Phil 102: Logic

1. Phil 102: Logic Fall 2019

2. This is not Blackboard! In addition to syllabus and schedule the home page will have announcements so please follow! You can come to either section for classes, tests, and final exam!

3. Homework Written homework will not be collected and does not contribute directly to your grade but will be discussed in class. In addition your instructor will be pleased to check, correct, and discuss any (tidy and legible) logic exercises you care to submit. It is expected that you will read assigned material and do exercises assigned for any given day prior to the class meeting for which they are scheduled. Grades Course Grade = (Quizzes + Midterm Test + Exam) / 3 There are no make-ups for quizzes (except, by university policy, for students involved in out-of-town university athletic or religious events). In lieu of make-ups the lowest quiz score for each half of the semester is dropped. Each quiz and test is curved: the top score, whatever it is, is 100%. YOURSCORE/HIGH is your percentage for each quiz, for the midterm test, and for the final exam. Your total score for the class is the average of quizzes (with the lowest score for each half of the semester dropped), midterm test, and final exam.

4. Taming the Logic Monster

5. Validity as a matter of form Logic studies criteria for distinguishing successful from unsuccessful argument.

6. 1.2 Arguments, Forms, and Truth Values • A statement is a declarative sentence; a sentence that attempts to state a fact—as opposed to a question, a command, an exclamation. • The truth value of a statement is just its truth or falsehood. • An argument is a (finite) set of statements, some of which—the premises—are supposed to support, or give reasons for, the remaining statement—the conclusion. • An argument form (or schema) is the framework of an argument that results when certain portions of the component statements are replaced by blanks, schematic letters, or other symbols. An argument instance is what results when the blanks, schematic letters, or other symbols in a form are appropriately filled in.

7. 1.3 Deductive Criteria Premises Deductive criteria, roughly speaking, require that the premises guarantee the truth of the conclusion. • An argument (form) is deductively valid if and only if it is NOT possible for ALL the premises to be true AND the conclusion false—otherwise invalid. Conclusion • An argument is sound if and only if it is deductively valid AND all its premises are true.

9. Counterexample • A counterexample to a general claim is a case that shows it to be false. • General claim: All mammals bear live young. • Counterexample: Platypuses lay eggs. • Counterexample to an argument (form) • an argument instance of exactly the same form having alltrue premises and a false conclusion. Production of a counterexample shows that the argument form and allinstances thereof are invalid. (Failure to produce a counterexample shows nothing, however.)

10. Logical Form and Counterexample Argument A All fathers are men. No women are fathers. Therefore, no women are men. Argument B All even numbers are odd numbers. No odd numbers are primes. Therefore, no even numbers are primes. Argument C All dogs are mammals. No cats are dogs. Therefore, no cats are mammals.

11. Logical Form and Counterexample Argument A All fathers are men. No women are fathers. Therefore, no women are men. Argument B All even numbers are odd numbers. No odd numbers are primes. Therefore, no even numbers are primes. Argument C All dogs are mammals. No cats are dogs. Therefore, no cats are mammals. T F T T T F F T F

12. Logical Form and Counterexample Argument A All ______ are ______. No ______ are ______ Therefore, no ______ are ______. Argument B All ______ are ______. No ______ are ______. Therefore, no ______ are ______. Argument C All ______are ______. No ______ are ______. Therefore, no c______ are ______. F T T T T F F F T

13. Logical Form and Counterexample Argument A All fathers are men. No women are fathers. Therefore, no women are men. Argument B All even numbers are odd numbers. No odd numbers are primes. Therefore, no even numbers are primes. Argument C All dogs are mammals. No cats are dogs. Therefore, no cats are mammals. T F T T T F T F F

14. Venn Diagrams: what there is—and isn’t • Closed figures represent sets of objects. • Shading says the set represented is empty; an X says it’s non-empty X Horses Unicorns

15. Venn Diagrams: sets and their complements • The complement of a set is the set of things that aren’t in the set. • The complement of the set of horses, is the set of things that aren’t horses. Horses Non-Horses

16. Venn Diagrams: the intersection of sets • The intersection of sets F and G is the set of things that are both F and G. • The intersection of mammals and non-horses on the right: mammals that aren’t horses F G horses mammals

17. Venn Diagrams: mapping logical space non-feline pets feral cats pet cats everything else cats pets

18. Venn Diagrams: Categorical Propositions S P S P All S are P No S are P X X S P S P Some S are P Some S are not P

19. Argument B is valid! All even numbers are odd numbers. No odd numbers are primes. Therefore, no even numbers are primes. odd numbers • An argument is validiff there’s no information in the conclusion that’s not already in the premises. • So an argument is valid iff representing the information in the premises (e.g. in a Venn diagram) automatically shows the information in the conclusion even numbers primes

20. Argument A is invalid! All fathers are men. No women are fathers. Therefore, no women are men. fathers • In this argument the premises don’t give you everything that’s in the conclusion. Conclusion says this region has to be empty too! men women

21. Some Valid Argument Forms

22. Some INVALID Argument Forms

23. Strange…But Valid • Ex contradictione (sequitur) quodlibet: from a contradiction, anything follows. • Any argument that has inconsistent premises is automatically valid. • Q: Given definition of validity, can you explain why?

24. 1.3.1 Quirky Cases of Validity • The conclusion is of the form ‘P or Not-P’—which is a tautology: a species of necessary truth. • Any argument with a conclusion that is necessarily true is automatically valid. • Q: Given the definition of validity, can you explain why?

25. Skip 1.4 on Inductive Criteria This page left intentionally blank

26. 1.5 Other Deductive Properties • Logically True/Logically False/Contingent • Can’t be false/can’t be true/can be either true or false • Logically Equivalent/Logically Contradictory • Necessary have same truth value/necessarily have opposite truth value • Logically Consistent/Inconsistent • Possible that all (not just each individually!) be true / not possible all be true • A set of statements logically entails a target statement if and only if it is NOT possible for every member of the set to be true AND the target statement false. We also say that the target statement logically follows from the set.

27. I show, we do, you do

28. Logical Truth, Falsity, and Contingency What can you infer about the validity or invalidity of an argument given these facts? ‘V’ for must be valid; ‘I’ for must be invalid; ‘?’ for dunno, not enough information, could be either valid or invalid depending on further information. • The conclusion is logically false. • The conclusion is logically true. • Some (at least one) of the premises are logically false. • All premises are logically true. ? V V F ?

29. Logical Equivalence and Contradiction Synonomy means ‘meaning the same thing’. True or false? • All pairs of logically equivalent sentences are synonymous. • If two sentences are each logically false then they are logically contradictory. What can you infer about the validity or invalidity of an argument given these facts? ‘V’ for must be valid; ‘I’ for must be invalid; ‘?’ for dunno, not enough information, could be either valid or invalid depending on further information. • The argument has one premise, which is logically equivalent to the conclusion. • The argument has one premises, which is logically contradictory to the conclusion. F F V ?

30. Logical Consistency, Inconsistency, Entailment What can you infer about the validity or invalidity of an argument given these facts? ‘V’ for must be valid; ‘I’ for must be invalid; ‘?’ for dunno, not enough information, could be either valid or invalid depending on further information. • {premises} logically entail the conclusion. • {premises} is consistent. • {premises} is inconsistent. • {premises, negation of conclusion} is consistent. • {premises, negation of conclusion} is inconsistent. V ? V I V

31. Logical Possibility A little bit of metaphysics because this is a philosophy class

32. Actual, Physically Possible Logically Possible • Some things that are not actual are possible, e.g. • You are now at the beach • Phil 102 meets in F 119 • Logical possibility is possibility in the broadest sense: a state of affairs is possible in this sense if it’s conceivable. • Broader than physical possibility: some states of affairs that are not physically possible are logically possible, e.g. • pigs flying • Things going faster than the speed of light

33. Having your cake and eating iyour cake Round Square Actual Precognition? Physically Possible Time Travel? Logically Possible Trisecting an angle with only compass and straight-edge P and not-P Logically Impossible

34. Is necessity ‘merely verbal’? ‘San Diego is in California’ is contingentlytrue if there’s some possible world at which the city in which we now are isn’t in California.

35. San Diego could be somewhere else

36. The man who was his own mother “Jane” is left at an orphanage as a foundling. When “Jane” is a teenager, she falls in love with a drifter, who abandons her but leaves her pregnant. Then disaster strikes. She almost dies giving birth to a baby girl, who is then mysteriously kidnapped. The doctors find that Jane is bleeding badly, but, oddly enough, has both sex organs. So, to save her life, the doctors convert “Jane” to “Jim.”

37. And then . . . “Jim” subsequently becomes a roaring drunk, until he meets a friendly bartender (actually a time traveler in disguise) who whisks “Jim” back way into the past. “Jim” meets a beautiful teenage girl, accidentally gets her pregnant with a baby girl. Out of guilt, he kidnaps the baby girl and drops her off at the orphanage. Later, “Jim” joins the time travelers corps, leads a distinguished life, and has one last dream: to disguise himself as a bartender to meet a certain drunk named “Jim” in the past…

38. 1945- A baby is an orphan who then grows up into a girl 1963- The girl becomes pregnant by a drifter who than disappears. The girl becomes a guy after labor complications and the baby is kidnapped. The girl who is now a guy becomes a drifter. 1970- The drifter walks into a bar and a bartender offers him a time machine ride to go back in time and change his past. 1963- the drifter meets a girl and gets her pregnant. 1985- the bartender drops the drifter off to enlist in the time travelers corps. 1963- the bartender kidnaps the newborn baby girl 1945- the bartender drops the baby off at an orphanage 1985- the drifter becomes a member of the corps and gets a mission to meet a drifter at a bar as a bartender in 1970

39. Is time travel logically possible? Suppose you travel back into the past to kill your baby-self…

40. Necessary or contingent? N ___All bachelors are unmarried. ___2 + 2 = 4 ___George Washington was the first President of the United States. ___The next US President will be a Democrat. ___Either the next US President will be a Democrat or the next US President will be a Republican. ___Either the next US President will be a Democrat or it is not the case that the next US president will be a Democrat. ___Que sera sera (whatever will be will be) ___Water is H2O N C C C N N ??

41. Twin Earth A Field Guide to the Philosophy of Mind ( A Field Guide to Philosophy of Mind), Twin Earth Thought Experiment (Wikipedia)

42. Are mathematical truths necessary? 2 + 2 = 4 Lucky for Mill things aren’t nailed down. The course of maintaining that the truths of logic and mathematics are not necessary or certain was adopted by Mill. He maintained that these propositions were inductive generalizations based on an extremely large number of instances.

43. 2 + 2 = 4 - true 2 + 2 = 5 - false English 4 = **** 5 = ***** The Way Things Are 2 + 2 = 4 - false 2 + 2 = 5 - true English* 4 = ***** 5 = **** A Way They Could Be How can there be necessary truths?(supposed to show there are no necessary truths)

44. This argument can be generalized! • It is contingent that any given word has the sense it does: we can change language! • So it seems there can be no necessary truths! • But this is crazy: changing language doesn’t change the world! So we have to respond to this threat!

45. They’re making the different noises… but expressing the same proposition--the same mathematical truth! ** + ** = **** ** + ** = **** 2 + 2 = 4 2 + 2 = 5 English-Speaker English*-Speaker

46. Now they’re making the same noises… but expressing the different propositions! ** + ** = ***** ** + ** = **** 2 + 2 = 4 2 + 2 = 4 English-Speaker English*-Speaker

47. 2 + 2 = 4 - true 2 + 2 = 5 - false English 4 = **** 5 = ***** Actual World 2 + 2 = 4 - false 2 + 2 = 5 - true English* 4 = ***** 5 = **** W* Changing language doesn’t change the world! True ** + ** = ****** + ** = ***** False

48. Lincoln’s Riddle If you call a tail a leg, then how many legs does a dog have?

49. Changing language doesn’t change the world! Four. Calling a tail aleg doesn’t makeit one. The End