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1
Traditional Logic II
Martin Cothran
Instructor
Traditional Logic II
Chapter 10
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Traditional Logic II
Polysyllogisms and Sorites
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
3
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
4
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
5
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
6
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
7
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
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Complex Syllogisms
Complex syllogisms are syllogisms that are made up of several simple syllogisms
Types of Complex Arguments
PolysyllogismsSorites
EpicheiremaDilemmas
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Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
10
What is a Polysyllogism?
A polysyllogism is a syllogism that links together several syllogisms in such a way that
the conclusion of one of the component syllogisms serves as a premise for the next
(1) All good students understand polysyllogisms(2) All students of logic are good students
(3) Therefore, all students of logic will understand polysyllogisms
(4) But all people who read this book are students of logic
(5) Therefore, all people who read this book will readily understand polysyllogisms
Polysyllogism
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(1) All good students understand polysyllogisms(2) All students of logic are good students
(3) Therefore, all students of logic will understand polysyllogisms
(4) But all people who read this book are students of logic
(5) Therefore, all people who read this book will readily understand polysyllogisms
Polysyllogism
(1) All good students understand polysyllogisms(2) All students of logic are good students
(3) Therefore, all students of logic will understand polysyllogisms
(4) But all people who read this book are students of logic
(5) Therefore, all people who read this book will readily understand polysyllogisms
Polysyllogism
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(1) All good students understand polysyllogisms(2) All students of logic are good students
(3) Therefore, all students of logic will understand polysyllogisms
(4) But all people who read this book are students of logic
(5) Therefore, all people who read this book will readily understand polysyllogisms
Polysyllogism
(1) All A is B(2) All C is A
(3) Therefore, All C is B(4) All D is C
(5) Therefore, all D is B
Polysyllogism
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(1) All A is B(2) All C is A
(3) Therefore, All C is B(4) All D is C
(5) Therefore, all D is B
Polysyllogism
(1) All A is B(2) All C is A
(3) Therefore, All C is B(4) All D is C
(5) Therefore, all D is B
Polysyllogism
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(1) All A is B(2) All C is A
(3) Therefore, All C is B(4) All D is C
(5) Therefore, all D is B
Polysyllogism
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
15
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
Validity of Polysyllogisms
A polysyllogism is valid if all of its component
syllogisms is valid.
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Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
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What is a Sorites?
A sorites is a polysyllogism which, through a chain of
premises (without the intermediate conclusions)
connects the subject of the first premise with the
predicate of the last premise
Types of Sorites
Aristotelian
Goclenian
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Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
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Aristotelian Sorites
An Aristotelian sorites is a series of fourth figure
syllogisms with all of the conclusions unexpressed
except the last one
(1) All students of logic are good students(2) All good students read this logic book
(3) All people who read this logic book will readily understand sorites
(4) All students who readily understand soritesare intelligent
(5) Therefore, all students of logic are intelligent
Aristotelian Sorites
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All A is BAll B is CAll C is DAll D is E
Therefore, all A is E
Aristotelian Sorites
All A is BAll B is CAll C is DAll D is E
Therefore, all A is E
Aristotelian Sorites
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All A is BAll B is CAll C is DAll D is E
Therefore, all A is E
Aristotelian Sorites
All A is BAll B is CAll C is DAll D is E
Therefore, all A is E
Aristotelian Sorites
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Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
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Extrapolation
Extrapolation is the process of bringing out all of the
unexpressed reasoning in a syllogism in order to see
the reasoning clearly
Steps in Extrapolation
Step #1: Switch the order of the first two premises
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(1) All students of logic are good students(2) All good students read this logic book
(3) All people who read this logic book will readily understand sorites
(4) All students who readily understand soritesare intelligent
(5) Therefore, all students of logic are intelligent
Aristotelian Sorites
All good students read this logic bookAll students of logic are good students
All people who read this logic book will readily understand sorites
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
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Steps in Extrapolation
Step #1: Switch the order of the first two premises
Step #2: Draw the conclusion
All good students read this logic bookAll students of logic are good students
All people who read this logic book will readily understand sorites
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
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All good students read this logic bookAll students of logic are good students
All people who read this logic book will readily understand sorites
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
All good students read this logic bookAll students of logic are good students
All people who read this logic book will readily understand sorites
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
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All good students read this logic bookAll students of logic are good students
Therefore, all students of logic read this logic book
All people who read this logic book will readily understand sorites
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
Steps in Extrapolation
Step #1: Switch the order of the first two premises
Step #2: Draw the conclusion
Step #3: Put the new conclusion under the next premise
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All good students read this logic bookAll students of logic are good students
Therefore, all students of logic read this logic book
All people who read this logic book will readily understand sorites
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
All good students read this logic bookAll students of logic are good students
Therefore, all students of logic read this logic bookAll people who read this logic book will readily
understand soritesAll students of logic read this logic book
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
29
All good students read this logic bookAll students of logic are good students
Therefore, all students of logic read this logic bookAll people who read this logic book will readily
understand soritesAll students of logic read this logic book
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
All good students read this logic bookAll students of logic are good students
Therefore, all students of logic read this logic bookAll people who read this logic book will readily
understand soritesAll students of logic read this logic book
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
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Steps in Extrapolation
Step #1: Switch the order of the first two premises
Step #2: Draw the conclusion
Step #3: Put the new conclusion under the next premise
Step #4: Repeat the procedure as needed
All good students read this logic bookAll students of logic are good students
Therefore, all students of logic read this logic bookAll people who read this logic book will readily
understand soritesAll students of logic read this logic book
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
31
All good students read this logic bookAll students of logic are good students
Therefore, all students of logic read this logic bookAll people who read this logic book will readily
understand soritesAll students of logic read this logic book
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
All good students read this logic bookAll students of logic are good students
Therefore, all students of logic read this logic bookAll people who read this logic book will readily
understand soritesAll students of logic read this logic book
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
32
All good students read this logic bookAll students of logic are good students
Therefore, all students of logic read this logic bookAll people who read this logic book will readily
understand soritesAll students of logic read this logic book
Therefore, all students of logic will readily understand sorites
All students who readily understand sorites are intelligent
Therefore, all students of logic are intelligent
Aristotelian Sorites
All good students read this logic bookAll students of logic are good students
Therefore, all students of logic read this logic bookAll people who read this logic book will readily understand
soritesAll students of logic read this logic book
Therefore, all students of logic will readily understand sorites
All students who readily understand sorites are intelligentTherefore, all students of logic will readily understand
soritesTherefore, all students of logic are intelligent
Aristotelian Sorites
33
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
Types of complex syllogismsWhat is a polysyllogism?
The validity of polysyllogismsWhat is a sorites?
The Aristotelian soritesExtrapolating Aristotelian soritesThe validity of Aristotelian sorites
Rules for sorites
Polysyllogisms and Sorites
34
Rules for Sorites
Rule #1: Only the premise which contains the minorterm may be particular
Rule #2: Only the premise which contains the majorterm may be negative
Rules for Sorites
Rule #1: Only the premise which contains the minorterm may be particular
Rule #2: Only the premise which contains the majorterm may be negative
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Rules for Sorites
Rule #1: Only the premise which contains the minorterm may be particular
Rule #2: Only the premise which contains the majorterm may be negative
Exercises