul><ul><li>P  Q ( but note that only one of P and Q will actually be true! ) </li></ul>
42. 42. Disjunction: <ul><li>You can have either the soup or the salad with dinner. </li></ul>
43. 43. Disjunction: <ul><li>You can have either the soup or the salad with dinner. </li></ul><ul><li>P=You can have the soup with dinner. </li></ul><ul><li>Q=You can have the salad with dinner. </li></ul>
44. 44. Disjunction: <ul><li>You can have either the soup or the salad with dinner. </li></ul><ul><li>P=You can have the soup with dinner. </li></ul><ul><li>Q=You can have the salad with dinner. </li></ul><ul><li>“ Excusive or” – can’t have both! </li></ul>
45. 45. Disjunction: <ul><li>You can have either the soup or the salad with dinner. </li></ul><ul><li>P=You can have the soup with dinner. </li></ul><ul><li>Q=You can have the salad with dinner. </li></ul><ul><li>“ Excusive or” – can’t have both! </li></ul><ul><li>(P  Q)  ~(P  Q) </li></ul>
46. 46. Disjunction: <ul><li>Julie will be on time unless she sleeps through her alarm. </li></ul>
47. 47. Disjunction: <ul><li>Julie will be on time unless she sleeps through her alarm. </li></ul><ul><li>P=Julie will be on time. </li></ul><ul><li>Q=Julie will sleep through her alarm. </li></ul>
48. 48. Disjunction: <ul><li>Julie will be on time unless she sleeps through her alarm. </li></ul><ul><li>P=Julie will be on time. </li></ul><ul><li>Q=Julie will sleep through her alarm. </li></ul><ul><li>P  Q </li></ul>
49. 49. What’s on the quiz Tuesday? <ul><li>Informal fallacies (identifying them, explaining what the problem is with them). </li></ul><ul><li>HW #5 (Informal fallacies workbook) </li></ul><ul><li>Informal fallacies: a list. </li></ul><ul><li>Propositional Logic (truth-table definitions of logical operators, recognizing wffs and main connectives, basic translation) </li></ul><ul><li>HW #6 </li></ul>