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: Hand Back “Nail that Claim” Exercise! & Discuss Exercise 8-11, all problems Next week: ESSAY DUE! FINAL EXAM 1

2. COURSE EVALUATION • Electronic/Online Course/Instructor Feedback • 13/WI Availability until February 20, 2013. • Instruction Sheet will be on Quia site.

3. Chapter EightDeductive Arguments:Categorical Logic

4. Categorical Syllogisms • A syllogism is a deductive argument that has two premises -- and, of course, one conclusion (claim). • A categorical syllogism is a syllogism in which: • each of these three statements is a standard form, and • there are three terms which occur twice, once each in two of the statements.

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 puppets 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. Puppets that are non self-supporters) • 3) the middle term (M) – the term that occurs in both premises but not in the conclusion (e.g. Muppets).

6. 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.

7. 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.

8. 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.

9. Class Workshop: • Exercise 8-11, #6

10. Power of Logic Exercises: http://www.poweroflogic.com/cgi/Venn/venn.cgi?exercise=6.3B ANOTHER GOOD SOURCE: http://www.philosophypages.com/lg/e08a.htm

11. 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.

12. Some Dogs are Not Poodles. Why is this a statement about all poodles? Say a boxer is a dog which is not a poodle. Thus, the statement above says that “all poodles are not boxers” and thus “poodles” is distributed.

13. 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.

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

15. 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.

16. 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

17. 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.

18. 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.

19. 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.

20. 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.