Chapter 3

Question 1

Argument analysis

Answer 1

extracting arguments from prose passages & putting them in standard form and the deciding whether these arguments are good arguments.

Question 2

Reconstructing the argument

Answer 2

the process of taking a prose passage & rewriting the argument it contains in standard form.

Question 3

Evaluating the argument

Answer 3

decide whether the argument is a good argument.

Question 4

Well-formed argument

Answer 4

any argument whose conclusion does follow from its premises. Fall into two categories: valid and cogent.

Question 5

Deductively valid

Answer 5

impossible for all the premises to be true and the conclusion false.

Question 6

Inductively cogent

Answer 6

the premises merely make the conclusions probable.

Question 7

Validity

Answer 7

an argument is valid if & only if it is impossible for the premises of the argument all to be true & the conclusion of the argument to be false.

Question 8

Invalid argument

Answer 8

an argument that is not valid.

Question 9

Predicate logic

Answer 9

• breaks sentences down in smaller units.

- uses A & B, and x & y.

Question 10

Letters P, Q, R

Answer 10

for complete sentences.

Question 11

Compound sentences

Answer 11

formed by combining two or more simpler sentences.

Question 12

Lowercase letters such as x & y

Answer 12

to abbreviate names of individuals.

Question 13

Uppercase letters such as A & B

Answer 13

to abbreviate words & phrases expressing properties or characteristics of individuals.

Question 14

Negation

Answer 14

• Not P.

- ~P.

Question 15

Conjunction

Answer 15

• P and Q.

- compound statement, made up of conjuncts.

Question 16

Disjunction

Answer 16

• Either P or Q.

- compound statement, made up of disjuncts.

Question 17

Conditionals

Answer 17

• If P, then Q.
• P -> Q.
• compound statement made up of an antecedent & a consequent.

Question 18

Bi-conditional

Answer 18

• P if and only if Q.

- (If P then Q) and (If Q then P).

Question 19

Antecedent

Answer 19

follows the word ‘‘if”.

Question 20

Consequent

Answer 20

follows the word “then”.

Question 21

Argument by Elimination

Answer 21

1.) Either P or Q.
2.) ~ P.
3.) therefore, Q.
________________________
1.) Either P or Q.
2.) ~Q.
3.) therefore, P.

Question 22

Conjunction Argument

Answer 22

1. ) P
2. ) Q
3. ) therefore, P & Q.

Question 23

Simplification Argument

Answer 23

1.) P & Q.
2.) therefore, P.
_________________________
1.) P & Q.
2.) therefore, Q.

Question 24

Affirming the Antecedent (Modus Ponens)

Answer 24

1. ) If P then Q.
2. ) P.
3. ) therefore, Q .

Question 25

Denying the Consequent (Modus Tollens)

Answer 25

1. ) If P then Q.
2. ) ~Q.
3. ) therefore, ~P.

Question 26

Hypothetical syllogism

Answer 26

1. ) If P then Q.
2. ) If Q then R.
3. ) therefore, If P then R.

Question 27

Contraposition

Answer 27

1. ) If P then Q.

2. ) therefore, If ~Q then ~P.

Question 28

Equivalence

Answer 28

1. ) P if and only if Q.
2. ) ~P.
3. ) therefore, ~Q.

Question 29

Universal Modus Ponens

Answer 29

1. ) All As are Bs.
2. ) x is an A.
3. ) therefore, x is a B.

Question 30

Universal Modus Tollens

Answer 30

1. ) All As are Bs.
2. ) x is not a B.
3. ) therefore, x is not an A.

Question 31

Uninversal hypothetical syllogism

Answer 31

1. ) All As are Bs.
2. ) All Bs are Cs.
3. ) therefore, All As are Cs.

Question 32

Universal Ruling Out

Answer 32

1. ) No As are Bs.
2. ) x is an A.
3. ) therefore, x is not a B.

Question 33

Generalization

Answer 33

do not say anything about any specific individual.

Question 34

Quantifier

Answer 34

“all”, “some” and “none”, use in generalizations.

Question 35

Ill-formed

Answer 35

An argument is ill-formed if and only if it is neither valid nor cogent.

Question 36

Cogency

Answer 36

An argument is cogent if and only if it is not valid but follows a pattern such that all arguments following that pattern have a conclusion that is probably true if the premises are true.

Question 37

Testing arguments for validity

Answer 37

• Find examples that prove invalidity, imagine a situation where the premises of the argument are all true, but the conclusion is false.
• Look for examples that show the invalidity of other arguments following the same pattern.
• Check the pattern.

Question 38

Incomplete arguments

Answer 38

arguments that are ill-informed but that can be made cogent or valid by the addition of a fairly obvious and simple premise.

Question 39

Deductive Arguments

Answer 39

intend to provide logically conclusive support for the conclusion.

Question 40

Pattern of argument

Answer 40

displays the underlying form or logical structure of an argument.

Question 41

Standard form

Answer 41

listing each premise, on a separate numbered line, drawing a line, writing the conclusion.

Question 42

Sentential/propositional logic

Answer 42

• letters standing for whole sentences.

- P, Q, R.

Question 43

Reasons for standard form

Answer 43

(1) avoid including extra steps in the argument.
(2) easier to spot the places where there are missing premises and easier to figure out what they are.
(3) arguments easier to understand & evaluate.
(4) discussion of arguments simpler & more convenient.