Review: Deductive Arguments Are 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 Critical Thinking Ninjas!

Quick Guide to Venn Diagrams 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.

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

Deductive Arguments Critical Thinking Ninjas!

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 Critical Thinking Ninjas!

Training Exercise #2: Turning an argument into a “categorical syllogism” Steps: 1. 2. 3. 4.

Identify premises and conclusion. Look out for unstated premises. Place them in order P(1), P(2), C. 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 Critical Thinking Ninjas!

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 Critical Thinking Ninjas!

Training Exercise #2: Turning an argument into a “categorical syllogism”. “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 Critical Thinking Ninjas!

Training Exercise #2: Turning an argument into a “categorical syllogism”. “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 Critical Thinking Ninjas!

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 Critical Thinking Ninjas!

Training Exercise #3: Check the validity of an argument with Venn Diagrams (method #1). Example: All Cowboys are Americans Some Americans are people who live overseas. 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 Critical Thinking Ninjas!

Training Exercise #3: Check the validity of an argument with Venn Diagrams (method #1). Example: All Cowboys are Americans Some Americans are people who live overseas. some Cowboys are people who live overseas.

A

C

All C are A Some A are O Some C are O

2

1

3

5 4

6

7

O

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

Deductive Arguments Critical Thinking Ninjas!

Training Exercise #3: Check the validity of an argument with Venn Diagrams (method #1). Example: All courses that will be offered are courses in the schedule. No History 105 courses are courses that will be offered. Therefore, no History 105 courses are courses in the schedule. All O are S No H are O No H are S How do we draw this?

Deductive Arguments Critical Thinking Ninjas!

Training Exercise #3: Check the validity of an argument with Venn Diagrams (method #1). Example: All courses that will be offered are courses in the schedule. No History 105 courses are courses that will be offered. Therefore, no History 105 courses are courses in the schedule.

O

All O are S No H are O No H are S

S

2

1

3

5 4

6

7

H

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

Deductive Arguments Critical Thinking Ninjas!

Training Exercise #3: Check the validity of an argument with Venn Diagrams (method #1). Example: All chicken bones are things dogs can choke on. No things dogs could choke on are things you should give to dogs. So, no chicken bones are things you should give dogs. All B are C No C are G No B are G How do we draw this?

Deductive Arguments Critical Thinking Ninjas!

Training Exercise #3: Check the validity of an argument with Venn Diagrams (method #1). Example: All chicken bones are things dogs can choke on. No things dogs could choke on are things you should give to dogs. So, no chicken bones are things you should give dogs.

B

All B are C No C are G No B are G

C 2

1

3

5 4

6

7

G

Is this valid? Yes! Since nothing in B is also in G.

Deductive Arguments Critical Thinking Ninjas!

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 Critical Thinking Ninjas!

Group Training! Time for Venn Diagram combat practice. #1 All caffeinated drinks are stimulants. All forms of coffee are caffeinated drinks. All forms of coffee are stimulants.

C

S

All CD are S All C are CD All C are S This is a valid syllogism!

CD

Deductive Arguments Critical Thinking Ninjas!

Group Training! Time for Venn Diagram combat practice. #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.

E

R

All E are R Some B are not E Some B are not R This is NOT a valid syllogism!

X B

Deductive Arguments Critical Thinking Ninjas!

Group Training! Time for Venn Diagram combat practice. #3 No islands are parts of the mainland. All Hawaiis are islands. No Hawaiis are parts of the mainland.

I

M

No I are M All H are I No H are M This is a valid syllogism!

H