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1

Traditional Logic II

Martin Cothran

Instructor

Traditional Logic II

Chapter 10

2

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

8

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

12

(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

14

(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.

16

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

17

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

19

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

22

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 Aristo