Chapter 9

Question 1

categorical logic

Answer 1

logic based on the relations of inclusion and exclusion among classes (or “categories”) as stated in categorical terms
-useful in clarifying and analyzing deductive arguments

Question 2

category

Answer 2

In logic, a c ategory is a group or a class or a population; any bunch of things can
serve as a category for our purposes

Question 3

terms

Answer 3

Terms are noun phrases, like “dogs,” “cats,”
“Christians,” “Arabs,” “people who read logic books,” and so on. These terms are
labels for categories or classes.
-NOUNS

Question 4

subject term (S)

Answer 4

subject of the conclusion

-goes in the first blank (All __ are __.)

Question 5

predicate term (P)

Answer 5

predicate of the conclusion

-goes in the second blank (All __ are __.)

Question 6

A-claims

Answer 6

ALL metals are conductors

• general law
• affirmative claim

Question 7

E-claims

Answer 7

NO metals are conductors

• general law
• negative claim

Question 8

I-claims

Answer 8

SOME metals are conductors
(this metal is a conductor)
-observational law
-affirmative claim

Question 9

O-claims

Answer 9

SOME metals are NOT conductors
(this metal is not an conductor)
-observational law
-negative claim

Question 10

venn diagramms

Answer 10

illustrations of categorical claims

- p.246 in critical thinking (newest edition)

Question 11

equivalent claims

Answer 11

if, and only if, they would be true in all and exactly the same circumstances— that is, under no circumstances could one of them be true and the other false

Question 12

“only”

Answer 12

The word “only,” used by itself, introduces the predicate term of an
A-claim.
The phrase “the only” introduces the subject term of an A-claim.
“only matinees are half-price shows” as well as “matinees are the only half-price shows” can be translated to:
“all half-price shows are matinees”

Question 13

square of opposition

Answer 13

shows the logical relationships of categorical claims that correspond with each other

p. 254
- very interesting, I

Question 14

corresponding claims

Answer 14

claims who have the same subjects and the same predicates.
NOTE: S = S and P = P is CORRECT/CORRESPONDING
S=P and P=S is NOT CORRECT/NOT CORRESPONDING

Question 15

contrary claims

Answer 15

can both be false but not both be true

-A and E claims (general laws) are contrary

Question 16

subcontrary claims

Answer 16

can both be true but cannot not both be false

-I and O claims (observational laws) are subcontrary

Question 17

contradictory claims

Answer 17

never have the same truth value

• A and O are contradictory, as well as E and I
  e. g. if A is true, O cannot be true

Question 18

conversion

Answer 18

switching S and P
E and I claims are equivalent to their converses
A and O claims are not

Question 19

universe of discourse

Answer 19

a closed system in which a discourse takes place
e.g. if the professor says: “everybody passed the exam” the universe of discourse are all the students. Your mother didn’t pass the exam.

Question 20

complementary class/term

Answer 20

contains everything in the universe of discourse that is not part of the first class
-e.g. student and nonstudents

Question 21

an obversion

Answer 21

1. change a claim from affirmative to negative or vice versa
2. change the predicate term to its complementary
   - all categorical claims are equal to their obversion

Question 22

All pairs of terms (S and P) of a true e-claim are complementary terms.
True or false?

Answer 22

False, but all complementary terms are pairs of terms of a true e-claim

Question 23

contra-positive

Answer 23

1. converse the claim (switch S and P)
2. replace both terms with complementary terms
   All A- and O-claims, but not E- and I-claims, are equivalent to their contrapositives

Question 24

Some mosquitoes carry West Nile virus. So it must be
that there are some that don’t.
Is this necessarily true?

Answer 24

No, The only way to get an I-claim from an O-claim is by obverting the O-claim.

Question 25

a syllogism

Answer 25

two-premise deductive arguement

Question 26

a categorical syllogism

Answer 26

A categorical syllogism (in standard form) is a syllogism whose every claim is a standard-form categorical claim and in which three terms each occur exactly twice and in exactly two of the claims.

Question 27

major term (P)

Answer 27

the term that occurs as the predicate term of the syllogism’s conclusion

Question 28

minor term (S)

Answer 28

the term that occurs as the subject term of the syllogism’s conclusion

Question 29

middle term (M)

Answer 29

the term that occurs in both of the premises but not at all in the conclusion

Question 30

validity

Answer 30

An argument is valid if, and only if, it is not possible for its premises to be true while its conclusion is false.
This is just another way of saying that, were the premises of a valid argument true (whether or not they are in fact true), then the truth of the conclusion would be guaranteed.

Question 31

a sound argument

Answer 31

If the premises of a valid argument are in fact true, then that argument is said to be sound, and its conclusion has been proven to be true

Question 32

The venn diagramm method of testing validity

Answer 32

a syllogism is valid only if diagramming the premises automatically produces a correct diagram of the conclusion. The exact process can’t be displayed here.
Handy rules to remember:
1. When one premise is an A- or E-premise and the other is an I- or O-premise, diagram the A or E-premise first
2. An X that can go in either of two areas goes on the line separating the areas
3. If any circle has only one area remaining uncolored,
an X should be put in that area

Question 33

Categorical Syllogisms with Unstated Premises

Answer 33

In everyday life, people often give syllogisms, but they leave out one premise, probably because they think it is too obvious to state. It might be sensible to question such unstated premises

Question 34

popular syllogisms

Answer 34

P1: All As are Bs; P2: All Bs are Cs; C: All As are Cs
or
P1: All As are Bs; P2: No Bs are Cs; C: No As are Cs

Question 35

affirmative and negative

Answer 35

A and I are affirmative; E and O are negative

Question 36

distribution

Answer 36

a claim is distributed if it says something about every member of a class
A claim: only S is distributed
E claim: both S and P are distributed
I claim: neither S nor P are distributed
O claim: only P is distributed

Question 37

The three rules to test validity

Answer 37

1. The number of negative claims in the premises must be the same as the number of negative claims in the conclusion. (Because the conclusion is always one claim, this implies that no valid syllogism has two negative premises.)
2. At least one premise must distribute the middle term.
3. Any term that is distributed in the conclusion of the syllogism must be distributed in its premises.