Test 2

Question 1

Types of Arguments?

Answer 1

• Deductive

- Non-Deductive (Inductive)

Question 2

Deductive

Answer 2

• An argument where the premises, if true, are intended to prove the conclusion with absolute certainty
• An argument where the conclusion is supposed to follow from the premises with absolute certainty
• Ex: Kangaroos are mammals and Jeffrey is a kangaroo. So Jeffrey is a mammal.
• Ex: Prince can run faster than David Bowie, but not as fast as Michael Jackson. Madonna cannot run faster than David Bowie. So Michael Jackson can run faster than Madonna.

Question 3

Non-Deductive (Inductive)

Answer 3

• An argument where the premises, if true, are intended to provide some reason to believe the conclusion, but not establish the conclusion with absolute certainty
• An argument where the conclusion is not supposed to follow from the premises with absolute certainty, but is nonetheless supposed to be supported by the premises to some extent
• Ex: Every time I”ve visited that taco shop, the “be back soon” sign is posted on the door and the door is locked. I don’t think it’s open for business anymore.
• Ex: The window at the victim’s apartment was open, despite outdoor temperatures of less than -10 degrees celsius. So it seems probable that the killer either entered or escaped through the window.

Question 4

Objection

Answer 4

• A reason for believing that the argument doesn’t supply good reasons to believe its conclusion
• Note: An objection is itself an argument – an argument about another argument.
• The conclusion of an objection is always, “Therefore, argument X doesn’t provide *good reasons to believe its conclusion.”
  
  • *or “very good,” or “ideally good,” or “as good as the arguer wants.”
• Be careful to distinguish between:
  
  • An objection to an argument
    
    • Ex: It’s not true that no one who’s gotten frostbite while climbing K2 has survived to tell about it. Therefore, the argument doesn’t provide any good reasons to believe its conclusion. (doesn’t provide good reasons to believe its conclusion)
  • An argument against another argument’s conclusion
    
    • Ex: Whatever difficulties human beings confront, as a species they always eventually overcome those difficulties. Therefore, eventually someone who gets frostbite while climbing K2 will survive to tell about it. (the argument’s conclusion is false)

Question 5

Formulating New Arguments vs. Making an Objection

Answer 5

• The problem with presenting an argument against another argument’s conclusion as if it were an objection to that argument is that giving new reasons to reject the argument’s conclusion doesn’t tell us what we should think about the reasons that have already been given (by the first argument) for accepting the conclusion.
• Essentially we’re left with two sets of reasons that pull in opposite directions.
• An objection, on the other hand, helps us to see the weaknesses in the reasons that the first argument gives in support of its conclusion. Formulating objections leads to an increased understanding of the extent to which a proposed argument actually provides justification for believing its conclusion.
• In sum: There’s a difference between
  1) formulating new arguments and
  2) making an objection to an argument that’s already been proposed.
• Both are important in debates and disagreements, as well as in individual reasoning, but they have different functions.
• So you should be able to do both, and not confuse the one with the other.

Question 6

Two Kinds of Objections

Answer 6

• 1) Premise Challengers -These challenge the truth (or likelihood, or acceptability) of the premises (attack numbers - where the evaluation of premises is focused)
  
  • Ex: “It’s not true that no one who’s gotten frostbite while climbing K2 has survived to tell about it. Therefore, the argument doesn’t provide any good reasons to believe its conclusion.”
• 2) Inference Challengers - These challenge the support (or degree of support) that the premises are supposed to provide to the conclusion (attack arrows - where the evaluation of inferences is focused – including validity or invalidity)
  
  • Ex: “Even if no one has yet gotten frostbite while climbing K2 and survived to tell about it, it’s quite possible that some one will. If life-saving and rescue technologies improve, this may even become more likely with each passing year. Therefore, the argument doesn’t provide good reasons to believe its conclusion.”

Question 7

Crossing Over Type of Argument and Type of Objections

Answer 7

• Top Left: Deductive x Premise Challengers
  
  • Challenge the truth (or acceptability) of the premises
• Bottom Left: Deductive x Inference Challengers
  
  • Challenge the validity of the argument
• Top Right: Non-Deductive x Premise Challengers
  
  • Challenge the truth (or acceptability) of the premises
• Bottom Right: Non-Deductive x Inference Challengers
  
  • Challenge the strength of the argument

Question 8

Crossing Over of Type of Argument and Result of an Ideally Complete Evaluation

Answer 8

• Top Left: Deductive x No legitimate challenge to premises
  
  • An argument with true (or acceptable) premises
• Middle Left: Deductive x No legitimate challenge to inference
  
  • A valid argument
• Bottom Left: Deductive x No legitimate challenge to premises or inference
  
  • A sound argument
• Top Right: Non-Deductive x No legitimate challenge to premises
  
  • An argument with true (or acceptable) premises
• Middle Right: Non-Deductive x No legitimate challenge to inference
  
  • A strong argument
• Bottom Right: Non-Deductive x No legitimate challenge to premises or inference
  
  • A cogent argument
• Valid/Invalid
• Sound/Unsound
• Strong/Weak
• Cogent/Not Cogent

Question 9

How to Evaluate the Truth of Premises?

Answer 9

• Use the same procedures you would use for evaluating the truth of any claim
• Corollary: The evaluation of the truth of premises can be expressed as the consideration of possible arguments, consistent with the available evidence, for and against believing the truth of the premises
• Further Note: There are some types of claims that tend to call for particular kinds of evaluation

Question 10

Three Types of Claims

Answer 10

• 1. Factual Claims - Non-Probabilistic
• 2. Factual Claims - Probabilistic
• 3. Evaluative Claims (Normative Claims)

Question 11

Factual Claims - Non-Probabilistic

Answer 11

-A non-evaluative claim about the way things are that is not qualified by any probabilistic term expressing less than full certainty

• Indicator Words:
  
  • Certainly
  • Necessarily
  • Not even possible that

Types of Evidence That Could Bear on Evaluation (types of evidence appropriate to evaluating research):

- Direct observation
- Testimony/reportage from reliable sources
- Objective measurement procedures
- Deductive inference from true premises
- [Anything from the “factual claims -- probabilistic” list, though these will provide less certainty]

• Ex: The cat is on its bed.
• Ex: Rembrandt lived and died in the 17th century
• Ex: Nevada’s state capital is Las Vegas.
• Ex: The Eagles won’t make the playoffs this year.
• Ex: There is intelligent life on other planets.

Question 12

Factual Claims - Probabilistic

Answer 12

-A non-evaluative claim about the way things are that is qualified by at least one probabilistic term (i.e. “possibly,” “probably,” etc.)

• Indicator Words:
  
  • Almost certainly
  • Probably/probable/more likely than not
  • Plausibly/plausible
  • Possibly/possible

Types of Evidence That Could Bear on Evaluation (types of evidence appropriate to evaluating research):

- Testimony from multiple sources
- Reasoned plausibility
- Anecdotal
- Direct observation or objective measurement of the same phenomenon in similar circumstances (though not in this one)
- [Anything from the “factual claims -- non-probabilistic” list above, except for “deductive inference from true premises”; though each of these can generate support coming close to certainty]

• Ex: The cat is probably on the bed.
• Ex: It’s possible that there is life on other planets.
• Ex: It’s highly probable that there is life on other planets.
• Ex: I think they’re more likely to buy a Rembrandt than a Van Gogh.
• Ex: The Eagles probably won’t make the playoffs this year.

Question 13

Evaluative Claims

Answer 13

• Normative Claims
• A claim about the way things should be (or ought to be, or would be better if they were, etc.) or about what is better and worse
• Indicator Words:
  
  • Good/bad
  • Ough/ought not
  • Should/should not
  • Better/worse
  • Best/worst
  • Most worthwhile/least worthwhile

Types of Evidence That Could Bear on Evaluation (types of evidence appropriate to evaluating research):

- Common/shared evaluative commitments/attitudes
- Personal evaluative commitments/attitudes
- Assumed evaluative commitments/attitudes
- Absurdity or embarrassment of holding the opposite view

• Ex: We should feed the cat.
• Ex: It’s wrong to insult people just for fun.

Ex: Rembrandt was a greater painter than Van Gogh.

• Ex: The most important task for humanity in the 21st century is the continued exploration of space.
• Ex: An important task for humanity in this century and the centuries to come is the continued exploration of space.

Question 14

How to evaluate the legitimacy of inferences?

Answer 14

• For Deductive:
  
  • The standard = validity: it’s not possible for the premises to be true and the conclusion false
  • Ex: Every dog is a mammal. Fido is a dog. Therefore, Fido is a mammal.
  • Validity is an “on-off” (or pass-fail) notion: Arguments are completely valid or completely invalid. No argument is “very valid”
• For Non-Deductive:
  
  • The standard = strength: the premises, if true, would provide strong reason to believe the conclusion is true
  • Ex: I’ve seen dozens of swans and every one has been white. Therefore, the next swan I see will probably be white.
  • Strength is a “more or less” notion.

Question 15

Valid Arguments

Answer 15

• Def 1: A valid argument is one where it’s not possible for the premises to be true and the conclusion false.
• Def 2: A valid argument is one where if the premises are true, the conclusion must be true
• Ex: All dogs are mammals. Fido is a dog. Therefore, Fido is a mammal.
• Ex: London is south of Edinburgh but north of Paris. So Paris is south of Edinburgh
• Ex: There’s a blind Corgi in the room, so there’s at least one Corgi in the room.

Question 16

Invalid Arguments

Answer 16

• Def 1: An invalid argument is one where it is possible for the premises to be true and the conclusion false
• Def 2: An invalid argument is one where even if the premises were true, the conclusion could still be false
• Ex: Philadelphia is no longer the capital of the United States, so Congress must meet elsewhere.
  
  • Congress wants to celebrate something.
• Ex: Joan is certainly dead. She jumped from an airplane at 10,000 feet without a parachute.
  
  • Big net at the bottom.
• Ex: All dogs are mammals. Fido is a mammal. Therefore, Fido is a dog.
  
  • Fido is a hedgehog. Hedgehogs are mammals.

Question 17

How can you tell whether an argument is valid or invalid?

Answer 17

• 2 Techniques:
  
  • 1. The counterexample test
  • 2. Identifying the form of the argument as matching a valid or invalid form
• These 2 techniques may be thought of as techniques for
  
  • (1) generating inference-challenger objections to deductive arguments wherever this is possible
  • (2) determining that there are no possible inference-challenger objections (i.e. that the argument is valid)

Question 18

Counterexample Test

Answer 18

• Step 1: Try to describe a possible scenario in which the conclusion is false while the premises are true
  
  • Note: The argument only needs to be logically possible. It may be extremely probable, “science fiction,” “crazy,” etc. As long as the scenario is not inherently self-contradictory, it is possible in the intended sense
• Step 2: If you can describe such a scenario, the argument is invalid
• Step 3: If you cannot describe such a scenario, the argument is valid
• REMEMBER: The argument’s validity or invalidity has nothing to do with the actual truth or falsity of the premises
• The truth of falsity of the premises is something you evaluate separately, since it concerns a different kind of objection (a different kind of flaw in the argument): that is, a premise-challenger
• (Never evaluating the truth of the premises)
• PRACTICE THE WS

Question 19

Identifying the Form of an Argument

Answer 19

-Includes the 4 different forms

• Ex. 1: “If Elly doesn’t eat her green peas, she won’t get any dessert. Elly didn’t eat her green peas. So she won’t have any dessert.”
  
  • Description of the Form:
    
    • If A, then B; A → B
    • A.; A
    • Therefore, B; three dots B

Ex. 2: “Jack is either a Democrat or an Independent. If he’s a Democrat, he wouldn’t have voted for a Republican Senator. But Jack did bote or a Replican Senator. So he must be an independent.”

- Description of the Form:
    - A or B; A v B
    - If A, then not C; A → ∼C
    - C; C
    - Therefore, B; three dots B

Question 20

Proposition Labels

Answer 20

• Upper-case letters, each of which represents an atomic proposition
• ”A,” “B,” “C,” etc.

Question 21

Connectives

Answer 21

-Symbols that represent logical relations between propositions.

• 4 connectives:
  
  • ∼ = negation (“not”)
  • & = conjunction (“and”)
  • v = disjunction (“or”)
  • → = implication (“if… then”)

-”Therefore” sign: Symbol placed at the start of the conclusion of an argument to indicate that it’s the conclusion

Question 22

Atomic Proposition

Answer 22

• Any part of a belief or claim that can itself be expressed as a single claim
• Ex: “If Elly didn’t eat her green peas, then she doesn’t get any dessert.”
• This is a single claim, but the claim includes two atomic propositions:
  
  • (1) “Elly didn’t eat her green peas”
  • (2) “Elly doesn’t get any dessert.”

-Atomic propositions are like beliefs and claims in that they can be true or false

• Sometimes atomic propositions are repeated in an argument
  
  • Ex: “Elly didn’t eat her green peas, then she doesn’t get any dessert. Elly didn’t eat her green peas. So she doesn’t get any dessert.”
  • This is a passage composed of three claims, but there are only two atomic propositions in the passage (same as above)
• By convention, we can represent each atomic proposition in a passage as a single, upper-case letter
  
  • A = “Elly didn’t eat her green peas”
  • B = “Elly doesn’t get any dessert.”
• Note: Sometimes, we can tell that the same proposition is expressed in different parts of a passage, even though the wording is slightly different in each part
  
  • If Elly doesn’t eat her green peas, then she won’t get any dessert. Elly refuses to eat even a single green pea. So she’s not going to get any dessert. (standard form = same as one above)
• PRACTICE WS
  
  • When doing the work, change the negative statements to positives

Question 23

Negation

Answer 23

-Symbol = ∼ (tilde)

• Can represent the expressions:
  
  • ”not”
  • ”It is not the case that”
  • ”It is false that”
  • It is untrue that”
• Ex: “I’m not a good swimmer.”
• Proposition Labels: S = I’m a good swimming
• Logical Representation: ∼S
• Note: When a true statement is negated, the resulting statement is false. When a false statement is negated, the resulting statement is true
• ∼A is true if and only if A is false. (Otherwise, it is true.)

Question 24

Conjunction

Answer 24

-Symbol = & (ampersand)

• Can represent the expressions:
  
  • ”and,” ”but”
  • ”while,” “even thought,” “yet”
  • ”although,” “however,” “plus”
• Ex: “I exercise every day, and I’m careful about what I eat.”
• Proposition Labels: E = I exercise every day; C = I’m careful about what I eat
• Logical Representation: E & C
• Conjunct: One side of a conjunction (i.e. one of the two parts that is linked by “&”). There are two conjuncts in the above example: E and C.
• Note: A conjunction is true only when both of the conjuncts (for instance, E and C in the above statement) are true. It is false if either one, or both, of the conjuncts are false.
• A and B is true if and only if A is true and B is true. (Otherwise, it is false.)

Question 25

Disjunction

Answer 25

-Symbol = v (wedge) - Can represent the expressions: - ”or” - ”either… or” - ”unless” - Ex: “Either I have time to pack a lunch, or I buy a cheap sandwich on campus.” - Proposition Labels: T = I have time to pack a lunch; S = I buy a cheap sandwich on campus - Logical Representations: T v S - Disjunct: One side of a disjunction (i.e. one of the two parts that is linked by “v”). There are two disjuncts in the above example: T and S. - Note: A disjunction is true when either of the disjuncts is true, or when both are true. It is false only when both of the disjuncts are false. - Technically, two kinds: - 1. Inclusive Disjunction → the disjunction is counted as true when both of the disjuncts are true - By convention, always use “v” to represent inclusive disjunction - 2. Exclusive Disjunction → the disjunction is counted as false when both of the disjuncts are true - In everyday language, the expressions “or,” “either… or,” and others like these sometimes signify exclusive disjunction. In these cases, we need to use more than just “v” to capture the logical form -A v B is false if and only if A is false and B is false. (Otherwise, it is true.)

Question 26

Implication

Answer 26

-Symbol = → (arrow) - Can represent: - ”if... , then…,” “unless” and similar expressions - It represents conditional statements -The expressions surrounding the proposition labels below can often be represented by “ → .” When they can be expressed in this way, each of the following expressions are equivalent: If A, then B; When A, B A only if B; Unless B, ∼A Unless ∼B, A - Ex: “If I want to live a long and healthy life, I should quit smoking.” - Proposition Labels: L = I want to live a long and healthy life; Q = I should quit smoking - Logical Representation: L → Q - Antecedent and Consequent. In above example, “L” is the antecedent and “Q” is the consequent - Note: A conditional statement is false only when the antecedent is true and the consequent is false. In all other cases, it is counted as true*. - Technically “→“ represents the relation between antecedent and consequent in one specific kind of conditional statement, one where the relation between antecedent and consequent is “material implication.” The clearest and simplest definition of material implication, for our purposes, is given by the “note.” In everyday language, there are some cases where the relation between antecedent and consequent in a conditional statement isn’t accurately represented by “→.” - A → B is false if and only if A is true and B is false. (Otherwise, it is true.)

Question 27

Special Note About Proposition Labels, Connectives, and the Therefore Sign

Answer 27

-There are many arguments where you cannot use only proposition labels, connectives, and the therefore sign to fully express the form of the argument - Some clues that you may be facing a case where the resources are inadequate: - 1. When the argument is not deductive - Note: One clue to an argument not being deductive is the appearance of probabilistic claims in the premises or the conclusion - 2. When quantity-words like “all,” “some,” “most,” or “no,” appear in the premises or conclusion - In these cases, the claims may be categorical and the form of the argument may be better represented with Venn Diagrams - 3. When the argument depends on relational properties like “taller than,” “North of,” etc.

Question 28

Modus Ponens

Answer 28

-Affirming the antecedent 1. If the alarm is sounding, there’s an intruder in the house. 2. The alarm is sounding. 3. Therefore, there’s an intruder in the house. If A, then B. A. Therefore, B. A → B A Three dots B -Valid Argument

Question 29

Denying the Antecedent

Answer 29

1. If the alarm is sounding, there’s an intruder in the house. 2. The alarming isn’t sounding. 3. Therefore, there’s not an intruder in the house. If A, then B. Not A. Therefore, not B. A → B ∼A Three dots ∼B -Invalid Argument

Question 30

Modus Tollens

Answer 30

-Denying the consequent 1. If it rained earlier, the sidewalk will be wet. 2. The sidewalk isn’t wet. 3. Therefore, it didn’t rain earlier. If A, then B. Not B. Therefore, not A. A → B ∼B Three dots ∼A -Valid Argument

Question 31

Affirming the Consequent

Answer 31

1. If it rained earlier, the sidewalk will be wet. 2. The sidewalk is wet. 3. Therefore, it rained earlier. If A, then B. B. Therefore, A. A → B B Three dots A -Invalid Argument

Question 32

Hypothetical Syllogism

Answer 32

1. If the bus is late, then I’ll be late to work. 2. If I’m late to work, then I’ll be reprimanded by my boss. 3. So, if the bus is late, then I’ll be reprimanded by the boss. If A, then B. If B, then C. Therefore, if A, then C. A → B B → C Three dots A → C -Valid Argument

Question 33

Disjunctive Syllogism

Answer 33

1. Either Susan will order eggs or she’ll order wine. 2. She’s not ordering eggs. 3. So she’ll order wine. Either A or B. Not A. Therefore, B. A v B ∼A Three dots B -Valid Argument ``` -Note: Disjunctive syllogism works for either disjunct Either A or B.; A v B Not B.; ∼B Therefore, A.; Three dots A -Still valid ```

Question 34

Conclusion for a premise-challenger objection

Answer 34

Therefore, there is a flaw in the reasons that the argument p voided for its conclusion

Question 35

Conclusions for inference-challenger objections

Answer 35

Therefore, there is a flaw in the argument's inference from its premises to its conclusion