deductive arguments ch8 - thinking differently · 2014. 5. 29. · 1. translate argument into...

Review:

Deductive ArgumentsAre these valid arguments?

• 2 + x = 7. Therefore, ‘x’ must equal 5.

• John is seven years old and Sarah is six years old. So Sarah is younger than John.

• Juan is rich. Everyone who is rich took Javy’s class in Critical Thinking and Juan took Javy’s class in

Critical Thinking.

• Everything that Pete won at the carnival must be junk. I know that Pete won everything that Bob

won, and all the stuff that Bob won is junk.

Review:

Deductive Arguments

Making it Easier to Check for Validity

1. Would be easier if we could “rephrase”

each claim into a form that is easier to

understand.

– Standard-Form Categorical Claim

2. Would be easier if we then reformatted

the argument into a form that is easier to

understand

– Syllogism

Deductive Logic Day II

What are we going to do?

Critical Thinking Ninjas!

Deductive Arguments

Quick Guide to Venn Diagrams


A-Claim:All S are P.

All humans are mammals. .

E-Claim:No S are P.

No cats are dogs.

I-Claim:Some S are P.

Some citizens are voters.

O-Claim:Some S are not P.

Some contestants are not winners

Grey out what does not exist.When you can’t grey anything out, place “x” where you

know there’s at least one member in the group.

Deductive Arguments

Training Exercise #1:

Turning a claim into a “standard-form

categorical claim.”

“Only reptiles can be lizards.”

Becomes…

“All lizards are reptiles.”


A-Claim: All ___ are ____. E-Claim: No ___ are ____.I-Claim: Some ___ are ___.O-Claim: Some ___ are not ____.

A-Claim:All S are P.

Groups

Exercise 8-1 #4, 5, 11, 17, 20

Exercise 8-2 #2, 5

(Turn into Categorical Claims – be sure to make categories)

Exercise 8-1

4. All members of the suborder Ophidia are snakes.

5. All members of the suborder Ophidia are snakes.

11. All times the frog population decreases are times the snake

population decreases.

17. No people identical to the bank robber are people identical to

Jane’s fiancé.

20. Some examples of corn are not things that make good popcorn.

Exercise 8-2

2. No students of mine are students who are failing.

5. All times Joan sings are times people make faces.

Deductive Arguments

Training Exercise #2:Turning an argument into a “categorical syllogism”

Steps:

1. Identify premises and conclusion.

2. Look out for unstated premises.

3. Place them in order P(1), P(2), C.

4. Turn all claims into standard-form claims (keep all

three terms the same!).

Example:

P(1): Some lizards are reptiles.

P(2): All reptiles are beautiful beasts.

C: Some beautiful beasts are lizards.


Recommended:

Write each of the

next three

examples on

separate pages.

Deductive Arguments

Training Exercise #2:Turning an argument into a “categorical syllogism”.

“Every Cowboy is an American, but I know a few Americans who

live overseas. So it’s pretty obvious that there are Cowboys who

don’t live here.”

P: Every Cowboy is an American.

All Cowboys are Americans

P: I know a few American’s who live overseas.

Some Americans are people who live overseas.

C: So it’s pretty obvious there are Cowboys who don’t live here.

Some Cowboys are people who live overseas.


Deductive Arguments


“Only those courses that are in the schedule will be offered.

Among the courses that will not be offered is History 105,

History of Europe. Therefore, History 105 is not in the

schedule.”

P: Only those courses that are in the schedule will be offered.

All courses that will be offered are courses in the schedule.

P: History 105, History of Europe will not be offered.

No History 105 courses are courses that will be offered.

C: Therefore, History 105 is not in the schedule.

No History 105 courses are courses in the schedule.


Deductive Arguments


“You shouldn’t give chicken bones to dogs. They could choke on

them.”

P: Dogs could choke on chicken bones.

All chicken bones are things dogs can choke on.

UP: You shouldn’t give dogs anything they can choke on.

No things dogs could choke on are things you should give to dogs.

C: You shouldn’t give chicken bones to dogs.

No chicken bones are things you should give dogs.


Deductive Arguments

Training Exercise #3:Check the validity of an argument with Venn Diagrams

(method #1).

Steps:

1. Translate argument into categorical syllogism form.

2. Draw three interlocking circles representing all three terms.

3. Shade and “x” according to the premises.

– Always shade first. Place “x” in non-shaded regions last.– If both of the areas where “x” could go are non-shaded, place

“x” on the line between the two ( = “maybe”).

4. Check validity.

– Valid argument if the conclusion is necessarily true given the diagram. (Note: “Maybe” is not the same as “Some”.)

I recommend using one abbreviations for terms.


Deductive Arguments


(method #1).

Example:



Some Cowboys are people who live overseas.

All C are A

Some A are O

Some C are O

How do we draw this?


Deductive Arguments


(method #1).

Example:



some Cowboys are people who live overseas.

All C are A

Some A are O

Some C are O


C A

O

12

3

45

6

7

Is this valid?

No. If valid, “x” would be in area #5.

Deductive Arguments


(method #1).

Example:



Therefore, no History 105 courses are courses in the schedule.

All O are S

No H are O

No H are S



Deductive Arguments


(method #1).

Example:



Therefore, no History 105 courses are courses in the schedule.

All O are S

No H are O

No H are S


O S

H

12

3

45

6

7

Is this valid?

No. If valid, area #6 should be shaded too.

Deductive Arguments


(method #1).

Example:



So, no chicken bones are things you should give dogs.

All B are C

No C are G

No B are G



Deductive Arguments


(method #1).

Example:



So, no chicken bones are things you should give dogs.

All B are C

No C are G

No B are G


B C

G

12

3

45

6

7

Is this valid?

Yes! Since nothing in B is also in G.

Deductive Arguments

Group Training!Time for Venn Diagram combat practice.

Using the Venn Diagram method, test to see if these are valid

arguments.

1. All forms of coffee are stimulants. It’s obvious since all

caffeinated drinks are stimulants and all coffees have caffeine.

2. All educated people respect books, but some bookstore

personnel are not truly educated. So some bookstore personnel

don’t respect books.

3. No islands are part of the mainland and Hawaii is an island.

Therefore, Hawaii is not on the mainland.


Deductive Arguments


#1

All caffeinated drinks are stimulants.

All forms of coffee are caffeinated drinks.

All forms of coffee are stimulants.


All CD are SAll C are CDAll C are S

This is a valid syllogism!

C S

CD

Deductive Arguments


#2

All educated people are people who respect books.

Some bookstore personnel are not educated people.

Some bookstore personnel are not people who respect books.


This is NOT a valid syllogism!

All E are RSome B are not ESome B are not R

E R

B

X

Deductive Arguments


#3

No islands are parts of the mainland.

All Hawaiis are islands.

No Hawaiis are parts of the mainland.


This is a valid syllogism!

I M

H

No I are MAll H are INo H are M

deductive arguments ch8 - thinking differently · 2014. 5. 29. · 1. translate argument into...

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