Lecture Notes

1. Lecture Notes Chapter 6 Invitation to Critical Thinking Chapter 6

2. Formats Mapping Conventional Casting Valid Syllogism Deductive Validity Invalidity Testing for validity Categorical Logic Statements to forms Square of Opposition Syllogisms Figure and Mood Venn Diagrams Deductive Reasoning: Overview Invitation to Critical Thinking Chapter 6

3. Mapping Formats All Americans are mortal. All humans are mortal. All Americans are humans. Invitation to Critical Thinking Chapter 6

4. Mapping Conventional (1) All humans are mortal. (2) All Americans are humans. _____________________ (3) All Americans are mortal. Formats All Americans are mortal. All humans are mortal. All Americans are humans. Invitation to Critical Thinking Chapter 6

5. Mapping Conventional Casting (1) All humans are mortal. (2) All Americans are humans. _____________________ (3) All Americans are mortal. (3) (1) (2) Formats All Americans are mortal. All humans are mortal. All Americans are humans. Invitation to Critical Thinking Chapter 6

6. Argument: Sentence Form Argument: Standard Form Major Premise Minor Premise Conclusion All humans are mortal. All Americans are humans. All Americans are mortal. All H’s are M’s All A’s are H’s All A’s are M’s A Format for a Valid Syllogism middle term subject term predicate term Invitation to Critical Thinking Chapter 6

7. Deductive Validity • Three statements • Two premises that lead to a conclusion (thesis) • Standard form always in this order • Major premise • Minor premise • Conclusion • If the premises are taken to be true, the conclusion must also be true. Invitation to Critical Thinking Chapter 6

8. Invalidity • Not all forms are valid forms • Unreliable if premises do not lead to the conclusion Sample Invalid Format (1)All Americans are human. (2)All Californians are human. (3) All Californians are Americans. • All A’s are B’s • All C’s are B’s • All C’s are A’s Invitation to Critical Thinking Chapter 6

9. Valid and Invalid Forms INVALID All frogs are mortal. All Americans are mortal. All Americans are frogs. VALID All humans are mortal. All Americans are humans. All Americans are mortal. All A are B All C are A All C are B All A are B All C are B All C are A Invitation to Critical Thinking Chapter 6

10. Testing for Deductive Validity Test 1: Ask, “Can I assert the premises and deny the conclusion without contradicting myself?” Test 2: Try to imagine a scenario in which the premises are all true and the conclusion is false. Test 3: Constructing Formal Analogies: using the same form (format or pattern) to construct an analogous set of statements that test the form for validity. Invitation to Critical Thinking Chapter 6

11. Translating Categorical Statements into Standard Form Some general rules • Begin with a quantity indicator: some, all, no • Use “are” or “are not” as the verb • Subject and predicate terms must be noun phrases; they each denote a category • The subject term is before the “are” or “are not” and the predicate term is after • All + not = Some—use the “Some” term instead of “All” + “not” • Turn adjectives into nouns or noun phrases. • Turn verbs into nouns or noun phrases. Invitation to Critical Thinking Chapter 6

12. Square of Opposition AFFIRMATIVE NEGATIVE Total Exclusion Total Inclusion E: Universal Negative No fathers are female. A: Universal Affirmative e.g. All mothers are female. O: Particular Negative e.g. Some women are not mothers. I: Particular Affirmative e.g. Some women are mothers. Partial Inclusion Partial exclusion Invitation to Critical Thinking Chapter 6

13. Mood and Figure When the syllogism is in standard form, the “mood” of a syllogism is determined by which of the four statement types appear as the major premise, the minor premise and the conclusion. Thus, you can represent the three statements in a syllogism using statement types from the Square of Opposition: e.g. AAA, EAE, EIO, AOO, etc. The“figure” of each syllogism, which is determined by the position of the middle term. Invitation to Critical Thinking Chapter 6

14. Mood:A Mood:I Mood:E Mood:O AFFIRMATIVE NEGATIVE A: Universal Affirmative e.g. All mothers are female. E: Universal Negative No fathers are female. I: Particular Affirmative e.g. Some women are mothers. O: Particular Negative e.g. Some women are not mothers. All humans are mortal. All Americans are humans. All Americans are mortal. A: A: A: Invitation to Critical Thinking Chapter 6

15. Mood:A Mood:I Mood:E Mood:O AFFIRMATIVE NEGATIVE A: Universal Affirmative e.g. All mothers are female. E: Universal Negative No fathers are female. I: Particular Affirmative e.g. Some women are mothers. O: Particular Negative e.g. Some women are not mothers. I: Some fruit are oranges. Some fruit are apples. Some oranges are apples. I: I: Invitation to Critical Thinking Chapter 6

16. Mood:A Mood:I Mood:E Mood:O AFFIRMATIVE NEGATIVE A: Universal Affirmative e.g. All mothers are female. E: Universal Negative No fathers are female. I: Particular Affirmative e.g. Some women are mothers. O: Particular Negative e.g. Some women are not mothers. E: No fruit are oranges. No fruit are apples. No oranges are apples. E: E: Invitation to Critical Thinking Chapter 6

17. Mood:A Mood:I Mood:E Mood:O AFFIRMATIVE NEGATIVE A: Universal Affirmative e.g. All mothers are female. E: Universal Negative No fathers are female. I: Particular Affirmative e.g. Some women are mothers. O: Particular Negative e.g. Some women are not mothers. O: Some fruit are not oranges. Some fruit are not apples. Some oranges are not apples. O: O: Invitation to Critical Thinking Chapter 6

18. Figure—based on position of middle termS = subject M = middle term P = predicate 1st figure All humans are mortal. All Americans are humans. All Americans are mortal. middle term predicate subject 1st figure M—P S—M S—P 2nd figure P—M S—M S—P 3rd figure M—P M—S S—P 4th figure P—M M—S S—P Invitation to Critical Thinking Chapter 6

19. Venn Diagrams System of intersecting circles • Each circle represents a category. • A shaded area is “vacant” – an area where there are no examples or members. • An X is used to indicate a “populated” area – an area where there is at least one member. • Using two intersecting circles and these simple symbols, we can represent any of the four standard forms of categorical statements (A, E, I, and O). Invitation to Critical Thinking Chapter 6

20. Venn Diagrams All humans are mortal. All Americans are humans. All Americans are mortal. Valid or invalid? Invitation to Critical Thinking Chapter 6

21. Venn Diagrams Some mysteries are entertaining. Some books are mysteries. Some books are entertaining. Valid or invalid? Invitation to Critical Thinking Chapter 6

22. Venn Diagrams All mysteries are suspenseful. Some books are not mysteries. Some books are not suspenseful. Valid or invalid? Invitation to Critical Thinking Chapter 6