Syllogisms And Validity

Unit 3b SYLLOGISMS AND VALIDITY

24 Testing Syllogisms by counter example  Validity is judged solely on form.  Many ways to test validity, we will focus on just two:

– Counterexamples – Rules Some girls are not critical thinkers. Some students are not critical thinkers. Therefore, some students are girls. Remember: A syllogism with true premises and a false conclusion is necessarily invalid. Some women are not lawyers. Some men are not lawyers. Therefore some men are women.

24 Testing Syllogisms by counter example  Both had the form OOI-2

– No man is a flying being – Some birds are not men. – Therefore some birds are flying beings.  Form: EOI-I  Test – No dogs are horses – Some cats are not dogs – Therefore some cats are horses • Can't find a counter example? There isn't one and it is a valid argument You are not being creative enough

24 Testing Syllogisms by counter example  How to test for counter example?  Start with a false conclusion  Plug in your major (P) and your minor (S) in your Major

and Minor premises.  Find a middle term that makes both premises true. – All Socrates writings are pre first century writings. – Some ancient documents are not Socrates writings. – Therefore some ancient writings are not pre first century writings. – All___________________ are people. – Some students are not ___________ – Therefore some students are not people.

25 Distributed Terms  Distributed term- the term refers to all members of its

category.  All S are P– S is distributed – P is undistributed • All Dogs are mammals (Tells us something about all dogs but not all mammals)  No S are P– S and P are distributed • No dogs are cats. We know something about all dogs and all cats.

25 Distributed Terms  Some S are P

– Both S and P are undistributed • Some mammals are cats (We don't know anything about all mammals nor all cats)  Some S are not P – S is undistrbuted – P is distributed • Some astronauts are not men. (We know nothing about all astronauts but we do know that all men are not those being referred to in the subject.)  UNIVERSAL subjects are distibuted  NEGATIVE predicates are distributed

26 Testing Syllogisms by Rules  Five Rules for testing a syllogism  If one is broken the syllogism is not valid  Rule 1: In at least one premise, the middle term must be

distributed  3 options – M must be subject of an A,  M is the subject or predicate of an E – M is predicate of an O

S

P

A

D

U

E

D

D

I

U

U

O

U

D

26 Testing Syllogisms by Rules – All men are mortals – No mortals are angels – Therefore, some angels are not men.  Passed rule 1?  If not...Fallacy of the Undistibuted Middle. – All men are living beings – Some living beings are dogs – Therefore some dogs are men.

26 Testing Syllogisms by Rules  Rule 2: If a term is distributed in the conclusion, it must

also be distributed in its premise.  A conclusion cannot go beyond its premise. – All men are mortals – No mortals are angels – Therefore, some angels are not men. • Which term is distributed in conclusion? • Is it distributed in the premise? – Fallacy of Illicit Major – Fallacy of Illicit Minor • Some rocks are granite • No granite is a sandstone • Therefore some sandstones are not rocks

26 Testing Syllogisms by Rules  Rule 3: A valid syllogism cannot have two negative

premises. – Some cats are not insects – No dogs are insects. – Therefore some dogs are not cats. • Fallacy of Two negative Premises  Rule 4: A valid syllogism cannot have a negative premise and an affirmative conclusion – All dogs are animals – No plants are animals – Therfore, some plants are dogs. • Fallacy of a Negative Premise and Affirmative Conclusion

26 Testing Syllogisms by Rules  Rule 5: A valid syllogism cannot have 2 affirmative

premises and a negative conclusion. – All whales are mammals. – No canaries are mammals. – Therefore, come canaries are not whales

– All whales are sea creatures – Some sea creatures are warm blooded animals. – Therefore, no warm blooded animals are whales.  Fallacy of Two Affirmative premises and a Negative Conclusion

26 Testing Syllogisms by Rules  Last 3 rules can be made into one rule:  The numer of negative conclusion must equal the numer of

negative premises.

 2 Options  There is a negative conclusion with one and only one

negative premise  There is a positive conclusion with ONLY positive premises.