Philosophy 1100

1. Philosophy 1100 Title: Critical Reasoning Instructor: Paul Dickey E-mail Address: pdickey2@mccneb.edu Website:http://mockingbird.creighton.edu/NCW/dickey.htm Today: Exercise 8-12, all problems Portfolios due Saturday (2/15): Final Exam will be posted on Quia. There will be some exercises that may require drawing. Next week: No Physical Class. Submit FINAL ESSAY & FINAL EXAM by email BEFORE 2/20, 6:00 P.M. Also submit mini-essay of “Time for Burning” For every 4 hours the essay and/or exam is late, a full grade will be reduced. NO EXCEPTIONS. 1

2. Movie A TIME FOR BURNING This movie makes a passionate statement exploring racism in Omaha in the 1960’s. As you watch this movie, you may be tempted to think this movie is ONLY about that. As such, it clearly is a moving experience. But as you watch this movie, I want you also to consider and evaluate what it suggests about the nature of critical thinking and its necessity in our lives and society.

3. Movie Discussion (if time available) & Assignment Due on the Last Night of Class Write one page ARGUMENT (complete with a clear claim and strong relevant premises) giving your view what this movie says on the issue of whether and/or how critical thinking is important in your life.

4. Chapter EightDeductive Arguments:Categorical Logic

5. Three Terms of a Categorical Syllogism • For example, the following is a categorical syllogism: (Premise 1) No Muppets are Patriots. (Premise 2) Some Muppets do not support themselves financially. (Conclusion) Some “call them whatever you want” that do not support themselves are not Patriots.. • The three terms of a categorical syllogism are: 1) the major term (P) – the predicate term of the conclusion (e.g. Patriots). 2) the minor term (S) – the subject term of the conclusion (e.g. Non self-supporters) 3) the middle term (M) – the term that occurs in both premises but not in the conclusion (e.g. Muppets).

6. Class Workshop: Exercise 8-12 “Categorical Logic Football”

7. USING VENN DIAGRAMS TO TEST ARGUMENT VALIDITY • Identify the classes referenced in the argument (if there are more than three, something is wrong). When identifying subject and predicate classes in the different claims, be on the watch for statements of “not” and for classes that are in common. Make sure that you don’t have separate classes for a term and it’s complement. 2. Assign letters to each classes as variables. 3. Given the passage containing the argument, rewrite the argument in standard form using the variables. M = “xxxx “ S = “ yyyy“ P = “ zzzz“ No M are P. Some M are S. ____________________ Therefore, Some S are not P.

8. Draw a Venn Diagram of three intersecting circles. • Look at the conclusion of the argument and identify the subject and predicate classes. Therefore, Some S are not P. • Label the left circle of the Venn diagram with the name of the subject class found in the conclusion. (10 A.M.) • Label the right circle of the Venn diagram with the name of the predicate class found in the conclusion. • Label the bottom circle of the Venn diagram with the middle term.

9. No M are P. Some M are S. • Diagram each premise according the standard Venn diagrams for each standard type of categorical claim (A,E, I, and O). If the premises contain both universal (A & E-claims) and particular statements (I & O-claims), ALWAYS diagram the universal statement first (shading). When diagramming particular statements, be sure to put the X on the line between two areas when necessary. 10. Evaluate the Venn diagram to whether the drawing of the conclusion "Some S are not P" has already been drawn. If so, the argument is VALID. Otherwise it is INVALID.

10. Using the Rules Method To Test Validity Background – ***If a claim refers to all members of the class, the term is said to be distributed. Table of Distributed Terms: A-claim: All S are P E-claim: No S are P I-Claim: Some S are P O-Claim: Some S are not P The bold, italic, underlined term is distributed. Otherwise, the term is not distributed.

11. The Rules of the Syllogism A syllogism is valid if and only if all three of the following conditions are met: • The number of negative claims in the premises and the conclusion must be the same. (Remember: these are the E- and the O- claims) • At least one premise must distribute the middle term. • Any term that is distributed in the conclusion must be distributed in its premises.

12. Class Workshop: Exercise 8-13, 8-14, & 8-15, 8-16

13. Chapter NineDeductive Arguments:Truth-Functional Logic

14. Truth Functional logic is important because it gives us a consistent tool to determine whether certain statements are true or false based on the truth or falsity of other statements. • A sentence is truth-functional if whether it is true or not depends entirely on whether or not partial sentences are true or false. • For example, the sentence "Apples are fruits and carrots are vegetables" is truth-functional since it is true just in case each of its sub-sentences "apples are fruits" and "carrots are vegetables" is true, and it is false otherwise. • Note that not all sentences of a natural language, such as English, are truth-functional, e.g. Mary knows that the Green Bay Packers won the Super Bowl.

15. Truth Functional Logic: The Basics • Please note that while studying Categorical Logic, we used uppercase letters (or variables) to represent classes about which we made claims. • In truth-functional logic, we use uppercase letters (variables) to stand for claims themselves. • In truth-functional logic, any given claim P is true or false. • Thus, the simplest truth table form is: P _ T F

16. Truth Functional Logic: The Basics • Perhaps the simplest truth table operation is negation: P ~P T F F T

17. Truth Functional Logic: The Basics • Now, to add a second claim, to account for all truth-functional possibilities our representation must state: P Q T T T F F T F F • And the operation of conjunction is represented by: P Q P & Q T T T T F F F T F F F F

18. Truth Functional Logic: The Basics • The operation of disjunction is represented by: P Q P V Q T T T T F T F T T F F F • The operation of the conditional is represented by: P Q P -> Q T T T T F F F T T F F T

19. Using Truth Tables To Test Validity • Now, consider the following argument: Premise: If Paula goes to work, then Quincy and Rogers will get a day off. Conclusion: If Paula goes to work and Quincy gets a day off, then Rogers will get a day off. • We symbolize the conclusion as (P & Q) -> R • Thus, the argument is: P -> (Q & R) (P & Q) -> R • Is this a valid argument?

20. Using Truth Tables To Test Validity • Is this a valid argument? We can determine whether or not it is by constructing a truth table that presents the premise(s) and conclusion. • In this case, to do so we add to the previous truth table the necessary columns to represent the conclusion. P Q R Q&R P -> (Q & R) P & Q (P & Q) -> R T T T T T T T T T F F F T F T F T F F F T T F F F F F T F T T T T F T F T F F T F T F F T F T F T F F F F T F T • Now, remembering the definition of a deductive argument, we look for a row in the table in which the premise(s) is true but the conclusion is not true. If we find one, the argument is invalid. If there is none, then the argument is valid.

21. Using Truth Tables To Test Validity We can determine whether or not a deductive argument is valid or invalid by constructing a truth table that presents the premise(s) and conclusion. A deductive argument is valid when if the premises are true, the conclusion has to be true. Or in other words, an argument is valid if there are no possible states or conditions in which the premises are true and the conclusion is false. And, of course, a truth table represents all the possible states or conditions of the claims. Thus, an argument is valid when there are NO rows of the truth table in which the premise(s) are true and the conclusion is not true. If there is even one, the argument is invalid.

22. Consider the following argument: P -> Q ~P _________ ~Q P Q T T T F F T F F • Construct the appropriate truth table to include all possible t-f scenarios for all variables in the argument. If there are x (e.g. 2) variables, note that there with always be x(so in this case, 2) columns in the truth table at this point and there will be 2**x (or 2 to the x power) number of rows (in this case, 4). P1 P Q P->Q T T T T F F F T T F F T 2. Add a column to the truth table to express the first premise based on the truth tables for the basic operations. You may have to do this in multiple steps.

23. P -> Q ~P _________ ~Q Consider the following argument: P1 P2 P Q P->Q ~P T T T F T F F F F T T T F F T T 3. For each remaining premise (there more may be more than one) add a column to the truth table to express the premise based on the truth tables for the basic operations. P1 P2 C P Q P->Q ~P ~Q T T T F F T F F F T F T T T F F F T T T 4. Add a column to the truth table to express the conclusion based on the truth tables for the basic operations. You may have to do steps #3 and #4 also in multiple steps.

24. Consider the following argument: P -> Q ~P ______ ~Q P1 P2 C P Q P->Q ~P ~Q T T T F F T F F F T F T T T F F F T T T • Ask yourself “Are there any rows in the truth table that I have just created in which all premises are true and the conclusion is false?” 6. If the answer is yes, then write “invalid.” If the answer is no, write “valid.” Invalid

25. Class Workshop: Exercise 9-7, #3

26. Team Game (if time available) You must perform all of the following on the given argument: • Translate the premises and conclusion to standard logical forms and put the argument into a syllogistic form. • Identify the type of logical form for each statement. • For each statement, give an equivalent statement and name the operation that you used to do so. • Identify the minor, major, and middle terms of the syllogism. • Draw the appropriate Venn Diagram for the premises. • Identify all distributed terms of the argument and the number of negative claims in the premises and conclusion. • What, if any, rules of validity are broken by the argument? • State if the argument is valid or invalid.

27. Everything that Pete won at the carnival must be junk. I know that Pete won everything that Bob won, and all the stuff Bob won is junk. • Translate the premises and conclusion to standard logical forms and put the argument into a syllogistic form. • Identify the type of logical form for each statement. Define terms – P: Pete’s winnings at the carnival J: Thing that are junk B: Bob’s winnings at the carnival A-claim – All B is P A-claim - All B is J A-claim – All P is J

28. Everything that Pete won at the carnival must be junk. I know that Pete won everything that Bob won, and all the stuff Bob won is junk. • For each statement, give an equivalent statement and name the operation that you used to do so. • Identify the minor, major, and middle terms of the syllogism. A-claim – All B is P Contrapositive is equivalent – All non-P are non-B. A-claim - All B is J Obverse is equivalent – No B is non-J. A-claim – All P is J Obverse is equivalent – No P is non-J. Minor term is P; Major term is J; and Middle term is B.

29. Everything that Pete won at the carnival must be junk. I know that Pete won everything that Bob won, and all the stuff Bob won is junk. • Draw the appropriate Venn Diagram for the premises.

30. Everything that Pete won at the carnival must be junk. I know that Pete won everything that Bob won, and all the stuff Bob won is junk. • Identify all distributed terms of the argument and the number of negative claims in the premises and conclusion. • What, if any, rules of validity are broken by the argument? • State if the argument is valid or invalid. All B is P All B is J All P is J Since A-claims distribute their subject terms, B is Distributed in the premises and P is distributed in the conclusion. There are no negative claims in either the premises or the conclusion. Since P is distributed in the conclusion, but not in either premise rule 3 is broken. Thus, the argument is invalid.

31. The Game You must perform all of the following on the given argument: • Translate the premises and conclusion to standard logical forms and put the argument into a syllogistic form. • Identify the type of logical form for each statement. • For each statement, give an equivalent statement and name the operation that you used to do so. • Identify the minor, major, and middle terms of the syllogism. • Draw the appropriate Venn Diagram for the premises. • Identify all distributed terms of the argument and the number of negative claims in the premises and conclusion. • What, if any, rules of validity are broken by the argument? • State if the argument is valid or invalid. Exercises 8-19, p. 290, Problems #8 & #19.