Section A General Questions about Logic

Question 1

1. What is the difference between inclusive and exclusive disjunction?

Answer 1

The disjunction of two propositions, p or q, is represented in logic by p ∨ q. This is evaluated as true if both p and q are true, and is called inclusive disjunction. A different notion, exclusive disjunction, is defined true only when exactly one of p, q is true, and as false if they are both true.

Question 2

2. What is the major operator of a complex propositional function?

Answer 2

If a sentence has only one logical operator, then that is the main operator. If a sentence has more than one logical operator, then the main operator is the one outside the parentheses.

Question 3

3. Why do ‘only if’ clauses go into the consequent of conditionals?

Answer 3

only if statements are exclusive propositions, when this kind of statement gets translated as a conditional the class term after “only” becomes the consequent

Question 4

4. Give a propositional logic translation of the following form: A or B, but not both.

Answer 4

(A v B) * ~(A * B)

Question 5

5. Explain why the following two propositional logic claims are equivalent: A ≡ B and (A ⊃ B) * (B ⊃ A).

Answer 5

If A then B, so this turns in to B; If B then A, so this turns into A. The final form is B * A. This is equivalent to A ≡ B because for both claims A and B both have to be true for the statement to be. If either A or B is false then the entire statement is false.

Question 6

6. Give an example of Modus Ponens in natural language.

Answer 6

If today is Tuesday, then John will go to work.
Today is Tuesday.
Therefore, John will go to work.

Question 7

7. Give an example of Modus Tollens in natural Language.

Answer 7

If you give up cigarettes, then you care about your health.
You did not give up cigarettes.
Therefore, you do not care about your health.

Question 8

8. Show with a truth table why Modus Ponens is a valid inference form.

Answer 8

P Q If P, then Q
T T T
T F F
F T T
F F T

Question 9

9. Show with a truth table why Modus Tollens is a valid inference form.

Answer 9

P Q If P then Q Not Q Therefore, not P
T T T F F
T F F T F
F T T F T
F F T T T

Question 10

10. Show with a truth table why Asserting the Consequent is an invalid inference form.

Asserting the Consequent:
1. If A then B
2. B
3. Therefore, A

Answer 10

P Q If P, then Q Q is true Therefore, P is true?
T T T T T
T F F F F
F T T T F
F F T F F

Question 11

11. Show with a truth table why Negating the Antecedent is an invalid inference form.

Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement. It is committed by reasoning in the form:
If P, then Q.
Therefore, if not P, then not Q.

Answer 11

P Q If P then Q If not P then not Q
T T T F
T F F T
F T T T
F F T T

Question 12

12. Show with a truth table why Double Negation is a valid replacement rule.

Answer 12

P ¬P ¬(¬P)
T F T
F T F

Question 13

13. Explain the following sentence: doing a proof is a way of demonstrating syntactic validity in Propositional
    Logic.

Answer 13

In Propositional Logic, a proof is a systematic way of demonstrating that a particular statement, called a proposition, can be derived from a set of premises using a set of rules of inference. The statement “doing a proof is a way of demonstrating syntactic validity in Propositional Logic” means that when a proof is performed in Propositional Logic, it shows that the proposition being proved is syntactically valid, meaning that it follows the rules of the formal language of propositional logic.

In other words, a proof provides a rigorous demonstration that the conclusion of an argument is logically valid based solely on the structure of the argument, without considering the truth or falsity of its propositions. By constructing a proof, we can determine if a statement follows logically from the premises or if it violates the rules of syntax of propositional logic. Thus, doing a proof is an essential tool for establishing the validity of propositions in propositional logic.

Question 14

14. Explain the following sentence: the negation of a tautology is a self-contradiction

Answer 14

A tautology is a statement that is always true, regardless of the truth values of its individual components. For example, the statement “either it is raining or it is not raining” is a tautology, because it is true no matter what the weather conditions are.

The negation of a tautology is a statement that is always false, regardless of the truth values of its individual components. For example, the negation of the tautology “either it is raining or it is not raining” is “it is both raining and not raining at the same time,” which is a self-contradiction because it is impossible for something to be true and false at the same time and in the same sense. Therefore, the negation of a tautology results in a statement that contradicts itself, and is thus a self-contradiction.

Question 15

15. Explain the following sentence: the negation of a self-contradiction is a tautology.

Answer 15

The given sentence, “the negation of a self-contradiction is a tautology,” means that if we negate a self-contradiction, we get a statement that is always true, regardless of the truth value of its components, which is a tautology. This is because the negation of a self-contradiction asserts the opposite of the contradiction, which is always true, since the contradiction is inherently false. Therefore, the negation of a self-contradiction is always true, and hence a tautology.

Question 16

16. Explain the following sentence: the negation of a contingency is a contingency.

Answer 16

In logic and philosophy, a contingency refers to a proposition that is neither necessarily true nor necessarily false, but can be true or false depending on the circumstances or facts.

The negation of a contingency refers to the opposite of that proposition, which is either necessarily true or necessarily false, depending on the original proposition. For example, if the original proposition is “It may rain tomorrow,” the negation would be “It will not rain tomorrow.”

Question 17

17. What is it for two propositions to be consistent? What is it for them to be inconsistent?

Answer 17

Two propositions are considered consistent if it is possible for both of them to be true at the same time.

On the other hand, two propositions are considered inconsistent if they cannot both be true at the same time, meaning that they are contradictory.

Question 18

18. Define tautology.

Answer 18

In logic, a tautology is a statement that is true in every possible interpretation or situation. Put differently, a tautology is a proposition that is always true, regardless of the truth values of its individual components.

Example: either it will rain today or it will not

Question 19

19. Define contingency.

Answer 19

In logic, a contingency is a statement that is neither necessarily true nor necessarily false. In other words, a contingency is a statement that could be true or false, depending on the circumstances or context in which it is evaluated.

Example of a contingency is “I will pass my exam”, as the truth of the statement will depend on factors such as how well the person has studied, the difficulty of the exam, and the grading criteria.

Question 20

20. Show with a truth table that Disjunctive Syllogism is a valid rule of implication.

Answer 20

P Q P v Q ~P ~P -> Q
T T T F T
T F T F T
F T T T T
F F F T F

Question 21

21. Show with a truth table that Addition is a valid rule of implication.

Answer 21

P Q P v Q
T T T
T F T
F T T
F F F

Question 22

22. Give a natural language example of Exportation as a valid rule of replacement.

Answer 22

“if it snows this afternoon and we buy a sled, then we go sledding” is the same as saying “if it snows this afternoon, then if we buy a sled, then we go sledding”

Question 23

23. Show with a truth table that one of the DeMorgan’s Rules is a valid rule of replacement.

Answer 23

P Q ~(P * Q) (~P v ~Q)
T T F F
T F T T
F T T T
F F T T

Question 24

24. Show with a truth table that Transposition is a valid rule of replacement.

Answer 24

P Q ~P ~Q P -> Q ~Q -> ~P
T T F F T T
T F F T F F
F T T F T T

Question 25

25. Explain the following sentence: Commutation of conjunction does not respect temporal indexing with ‘and’.

Answer 25

In logic, Commutation of Conjunction is a valid rule of replacement that allows us to switch the order of two conjuncts in a conjunction. For example, if we have the statement “P and Q”, we can apply Commutation of Conjunction to obtain the equivalent statement “Q and P”.

However, when we use “and” as a temporal operator, the order of the conjuncts can have a different meaning depending on the context. For example, consider the following two statements:

“I will eat dinner and then watch a movie.”
“I will watch a movie and then eat dinner.”
In these statements, the order of the conjuncts is important because it specifies the temporal relationship between the events. Statement 1 implies that eating dinner will happen before watching a movie, while statement 2 implies the opposite.

Therefore, when “and” is used as a temporal operator, Commutation of Conjunction does not respect the temporal indexing, because switching the order of the conjuncts can change the meaning of the statement. This is why we must be careful when applying logical rules like Commutation of Conjunction in natural language contexts, especially when dealing with temporal relationships.

Question 26

26. What is the major operator rule for rules of implication?

Answer 26

The major operator rule for rules of implication is the rule that specifies that any rule of implication must preserve the truth value of the major operator in the original statement. In other words, if the major operator in the original statement is a conjunction, the rule of implication must preserve the truth value of the conjunction.

For example, consider the following statement:

“If it is raining and I don’t have an umbrella, then I will get wet.”

In this statement, the major operator is the conditional “if…then”. Any rule of implication that we apply to this statement must preserve the truth value of the conditional. For instance, we could apply the rule of Modus Ponens to infer the truth of the consequent:

“If it is raining and I don’t have an umbrella, then I will get wet.
It is raining and I don’t have an umbrella.
Therefore, I will get wet.”

In this argument, the rule of implication preserves the truth value of the conditional, which is the major operator in the original statement. This is the major operator rule for rules of implication.

Question 27

27. Explain how the Law of Non-Contradiction bears on the relationship between objects and classes in Categorical Logic.

Answer 27

Objects are individual entities that have specific attributes and exist in time and space. Classes, on the other hand, are groups or categories of objects that share common characteristics or attributes. The Law of Non-Contradiction asserts that an object cannot simultaneously belong to two classes that are mutually exclusive or contradictory. For example, a square cannot be both a polygon and a circle at the same time and in the same respect.

Question 28

28. Explain how the Law of Excluded Middles bears on the relationship between objects and classes in Categorical Logic.

Answer 28

In the context of objects and classes, the Law of Excluded Middle asserts that every object must either belong or not belong to a specific class. There is no middle ground or ambiguous state where an object might partially belong to a class. For example, a cat is either a member of the class of mammals or not. It cannot be partially a mammal and partially not a mammal.

Question 29

29. Explain what Existential Assumption is for Traditional Categorical Logic and why it is, for certain purposes, a
    reasonable assumption.

Answer 29

existential assumption states that the only way to have a class is to have an object, and the only way to be an object is to exist

Question 30

30. What are the four standard forms in Categorical Logic?

Answer 30

A form: complete overlap, All S are P
E form: complete non-overlap, No S are P
I form: incomplete overlap, Some S are P
O form: incomplete non-overlap, Some S are not P

Question 31

31. Give an explanation with a Venn Diagram why “Only X are Y” should be translated in Standard form as “All
    Y are X.” Provide an (intuitive) example.

Answer 31

only vandy grads are well-dressed = all well-dressed people are vandy grads

venn diagram with two circles crossed with v on left and w on right. have the w part shaded. then with an arrow pointing next to the diagram write all w are v.

Question 32

32. Give an explanation with a Venn Diagram why “The only X are Y” should be translated in Standard Form as
    “All X are Y.” Provide an (intuitive) example.

Answer 32

the only millionaires at the party are vandy grads = all millionaires at the party are vandy grads

venn diagram m on left v on right with m section shaded.

Question 33

33. Explain with Venn Diagrams why A- and O- form propositions are contradictories.

Answer 33

x

Question 34

34. Explain with Venn Diagrams why E- and I- form propositions are contradictories.

Answer 34

x

Question 35

35. Explain with Venn Diagrams why E- and O- form propositions are subalterns.

Answer 35

x

Question 36

36. Explain with Venn Diagrams why A- and I- form propositions are subalterns.

Answer 36

x not totally sure

Question 37

37. Explain with Venn Diagrams why I- and O- form propositions are subcontraries.

Answer 37

x

Question 38

38. Explain with Venn Diagrams why A- and E- form propositions are contraries.

Answer 38

x

Question 39

39. Explain with Venn Diagrams why Conversion with A-Form Propositions is invalid. Provide an (intuitive)
    counter-example.

Answer 39

x

Question 40

40. Explain with Venn Diagrams why Conversion with E-Form Propositions is valid. Provide an (intuitive)
    example.

Answer 40

x

Question 41

41. Explain with Venn Diagrams why Contraposition with A-Form Propositions is valid. Provide an (intuitive)
    example.

Answer 41

x

Question 42

42. Explain with Venn Diagrams why Obversion with A-Form Propositions is valid. Provide an (intuitive)
    example.

Answer 42

x

Question 43

43. Explain with Venn Diagrams why Conversion with I-Form Propositions is valid. Provide an (intuitive)
    example.

Answer 43

x

Question 44

44. Explain the following sentence: Use the Traditional Square of opposition only in cases where you know that
    the things you’re reasoning about exist.

Answer 44

the outside of the traditional square of opposition can only be applied under the assumption that the object exists
- if you do not know that something doesn’t exist, you CANNOT apply existential assumption, therefore you must use the modern square of opposition

How do you decide whether to use the traditional or modern interpretations of logic?
- traditional–> KNOW the thing exists
- modern–> DON’T KNOW if the thing exists OR know the thing DOES NOT exist

Question 45

45. Show why Subalternations from True A- to I- form propositions are not valid relations if we do not use
    existential assumption.

Answer 45

We must use existential assumption when showing sub alternation between true A- to -I form propositions because sub alternation when the truth of the first (A) proposition implies the truth of the second (I) proposition.

Question 46

46. Explain the following sentence: The Venn method for testing syllogisms runs that a syllogism is valid iff a
    diagram of the premises yields a diagram of the conclusion.

Answer 46

When the venn diagram of the premises yields the diagram of the conclusion, the syllogism is proven valid because this shows that the conclusion follows from the premises.

Question 47

47. Explain the following sentence: It’s just best, when testing syllogisms with Venn diagrams, to shade the
    universals before placing objects for particulars.

Answer 47

If you place the objects for particulars first, the x would go on a line, then shading the universals might force you to move the x if the shaded premise empties its first placement

Question 48

48. Explain the following sentence: For categorical logic, proper names work as names of classes with exactly
    one member. Why, then, must claims about named things (like ‘Socrates’) be A-form or E-form
    propositions?

Answer 48

When you are asserting something about a proper name, you are asserting something about a singular proposition. That singular person, place, or thing is an object and therefore, must belong to a class. However, it will be the only object in the class. For example, Socrates belongs to a class that is titled something along the lines of “all individuals identical to Socrates.” Since nobody is exactly identical to Socrates, Socrates is the only member of that class. Claims about named things must be A-form or E-form because claims about the individual named thing are also true for the entire class, since the class is only made up of that one member, and therefore are universal claims.

Question 49

49. Show why Contrariety between A- and E-form propositions depends on existential assumption

Answer 49

Venn and:

A and E form propositions are never both true because of what existential assumption says about where objects exist within their classes. As shown below, if it is true that all S are P, then we shade the left side of S. However, we know that S exists so we must place an x in the overlap of S and P by existential assumption. Therefore, it has to be false that No S are P, which would mean that the overlap was completely shaded. On the other hand, if it is true that No S are P, then you shade the area in between S and P. However, we know that S exists, so there must be an object within S by existential assumption, so we place an x in S. Therefore, it must be false than All S are P, which would shade out the left side of S.

Question 50

50. What is the rule of X-Conclusivity for testing syllogisms on Venn Diagrams in Categorical Logic?

Answer 50

In order for Some S are P and Some S are not P arguments to be true - the x must be in one category not on the line and not in two .

Question 51

51. Explain the following sentence for informal logic: There are arguments that are semantically valid, but still
    logically unacceptable.

Answer 51

Begging the question is a prime example of this since its conclusion is some version of the premise which is valid. But, it is not a good argument form since it is a fallacy.

Question 52

52. Explain the following sentence for informal logic: There are inferences that are semantically invalid, but are
    informally acceptable.

Answer 52

Some arguments do not fulfill the requirements for being semantically valid but through context can be informally acceptable. For example, “Some S are not P” can be reasonably deduced from “Some S are P” because one assumes that if “All S are P,” the speaker would have stated that and not “some.” However, this logic is still formally invalid while being reasonable.

Question 53

53. Explain the following sentence for informal logic: It is possible to communicate something true by saying
    something false.

Answer 53

It is possible to communicate something true by saying something false through the use of pragmatics such as tone, which can signify sarcasm, reversing the meaning of a statement.

Question 54

54. Explain the informal reasoning when someone infers Some S are not P from a speaker’s claim that Some S
    are P.

Answer 54

One can infer Some S are not P from a speaker’s claim that Some S are P using the informal logic that if All S are P were true, the speaker would have said that instead of Some S are P.

Question 55

55. Explain the following sentence: Many false dilemmas are cases of semantically valid reasoning, but are
    pragmatically unacceptable responses to the disagreements.

Answer 55

False dilemmas (false dichotomy) take the form of a disjunctive syllogism and can be formally valid reasoning; however, when the two potential options are not exclusive or when a third option exists, the disjunctive syllogism is invalid.

Question 56

56. Explain the following sentence: Circular arguments are cases of semantically valid reasoning, but are
    pragmatically unacceptable responses to the disagreements.

Answer 56

A circular argument is a type of reasoning where the conclusion of the argument is already assumed in one of the premises. In other words, the argument assumes what it is trying to prove.

While circular arguments can be semantically valid (i.e., the conclusion follows logically from the premises), they are considered pragmatically unacceptable because they don’t provide any new information or evidence to support the conclusion.

When people engage in disagreements or debates, they expect to hear new information or evidence that supports a particular position. Circular arguments, however, fail to meet this expectation because they simply restate the conclusion without providing any additional reasons or evidence.

Question 57

57. Explain the difference between extensional and intensional definitions.

Answer 57

Extensional definitions define a term by listing all the individual objects or instances that it refers to. For example, an extensional definition of the term “dog” would be a list of all the individual dogs in the world. This type of definition is useful when dealing with concrete and specific objects or concepts.

Intensional definitions define a term by stating its defining characteristics or attributes. For example, an intensional definition of the term “dog” might be “a domesticated mammal with four legs, a tail, and a barking sound.” This type of definition is useful when dealing with abstract or complex concepts that cannot be easily listed.

Question 58

58. Give an example of intensional definition by synonym.

Answer 58

an attorney is a lawyer

Question 59

59. Give an example of extensional definition by ostension.

Answer 59

An example of an extensional definition by ostension is when a teacher points to a triangle drawn on a board and says “this is a triangle.” The teacher is defining the term “triangle” by pointing to an actual instance of it rather than using words to describe its defining characteristics. Another example could be a museum exhibit that has a label next to a painting with the artist’s name and birth and death dates, defining that specific painting.

Question 60

60. Give an example of a stipulative definition.

Answer 60

A stipulative definition is a type of definition where a new meaning or use of a term is introduced for a specific purpose or context. It is often used in technical or specialized fields to clarify the meaning of a term. An example of a stipulative definition could be:

these pants are so tight

Question 61

61. Define and give an example of ad hominem abusive fallacies. Explain what makes them fallacious.

Answer 61

The fallacy is distinguished by an attack on alleged character flaws of a person instead of the person’s argument.

An example of an ad hominem abusive fallacy is when a politician responds to a criticism of their policy by attacking the person who made the criticism rather than addressing the criticism itself. For instance, a politician might say “You’re just an uneducated person who doesn’t understand the complexity of the issue” in response to a critic who argues against their policy.

What makes ad hominem abusive fallacies fallacious is that they do not address the substance of the argument being made. Instead, they attempt to undermine the credibility or character of the person making the argument. This is a flawed way to respond to an argument, as it does not address the issues or ideas being debated, and instead tries to discredit the person making the argument.

Question 62

62. Define and give an example of arguments from ignorance. Explain what would make an argument from
    ignorance fallacious.

Answer 62

An argument from ignorance is a type of fallacy that occurs when an argument is based on the absence of evidence for a claim rather than on the presence of evidence. In other words, it involves asserting that something is true simply because there is no evidence that it is false or vice versa.

An example of an argument from ignorance is “There is no evidence that ghosts don’t exist, so they must exist.” This argument assumes that the lack of evidence against the existence of ghosts is evidence in favor of their existence. Another example could be “There is no evidence that aliens haven’t visited Earth, so they must have visited.”

What makes an argument from ignorance fallacious is that it relies on a lack of evidence rather than positive evidence to support a claim. Absence of evidence does not necessarily imply evidence of absence. Just because there is no evidence against a claim, it does not mean that there is evidence for the claim.

Question 63

63. Give an example of extensional definition by enumeration.

Answer 63

An example of extensional definition by enumeration is listing all of the U.S. states, such as Alabama, Alaska, Arizona, Arkansas, California, Colorado, and so on. By listing each individual state, this extensional definition defines the concept of “U.S. states” by identifying all of the specific instances that fall under that concept. Another example could be listing all the fruits in a basket to define the contents of the basket.

Question 64

64. Give an example of hasty generalization.

Answer 64

An example of hasty generalization is when someone meets a few people from a certain country who are rude and concludes that all people from that country are rude. For instance, if a person meets a few rude French people and concludes that all French people are rude, this is a hasty generalization. Another example could be if a person eats a single bad apple and concludes that all apples are bad.

Question 65

65. Give an example of an argument from pity.

Answer 65

An example of an argument from pity is a politician who argues that their policy should be supported because it will help poor people who are struggling to make ends meet. The politician might say, “We should support this policy because there are so many poor people in our country who are suffering, and we need to do something to help them.”

Question 66

66. Explain the following sentence: Given the pragmatic requirements of argument, successful arguers must
    have a cognitive command of an issue and the debate in order to give dialectically proper arguments.

Answer 66

To be successful in argument, one must have a cognitive command of the issue, which means having a deep understanding of the facts, concepts, and principles involved. This includes understanding the strengths and weaknesses of one’s own position as well as the positions of one’s opponents. Without this knowledge, it is difficult to make persuasive arguments or respond effectively to the arguments of others.

The sentence means that in order to be successful in argument, one must have a thorough understanding of the issue being debated and be able to give arguments that are appropriate to the context of the debate. This is because arguments are not just about presenting facts or making claims, but about convincing others to accept a particular point of view.

Question 67

67. Define equivocation. Give an example of an equivocal inference (or fallacy of equivocation).

Answer 67

The fallacy occurs when the conclusion of the argument relies on an intentional or unintentional shift in the meaning of a term or phrase in the premises

“Feathers are light. What is light cannot be dark. Therefore, feathers cannot be dark.”

Question 68

68. What is a complex question? Explain the following sentence: all questions are complex in some way or
    other – the issue is whether they are objectionably complex.

Answer 68

A complex question is a type of fallacy that occurs when a single question actually contains multiple parts and an unestablished hidden assumption. In other words, it is a question that contains an assumption or presupposition that is hidden or implied within it, and which may be false or misleading.

For example, consider the following question: “Have you stopped beating your spouse?” This is a complex question because it assumes that the person being asked has been beating their spouse, even though this has not been established or may not be true.

The sentence “all questions are complex in some way or other – the issue is whether they are objectionably complex” means that all questions involve some level of complexity or presupposition, but not all of them are objectionable or fallacious. In other words, all questions have some level of implicit assumptions or presuppositions, but not all of them are problematic or misleading.

Question 69

69. What are the three primary critical questions to ask of any argument from authority?

Answer 69

Is the authority an expert in the relevant field?

Is the authority impartial or biased?

Is the authority’s testimony consistent with other evidence?

Question 70

70. Distinguish between the representational and selectional versions of the straw man fallacy (or: the straw
    man and the weak man).

Answer 70

The representational straw man occurs when an arguer misrepresents the opponent’s argument by distorting or exaggerating it in a way that makes it easier to refute. The arguer then proceeds to attack or refute the distorted version of the argument, rather than the original argument. For example, suppose someone argues that we should reduce carbon emissions to combat climate change, and their opponent misrepresents their argument by saying they want to shut down all industry and return to a pre-industrial society. This is a misrepresentation of the original argument and makes it easier to attack, but it is not an accurate representation of what the original argument actually said.

The selectional straw man, or weak man, is a type of straw man fallacy that occurs when an arguer misrepresents the opponent’s argument by selectively choosing the weakest or least representative version of it to attack or refute. This is different from the representational straw man because the arguer is not distorting the argument in any way, but rather selectively choosing the weakest or most vulnerable version of it to attack. For example, suppose someone argues that we should reduce carbon emissions to combat climate change, and their opponent selectively chooses to attack the argument of a poorly informed individual who thinks that climate change is a hoax, rather than engaging with the actual argument presented. By doing so, the opponent is attacking a weaker version of the argument that is not representative of the original argument.

Question 71

71. What is the freedom rule of argument (on the pragma-dialectical model)?

Answer 71

It states that all participants in a critical discussion should be free to advance any standpoint they wish, provided that they observe the rules for critical discussion. This means that every participant has the right to express their opinions and present arguments in support of their standpoint, and no participant should be prevented from doing so.

Question 72

72. What is the defend and clarify rule of argument (on the pragma-dialectical model)?

Answer 72

The defend and clarify rule is one of the key rules of critical discussion in the pragma-dialectical model of argumentation. This rule states that participants in a discussion have a dual responsibility to defend their own standpoint and to clarify the argumentation of their opponent.

This means providing reasons and evidence in support of their position, and responding to any challenges or objections that are raised by their opponents.

This involves asking questions, seeking clarification, and identifying any misunderstandings or misrepresentations of their opponents’ arguments. By engaging in this process, participants can ensure that they are addressing their opponents’ actual arguments and not just attacking a straw man.

Question 73

73. What is the conclusion rule of argument (on the pragma-dialectical model)?

Answer 73

The conclusion rule is a fundamental principle in the pragma-dialectical model of argumentation. It states that the goal of a critical discussion is to arrive at a conclusion that is jointly acceptable to all participants.

Question 74

74. Explain the following sentence: Slippery slope arguments are inductive arguments. What makes the
    difference between weak and strong versions of the argument is whether there are, really, bumps in the
    staircase.

Answer 74

The strength of a slippery slope argument depends on whether there are actual “bumps in the staircase” or if the argument is based on unfounded or exaggerated claims. In other words, the strength of the argument is based on the strength of the causal links between the proposed action or policy and the predicted negative consequences.

A weak slippery slope argument may be based on vague or unsupported causal links, such as claiming that a small change will inevitably lead to a series of catastrophic events without providing any evidence to support this claim. A strong slippery slope argument, on the other hand, would be based on well-supported causal links that demonstrate a clear and direct connection between the proposed action or policy and the predicted negative consequences.

Question 75

75. What is the basic form of an argument by analogy?

Answer 75

Object A has properties P, Q, and R.
Object B is similar to Object A in many ways.
Therefore, Object B probably has property Q.

Question 76

76. Why are ad hominem abusive arguments both synchronically and diachronically bad as arguments?

Answer 76

Ad hominem arguments are synchronically bad arguments because they are not relevant to the topic being debated. Ad hominem arguments are also diachronically bad arguments because deliberation over time is made more difficult by the use of irrelevant claims that do not make a conclusion false, hindering progress.

Question 77

77. Why are Straw Man Arguments both synchronically and diachronically bad as arguments?

Answer 77

Synchronically, a Straw Man Argument is a bad argument because it misrepresents the position of the opponent, creating a distorted or exaggerated version of their argument that is easier to attack.

Diachronically, a Straw Man Argument is a bad argument because it fails to contribute to the development of knowledge and understanding. A Straw Man arguer is not engaging with the actual argument of the opponent, and therefore is not contributing to the development of knowledge and understanding that comes from a robust exchange of ideas.

Question 78

78. How is logic a metalanguage?

Answer 78

When we reason, we think about the things we reason about. But with logic, we reason about how we reason about the things we reason about. So, with logic we explain and evaluate how we’ve reasoned

Question 79

79. Define argument, for the purposes of logic.

Answer 79

A group of statements in which the conclusion is claimed to follow from the premises

Question 80

80. What does it mean to say an argument is inductively strong?

Answer 80

succeeds in providing probable, but not conclusive, support for its conclusion.

Question 81

81. What does it mean to say an argument is inductively cogent?

Answer 81

An inductive argument is cogent when the argument is strong and the premises are true

Question 82

82. Give two examples of premise indicators.

Answer 82

Because and Since

Question 83

83. Give two examples of conclusion indicators.

Answer 83

So and Therefore

Question 84

84. What does it mean to say an argument is deductively valid?

Answer 84

An argument in which, assuming the premises are true, it is impossible for the conclusion to be false.

Question 85

85. Give an example of a deductively valid, but unsound argument.

Answer 85

Premise 1: All birds can swim.
Premise 2: Penguins are birds.
Conclusion: Therefore, penguins can swim.

Question 86

86. What does it mean to say an argument is deductively sound?

Answer 86

a deductive argument is sound when the argument is valid and all the premises are true

Question 87

87. What is it for an argument to have a logical form?

Answer 87

The logical form of an argument is the structure or pattern that the argument follows, and it is often represented symbolically or diagrammatically. Logical form allows us to see the logical relationships between the premises and conclusion of an argument, abstracting away from the specific details of the argument’s content.

Question 88

88. How do counterexamples show deductive invalidity?

Answer 88

Since counterexamples have true inputs and false outputs, they show invalidity. Validity is when premises are true and the conclusion is true.

Question 89

89. Give an invalid argument, show it is invalid with a counterexample.

Answer 89

Premise - All T are P
Conclusion - All P are T

Counterexample is diagram of both

Question 90

90. Of the three questions to ask about argument success, what is the question of rhetorical success?

Answer 90

The question of rhetorical success in evaluating an argument is whether the argument is persuasive or effective in convincing the audience to accept the conclusion.

Question 91

91. Of the three questions to ask about argument success, what is the question of logical success?

Answer 91

The question of logical success in evaluating an argument is whether the argument follows valid reasoning or logical principles. Logical success is concerned with the structure of the argument, including the relationship between the premises and the conclusion. To determine logical success, one needs to assess whether the premises are true, whether the reasoning is valid, and whether the conclusion logically follows from the premises.

Question 92

92. Of the three questions to ask about argument success, what is the question of material success?

Answer 92

The question of material success in evaluating an argument is whether the premises of the argument are true or well-supported.

Question 93

93. What is the notion of semantic validity in a logic?

Answer 93

The notion of semantic validity in logic is concerned with the relationship between the premises and the conclusion in terms of their truth values, rather than the form or structure of the argument.

Question 94

94. What is the notion of syntactic validity in a logic?

Answer 94

The notion of syntactic validity in logic refers to whether an argument is valid based on the form or structure of the argument, rather than the meanings of the terms used in the argument.

Question 95

95. Why are semantic and syntactic validity indexed to logics?

Answer 95

Semantic and syntactic validity are indexed to logics because logic is the study of reasoning and argumentation, and provides a systematic framework for evaluating the validity of arguments.

Question 96

96. Explain the following sentence: for classical logics, syntactic validity depends on the semantic validity of the
    rules.

Answer 96

Means that in classical logic, the rules of inference that are used to determine the syntactic validity of an argument are themselves semantically valid. This means that the truth-preserving rules of inference in classical logic are based on the truth values of the premises and the conclusion.

Question 97

97. Explain the following sentence: We must choose the logic to use to evaluate arguments depending on the
    kind of reasoning in the argument.

Answer 97

This means that the choice of logic to use in evaluating an argument depends on the type of reasoning or inference used in the argument. Different types of reasoning require different logics to evaluate them properly, and selecting the appropriate logic is important for accurately assessing the validity of an argument. For example, propositional logic may be used to evaluate statements that are composed of logical connectives such as “and,” “or,” and “not,” while categorical logic may be used to evaluate statements that involve quantifiers such as “all” or “some.”

Question 98

98. Explain the following sentence: What is evaluated as valid in categorical logic will not be evaluated as valid
    in propositional logic.

Answer 98

Means that there are differences in the rules of inference and logical structure between categorical logic and propositional logic, such that an argument that is valid in one logic may not be valid in the other.

Categorical logic deals with relationships between categories or classes, and uses statements that contain terms such as “all,” “some,” or “no” to make claims about the relationships between these categories. Categorical logic has its own set of rules of inference and logical structure that are used to evaluate arguments.

Propositional logic, on the other hand, deals with propositions or statements, and uses logical connectives such as “and,” “or,” and “not” to construct complex propositions from simpler ones. Propositional logic also has its own set of rules of inference and logical structure that are used to evaluate arguments.

Question 99

99. Explain how ad hominem abusive might work on an audience in the third and in the second person.

Answer 99

In the third person, ad hominem abusive can work by influencing the audience’s perception of the opponent’s credibility and character. When the audience hears an attack on the opponent’s character, they may begin to view the opponent as less trustworthy, less knowledgeable, or less deserving of their attention. This can lead the audience to discount the opponent’s argument or to be less open to considering their perspective. By attacking the opponent’s character, the arguer may be able to deflect attention away from the actual argument and towards the opponent’s perceived flaws, thus undermining their credibility in the eyes of the audience.

In the second person, ad hominem abusive can work by creating a hostile or aggressive tone that is directed towards the opponent. This can cause the opponent to become defensive or emotional, making it harder for them to effectively present their argument. By using personal attacks or insults, the arguer may be able to intimidate or upset the opponent, making it more difficult for them to stay focused or to effectively respond to the argument. This can also create a sense of polarization or divisiveness, making it harder for the two parties to find common ground or to engage in constructive dialogue.

Question 100

100. Explain how straw man arguments might work on an audience in the third and in the second person.

Answer 100

In the third person, a straw man argument can work by influencing the audience’s perception of the opponent’s position. When the audience hears the opponent’s position being misrepresented, they may begin to view it as less reasonable, less coherent, or less deserving of serious consideration. This can lead the audience to discount the opponent’s argument or to be less open to considering their perspective. By misrepresenting the opponent’s position, the arguer may be able to deflect attention away from the actual argument and towards a weaker or more extreme version of the opponent’s position, thus making it easier to attack or refute.

In the second person, a straw man argument can work by putting the opponent on the defensive or by creating confusion or doubt in their mind. By misrepresenting the opponent’s position, the arguer may be able to create a sense of uncertainty or confusion in the opponent’s mind, making it harder for them to effectively respond or to stay focused on the actual argument. This can also create a sense of frustration or annoyance in the opponent, making it more difficult for them to engage in productive dialogue or to effectively present their argument.

Question 101

101. Explain the following sentence: Straw man arguments are essentially dialectical fallacies.

Answer 101

The sentence means that straw man arguments are fallacies that occur in the context of argumentation or dialogue, as opposed to being fallacies of inference or reasoning. More specifically, straw man arguments involve misrepresenting or distorting the opponent’s position in order to make it easier to attack, rather than addressing the opponent’s actual argument. This tactic can be seen as a violation of the rules of rational discussion and an attempt to manipulate the dialogue in one’s own favor. Because straw man arguments involve a distortion of the opponent’s position, they are considered dialectical fallacies.

Question 102

102. Explain the following sentence: Stipulative definitions are never false, but they can be inappropriately made.

Answer 102

The sentence means that stipulative definitions, which are definitions that assign meaning to a term for a particular context or purpose, are always true within the context in which they are made. However, they can be inappropriate if they are not well-suited to the purpose for which they are made, or if they are not accepted by the audience to which they are addressed. In other words, a stipulative definition may accurately describe the intended meaning of a term for a particular context, but it may still be ineffective or even misleading if it is not accepted or understood by the intended audience. Therefore, while stipulative definitions are not inherently false, they can still be problematic if they are not well-suited to the context or audience in which they are used.

Question 103

103. Explain the following sentence: Lexical definitions can be true or false.

Answer 103

For example, the lexical definition of “chair” might be “a piece of furniture designed for one person to sit on, typically with a back and four legs.” This definition can be evaluated for its truthfulness by examining whether it accurately describes the way in which the term “chair” is commonly used in English. If the definition accurately reflects common usage, it can be considered true; if not, it can be considered false.

Question 104

104. Are operational definitions intensional or extensional? Why?

Answer 104

Operational definitions are generally considered to be intensional, rather than extensional. An operational definition defines a term or concept by specifying the procedures or operations that are used to measure or manipulate it. In other words, an operational definition defines a term or concept by describing the way in which it is used in a particular research study or experiment.

An intensional definition is a type of definition that explains the meaning of a term by specifying its essential properties, characteristics, or features. It defines a term by identifying a set of qualities or attributes that are necessary and sufficient for an object or concept to be included under that term.