Chapter 9-10

Question 1

Deductive Argument

Answer 1

-an argument whose purport is that the conclusion follows necessarily from the premises
- An argument is deductively valid if and only if there is no logical possibility in which every premise is true but the conclusion is false
- It is the structure of the argument itself that determines its validity
~ The formal relation of the premises to the conclusion, not the content of the statements

Question 2

Valid

Answer 2

• It is not possible for the premises to be true and the conclusion to be false (if the premises are true, the conclusion must be true)

Question 3

Sound

Answer 3

• An argument is sound if and only if it is both valid and the premises are true

Question 4

Truth-Function Logic

Answer 4

• remember, a statement is a sentence with truth-value

Question 5

Simple statement

Answer 5

• a statement that doesn’t contain any other statements as constituents
  ~ “Today is Tuesday.”

Question 6

Compound statement

Answer 6

-Composed of at least two simple statements

Question 7

Types of truth-functional statements

Answer 7

• Negation
• Conjunction
• Dis junction
• Implication (conditional)

Question 8

Negation

Answer 8

• It is not the case that p
• P
• Example
  ~ “it is not Tuesday”
  ~ “ Alice did not ride her bike.”
• It is not the case that Alice rode her bike
  -~ “The price of gas is not high.”
• The denial of a statement
• The truth-function of negation reverses the truth-value of the component (simmple) statement
• True if the component statement is false

Question 9

Conjunction

Answer 9

• P and Q
• Examples
  ~ “Alice rode her bike, and Belinda walked.”
• “Today is Tuesday, and I forgot to pay the rent.”
• Two simple statement joined by a connective to form a compound statement
• The grammatical term “and” is one of several terms that can express logical conjunction
• Other include “but,” “yet,” “while,” “also,” “moreover.”
• Caution
  ~ Make sure that connective really is conjoining two distinct statement
• True if both the component claims (conjunts) are true
  ~ So, if either conjunct is false, the conjunction itself is false

Question 10

Disjunction

Answer 10

• P or Q
• Example
  ~ “Alice rode her bike or Belinda is upset
  ~ “Jamie will drive the car or Andy will drive the van.”
• Complex statement composed of two simple statements (disjuncts)
• False if both of its disjuncts are false
• The grammatical term “or” is usually found in a disjunction, through sometimes “unless” is used

Question 11

Implication

Answer 11

• if P, then Q
• Example
  ~ “If Alice went to work, then Lewis took the day off.”
  ~ “I’ll walk the dog unless it’s raining.”
  ~ “Whenever I stay up late, I sleep in.”
• Basic form: “if… then…”
• False if its antecedent is true and its consequent is false

Question 12

Modus Ponens ( Affirming the Antecedent)

Answer 12

-If p then q
-p
- therefore, q
- Examples
~If zero bark, an intruder is in the house
~Zeno is barking
~Therefore, an intruder is in the house

Question 13

Modus Tollens (Denying the Conquent)

Answer 13

• If P then Q
• Not P
• Therefore, Not Q
• Example
  ~ If that thing is a spider, then it’s poisonous
  ~ It is not poisonous
  ~ So, it’s not a spider

Question 14

Disjunctive Syllogism

Answer 14

• P or Q
• Not P
• Therefore, Q
• Example
  ~ Either Miles drove home or he walked
  ~ Miles didn’t drive home
  ~ So, he walked

Question 15

Chain Argument (Hypothetical Syllogism)

Answer 15

• If P then Q
• If Q then R
• Therefore, If P then R
• Example
  ~ If Jackson spends his paycheck on a new stereo, then he won’t buy his mom a birthday gift
  ~ If Jackson doesn’t but his mom a birthday gift, she’ll be sad
  ~ So, if Jackson spends his money on a new stereo, his mom will be sad

Question 16

Statistical Syllogism

Answer 16

• Example
  ~ 60% of students at the University of El Dorado believe in God. Cacambo goes to the University of El Dorado. Therefore Cacambo believes in God.

Question 17

Statistical Syllogism

Answer 17

• Example
  ~ 60% of students at the University of El Dorado believe in God. Cacambo goes to the University of El Dorado. Therefore Cacambo believes in God.

Question 18

Induction by Confirmation

Answer 18

• If H then O
• O
• Therefore H is probable
• The higher the number of confirming instances, the stronger the argument.
• Disconfirming instances refute the hypothesis
• Example
  ~ What’s causing the mess in the yard? I thought it might be a raccoon getting into the trash, so I put the lid on to see if it was still spilled: raccoons can open trash lids with their hands, so if it was a raccoon, then it would still be pilled. In the morning, the trash can was knocked over, open, and the garbage was spilled. If it was a raccoon, then there would be dirty paw-prints in the vicinity and there were. If it was a raccoon, then all sorts of garbage bits would be gnawed and eaten. They were. I’ve got raccoons.