invitation to critical thinking chapter 6 lecture notes chapter 6

Invitation to Critical Thinking Chapter 6

Lecture Notes

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


Formats

All Americans are mortal.

All humans are mortal.

All Americans are humans.

Mapping


Formats




Mapping Conventional

(1) All humans are mortal. (2) All Americans are humans._____________________ (3) All Americans are mortal.


Formats




Mapping Conventional Casting

(1) All humans are mortal. (2) All Americans are humans._____________________ (3) All Americans are mortal.

(3)

(1) (2)


A Format for a Valid Syllogism

Argument: Sentence Form

Argument: Standard Form

Major Premise

Minor Premise

Conclusion




All H’s are M’s

All A’s are H’s

All A’s are M’s

subject term predicate term

middle term


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.


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


Valid and Invalid FormsVALID




INVALID

All frogs 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


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.


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.


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


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.


Mood:A Mood:I Mood:E Mood:OAFFIRMATIVE NEGATIVE












A:

A:

A:











Some fruit are oranges.

Some fruit are apples.

Some oranges are apples.

I:

I:

I:











No fruit are oranges.

No fruit are apples.

No oranges are apples.

E:

E:

E:











Some fruit are not oranges.

Some fruit are not apples.

Some oranges are not apples.

O:

O:

O:


Figure—based on position of middle termS = subject M = middle term P = predicate

1st figure

M—P

S—M

S—P




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


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).


Venn Diagrams




Valid or invalid?


Venn Diagrams

Some mysteries are entertaining.

Some books are mysteries.

Some books are entertaining.

Valid or invalid?


Venn Diagrams

All mysteries are suspenseful.

Some books are not mysteries.

Some books are not suspenseful.

Valid or invalid?

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