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Philosophy 1100

Philosophy 1100. Title: Critical Reasoning Instructor: Paul Dickey E-mail Address: pdickey2@mccneb.edu Website: http://mockingbird.creighton.edu/NCW/dickey.htm. Today: Return your Essay #2 Final Essay Questions? Exercises 8-2 Continue Chapter 8 Next Week:

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Philosophy 1100

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  1. Philosophy 1100 Title: Critical Reasoning Instructor: Paul Dickey E-mail Address: pdickey2@mccneb.edu Website:http://mockingbird.creighton.edu/NCW/dickey.htm Today: Return your Essay #2 Final Essay Questions? Exercises 8-2 Continue Chapter 8 Next Week: Portfolio Assignment #7 Student Portfolios are Due! Exercises 8-12 1

  2. What is formal Deductive Logic and is it relevant to your life? ·“Collect” from your daily experience 2-3 “artifacts” that describe a use of a formal logical argument and show its relevance to daily living. ·For each, write a description or explanation of the artifact selected and evaluate for yourself whether this shows whether formal deductive logic is significant in your life. (1 paragraph) ·Write a brief assessment of your analyses of Rhetoric & Logical Fallacies in Section Six of your portfolio. Portfolio Assignment #7

  3. Chapter EightDeductive Arguments:Categorical Logic

  4. Class Workshop: Exercise 8-2

  5. Three Categorical Operations • Conversion – The converse of a claim is the claim with the subject and predicate switched, e.g. The converse of “No Norwegians are Swedes” is “No Swedes are Norwegians.” • Obversion – The obverse of a claim is to switch the claim between affirmative and negative (A -> E, E -> A, I -> O, and O -> I and replace the predicate term with the complementary (or contradictory) term, e.g. The obverse of “All Presbyterians are Christians” is “No Presbyterians are non-Christians.” • Contrapositive – The contrapositive of a claim is the cliam with the subject and predicate switched and replacing both terms with complementary terms (or contradictory terms), e.g. The contrapositive of “Some citizens are not voters” is “Some non-voters are not noncitiizens.

  6. OK, So where is the beef? By understanding these concepts, you can apply the three rules of validity for deductive arguments: • Conversion – The converses of all E- and I- claims, but not A- and O- claims are equivalent to the original claim. • Obversion – The obverses of all four types of claims are equivalent to their original claims. • Contrapositive – The contrapositives of all A- and O- claims, but not E- and I- claims are equivalent to the original claim.

  7. Class Workshop: Exercise 8-4 & 8-5

  8. Categorical Logic • Translate the following claims: • Everybody who is ineligible for Physics 1A must take Physical Science 1. I = “Ineligible for Physics 1A” M = “Must take Physical Science 1.” All I are M 2) No students who are required to take Physical Sciences 1 are eligible for Physics 1A. No M are non-I

  9. Are these different claims or the same claim? 1) All I are M 2) No M are non-I -- Obverse is: All M are I. -- Obverse is equivalent for all claims. Draw the Venn diagrams! Or alternately, consider: The contrapositive of 2) is: No I are Non-M. The obverse of 1) is: No I are Non-M. But although the obverse of an A-claim is equivalent, the contrapositive of an E-claim is not!

  10. 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.

  11. 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).

  12. 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.

  13. 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.

  14. 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.

  15. Class Workshop: Exercise 8-11, #6 More from 8-11?

  16. 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

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