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Quiz about Logically Speaking
Quiz about Logically Speaking

Logically Speaking Trivia Quiz


STOP! WAIT! You can do this quiz. You can even enjoy this quiz. A few little logical puzzles, some perfectly innocent terminology and an application that reflects on the character of Plato. Just one little click...

A multiple-choice quiz by uglybird. Estimated time: 6 mins.
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Author
uglybird
Time
6 mins
Type
Multiple Choice
Quiz #
169,678
Updated
Dec 03 21
# Qns
10
Difficulty
Tough
Avg Score
6 / 10
Plays
4093
Awards
Top 10% Quiz
- -
Question 1 of 10
1. Ah, good. You're safe inside the quiz now. If you leave (A), then you'll miss out (B). So, if it's true that if you leave then you'll miss out (A-->B), and you do leave (A), could you then deduce that you'll miss out?


Question 2 of 10
2. And you're still here. Now if we use a valid deductive logic of sentences it should be impossible for our premises to be true and our conclusions false. Suppose it's true that if you're bored (C), you leave(A), ie. (C-->A). What is a valid conclusion according to sentential logic if you are bored(C)? (Remember if you leave (A), you miss out (B), ie (A-->B).
Hint


Question 3 of 10
3. You're still here. I don't think we need to speak further about leaving and missing out. Instead suppose that P stands for the sentence, "A person is a man." Suppose that Q stands for the sentence "A person makes male hormones." Symbolically speaking P-->Q means that if a person is a man, then a person makes male hormones. Suppose P-->Q is true. If ~Q, that is, if it is not the case that a person makes male hormones, then what could be a valid logical conclusion? Hint


Question 4 of 10
4. Four rules of inference are used in the sentential logic of Kalish and Montague. Here is one: If it's not the case that a sentence is false, then the sentence is true. What is this rule termed? Hint


Question 5 of 10
5. Another inference rule that seems trivial and yet becomes necessary in many proofs is that if it is the case that a sentence is true then it's true. A --> A. What is this rule termed? Hint


Question 6 of 10
6. The fact that if a sentence A is true, this requires sentence B to also be true is notated A-->B. If in a proof you establish the truth of A as well as the truth of A-->B and want to claim that B is true, what is the name of the rule that substantiates your claim? Hint


Question 7 of 10
7. The fourth rule of inference is the one that is counterintuitive and confuses many. If A implies B (A-->B) and B is false (~B), then A is false (~A). For example: if a figure being square implies it has four sides then if a figure does not have four sides it is not a square. (If a figure is not a square it can still have 4 sides, a rectangle for example.) What is the rule that says "A-->B and ~B entails ~A" called? Hint


Question 8 of 10
8. You start out with premises and wish to construct a valid argument proving your conclusion. You proceed step by step justifying each one with an appeal to a valid inferential rule and the result is your conclusion. What have you constructed? Hint


Question 9 of 10
9. You have a list of premises and a conclusion you wish to prove. You begin by assuming your conclusion to be false. You then proceed step by step using valid rules of inference ultimately showing that assuming your conclusion to be false and your premises true produces a contradiction. What have you constructed? Hint


Question 10 of 10
10. You cleverly devise your premises so that they include a contradiction. If you are permitted to use these premises sentential logic can be used to produce an argument having any sentence you chose as a conclusion: "Plato is a twit," for instance. If fact, contradictory premises can be used to show that a sentence is both true and not true.



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Quiz Answer Key and Fun Facts
1. Ah, good. You're safe inside the quiz now. If you leave (A), then you'll miss out (B). So, if it's true that if you leave then you'll miss out (A-->B), and you do leave (A), could you then deduce that you'll miss out?

Answer: Yes

A deductive logical system for sentences can be viewed as a method for restating meaning (tautology) or showing what the meaning entails (implication). It does not lead to anything that could be considered "new truth."
2. And you're still here. Now if we use a valid deductive logic of sentences it should be impossible for our premises to be true and our conclusions false. Suppose it's true that if you're bored (C), you leave(A), ie. (C-->A). What is a valid conclusion according to sentential logic if you are bored(C)? (Remember if you leave (A), you miss out (B), ie (A-->B).

Answer: If you're bored, you miss out because C and C-->A imply A and A with A-->B implies B.

You can come to a valid logical conclusion, but of course, if your premises are wrong, your conclusion may be wrong as well. Note though that poor logic does not ensure a wrong conclusion, only a logically invalid one. The other two choices are perfectly reasonable but not logically valid conclusions derived from the premises.
3. You're still here. I don't think we need to speak further about leaving and missing out. Instead suppose that P stands for the sentence, "A person is a man." Suppose that Q stands for the sentence "A person makes male hormones." Symbolically speaking P-->Q means that if a person is a man, then a person makes male hormones. Suppose P-->Q is true. If ~Q, that is, if it is not the case that a person makes male hormones, then what could be a valid logical conclusion?

Answer: ~P, that is, it is not the case that a person is a man.

Logical systems are developed utilizing "metalogic". A good system will use a small number of rules of inference that allow only conclusions consistent with the premises to be derived and allow all possible conclusions to be derived.
4. Four rules of inference are used in the sentential logic of Kalish and Montague. Here is one: If it's not the case that a sentence is false, then the sentence is true. What is this rule termed?

Answer: Double negation

Putting the four rules of inference together will allow every possible derivation in sentential logic. A statement is considered proven when every step in the proof is a premise or can be justified by an inference rule.
5. Another inference rule that seems trivial and yet becomes necessary in many proofs is that if it is the case that a sentence is true then it's true. A --> A. What is this rule termed?

Answer: Repetition

This might be called "The Ayn Rand Rule" since an entire section of her opus, "Atlas Shrugged" is entitled "A is A". In longer proofs after you have proven A on one line, you may need to claim it on a later line. Repetition is the inference rule that permits this.
6. The fact that if a sentence A is true, this requires sentence B to also be true is notated A-->B. If in a proof you establish the truth of A as well as the truth of A-->B and want to claim that B is true, what is the name of the rule that substantiates your claim?

Answer: Modus Ponens

Modus ponens is Latin for "the form or method that affirms". If A implies B (A-->B), then modus ponens is the rule that affirms the implication of B when A is true. Sometimes the arrow is inappropriately reversed in arguments, eg arguing as follows: if Joe is bald then Joe is a man therefore since Joe is a man then Joe is bald.
7. The fourth rule of inference is the one that is counterintuitive and confuses many. If A implies B (A-->B) and B is false (~B), then A is false (~A). For example: if a figure being square implies it has four sides then if a figure does not have four sides it is not a square. (If a figure is not a square it can still have 4 sides, a rectangle for example.) What is the rule that says "A-->B and ~B entails ~A" called?

Answer: Modus tollens

Modus tollens is literally "the form or mode that denies." It refers to the fact that if A implies B (A-->B), then if B is false (~B), this denies A, ie (~A). Too often it is erroneously reasoned that ~A implies ~B eg. if Joe is bald then Joe is a man, therefore if Joe is not bald he is not a man.
8. You start out with premises and wish to construct a valid argument proving your conclusion. You proceed step by step justifying each one with an appeal to a valid inferential rule and the result is your conclusion. What have you constructed?

Answer: A direct proof.

The proof, of course, is in the premises not in the pudding. The actual process of formal proof is entirely mechanical; if done correctly, it results in the truth of the premises requiring the truth of the conclusions.
9. You have a list of premises and a conclusion you wish to prove. You begin by assuming your conclusion to be false. You then proceed step by step using valid rules of inference ultimately showing that assuming your conclusion to be false and your premises true produces a contradiction. What have you constructed?

Answer: An indirect proof.

Indirect proof depends on the notion that a sentence which is a proposition must, by its nature, be either true of false. Sentences with no truth value or ambiguous truth value are not permitted. Therefore if the assumption that the conclusion is false leads to a contradiction of one of the premises the conclusion can't be false and has been proven true.
10. You cleverly devise your premises so that they include a contradiction. If you are permitted to use these premises sentential logic can be used to produce an argument having any sentence you chose as a conclusion: "Plato is a twit," for instance. If fact, contradictory premises can be used to show that a sentence is both true and not true.

Answer: True

With a contradiction in the premises you can choose any conclusion you like and construct an indirect but fallacious proof. An example will be given. A thorough explanation of the example is a bit beyond the scope of a quiz. Premises: It is hot (P) It is not the case it is hot (~P). Conclusion: Plato was a twit(Q). Assume Plato was not a twit (~Q).
~Q - Assumption for indirect proof
P - 1st assumption
~P - Second assumption
Q (Plato is a twit) - by indirect proof.
Source: Author uglybird

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