Chapters 8-12

Question 1

What is Categorical Logic?

Answer 1

A system of logic based on the relations of inclusion and exclusion among classes (“categories”). This branch of logic specifies the logical relationships among claims that can be expressed in the forms: “All ___ are ___,” “No __ are __,” “Some ___ are ____,” and “Some ___ are not ____.”

Question 2

Categorical Logic was developed by _______ in the ____ century B.C.E.

Answer 2

Aristotle in the fourth century B.C.E. it is also known as Aristolian or traditional logic

Question 3

Truth-Functional logic and Categorical logic are useful in

Answer 3

clarifying and analyzing deductive arguments.

Question 4

Do these claims mean the same thing? 1. Everybody who is ineligible for Physics 1A must take Physical Science 1. 2. No students who are required to take physical science 1 are eligible for physics 1A.

Answer 4

NO

Question 5

What is a Categorical Claim?

Answer 5

Any standard-form categorical claim or any claim that means the same as some standard-form categorical claim.

Question 6

A Categorical Claim says something about

Answer 6

classes or categories of things.

Question 7

A ____________ is a claim that results from putting names or descriptions of classes into the blanks of the following structures: A: All ___ are ___. E: No ___ are ___. I: Some ___ are ___. O: Some ___ are not ___.

Answer 7

Standard-Form Categorical Claim

Question 8

In the example: Some Muslims are not Sunnis what type of claim is being used?

Answer 8

O-Claim

Question 9

In the example: All Presbyterians are Christians what type of claim is being used?

Answer 9

A-Claim

Question 10

In the example: Some Christians are Arabs what claim is being used?

Answer 10

I-Claim

Question 11

In the example: No Muslims are Christians what claim is being used?

Answer 11

E-Claim

Question 12

A: All ___ are ___. The phrases that go in the blanks are called?

Answer 12

terms

Question 13

A: All ___ are ___. The one that goes into the second blank is called the

Answer 13

predicate term

Question 14

A: All ___ are ___. The one that goes into the first blank is called the

Answer 14

subject term

Question 15

A: All S are P stands for

Answer 15

A-Claim: All ___ are ___. S stands for subject term and P stands for predicate term.

Question 16

Only ___ and ___ will work as terms.

Answer 16

nouns and noun phrases

Question 17

“All fire engines are red” is this an example of a standard form categorical claim?

Answer 17

No because red is an adjective not a noun or noun phrase.

Question 18

How do you check if something is a standard-form categorical claim?

Answer 18

Switch the S and P. For example with the sentence “All fire engines are red” to check you would switch it to “All red are fire engines” since it does not make sense it is not a standard-form categorical claim.

Question 19

“All red vehicles are fire engines” is this a standard-form categorical claim?

Answer 19

Yes even though it is false it makes sense.

Question 20

What claim does this represent?

Answer 20

A-Claim

All S are P

Question 21

What claim does this represent?

Answer 21

E-Claim

No S are P

Question 22

What claim does this represent?

Answer 22

I-Claim

Some S are P

Question 23

What claim does this represent?

Answer 23

O-Claim

Some S are not P

Question 24

Notice in the diagram for the A-Claim that area that would contain any members of the S class that were not members of the P class is _____ which means _______.

Answer 24

colored which means that is empty.

Question 25

This diagram represents the claim that “All S are P” since

Answer 25

there is no S left that isn’t P

Question 26

In the diagram for E-Claim the area where S and P overlap is ___

Answer 26

Empty; any S that s also a P has been eliminated. Hence “No S are P”

Question 27

I-Claim Some S are P

At least one S is P and the X in the middle shows that

Answer 27

at least one thing inhabits this area

Question 28

O-Claim Some S are not P

X in the area of the S circle that is outside the P circle representing

Answer 28

the existence of at least one S that is not a P