Invitation to Critical Thinking Chapter 6
Lecture Notes
Chapter 6
Invitation to Critical Thinking Chapter 6
Deductive Reasoning: Overview
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
Invitation to Critical Thinking Chapter 6
Formats
All Americans are mortal.
All humans are mortal.
All Americans are humans.
Mapping
Invitation to Critical Thinking Chapter 6
Formats
All Americans are mortal.
All humans are mortal.
All Americans are humans.
Mapping Conventional
(1) All humans are mortal. (2) All Americans are humans._____________________ (3) All Americans are mortal.
Invitation to Critical Thinking Chapter 6
Formats
All Americans are mortal.
All humans are mortal.
All Americans are humans.
Mapping Conventional Casting
(1) All humans are mortal. (2) All Americans are humans._____________________ (3) All Americans are mortal.
(3)
(1) (2)
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A Format for a Valid Syllogism
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
subject term predicate term
middle term
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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.
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Invalidity
• Not all forms are valid forms– Unreliable if premises do not lead to the
conclusionSample 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
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Valid and Invalid FormsVALID
All humans are mortal.
All Americans are humans.
All Americans are mortal.
INVALID
All frogs are mortal.
All Americans are mortal.
All Americans are frogs.
All A are B
All C are A
All C are B
All A are B
All C are B
All C are A
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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.
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Translating Categorical Statements into Standard Form
Some general rules 1. Begin with a quantity indicator: some, all, no2. Use “are” or “are not” as the verb3. Subject and predicate terms must be noun phrases; they
each denote a category4. The subject term is before the “are” or “are not” and the
predicate term is after5. All + not = Some—use the “Some” term instead of
“All” + “not”6. Turn adjectives into nouns or noun phrases. 7. Turn verbs into nouns or noun phrases.
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Square of Opposition
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.
Total Inclusion Total Exclusion
Partial Inclusion Partial exclusion
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Mood and FigureWhen 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.
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Mood:A Mood:I Mood:E Mood:OAFFIRMATIVE 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
Mood:A Mood:I Mood:E Mood:OAFFIRMATIVE 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.
Some fruit are oranges.
Some fruit are apples.
Some oranges are apples.
I:
I:
I:
Invitation to Critical Thinking Chapter 6
Mood:A Mood:I Mood:E Mood:OAFFIRMATIVE 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.
No fruit are oranges.
No fruit are apples.
No oranges are apples.
E:
E:
E:
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Mood:A Mood:I Mood:E Mood:OAFFIRMATIVE 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.
Some fruit are not oranges.
Some fruit are not apples.
Some oranges are not apples.
O:
O:
O:
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Figure—based on position of middle termS = subject M = middle term P = predicate
1st figure
M—P
S—M
S—P
All humans are mortal.
All Americans are humans.
All Americans are mortal.
subject predicate
middle term
2nd figure
P—M
S—M
S—P
3rd figure
M—P
M—S
S—P
4th figure
P—M
M—S
S—P
1st figure
Invitation to Critical Thinking Chapter 6
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
Venn Diagrams
All humans are mortal.
All Americans are humans.
All Americans are mortal.
Valid or invalid?
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Venn Diagrams
Some mysteries are entertaining.
Some books are mysteries.
Some books are entertaining.
Valid or invalid?
Invitation to Critical Thinking Chapter 6
Venn Diagrams
All mysteries are suspenseful.
Some books are not mysteries.
Some books are not suspenseful.
Valid or invalid?