Phil2033- Prof. Harding HW Questions 3a-4d

Instructions: Use your knowledge of truth tables to identify the following statements as contingent, tautology, or self-contradiction. ( P · ~ P ) v Q

Contingent

Instructions: Use your knowledge of truth tables to identify the following statements as contingent, tautology, or self-contradiction. P v Q

Contingent

Instructions: Use your knowledge of truth tables to identify the following statements as contingent, tautology, or self-contradiction. P · S

Contingent

Which fallacy of ambiguity or diversion best fits the following passage? According to the census data, the population of that city is 10% atheists. My Uncle Sam lives there, so he must be 10% atheist.

Division -The population of the city is around 50% female. Is Uncle Sam a hermaphrodite? This is question 13 in the book.

True or False A compound statement has at least three simple statements as a component.

False

True or False A controlled experiment is one in which the experimental setup tests several variables at once.

False

True or False A precipitating cause is the object or event indirectly involved in bringing about an effect.

False

True or False A verifiable prediction means that the prediction must be true.

False

True or False An exclusive disjunction is where both disjuncts can be true at the same time.

False

True or False In ordinary language the words "only if" typically precedes the antecedent of a conditional.

False

True or False In ordinary language, the word "if" typically precedes the consequent of a conditional.

False

True or False Mill's methods provide conclusive proof of causality.

False

True or False The horseshoe symbol is used to translate a conjunction.

False

True or False The main operator cannot be the negation operator.

False

True or False The method of agreement looks at only one instance of an event to determine the cause.

False

True or False The word "cause" has only one meaning.

False

True or False Two (or more) statements are consistent when they have at least one line on their respective truth tables where the main operators are false.

False

True or False Two statements that have opposite truth values on every line of their respective truth tables are logically equivalent.

False

True or False Two truth-functional statements that have identical truth tables are contradictory statements.

False

True or False Appeals to authority are always fallacious.

False -Appeals to unqualified authorities are fallacious.

True or False A straw man fallacy is a mistake in grammar.

False -Straw man is a distortion fallacy, which occurs when someone's written or spoken words are taken out of context. It purposely distorts the original argument to create a new, weak argument that can be easily refuted (a straw man that is easily knocked down).

True or False An argument against the person always has a false conclusion.

False -Though an argument ad hominem is fallacious, it does not necessarily have a false conclusion.

True or False Baronett New Custom Exercises Chapter 4 (Rooney) An appeal to ignorance is a type of argument against the person.

False -An appeal to ignorance does not criticize a person.

True or False An inclusive disjunction is where both disjuncts cannot be true at the same time.

Flase

Instructions: Choose the symbolic notation translation of the following statements that captures as closely as possible the logical structure of each statement. My house is painted red and my car is painted green.

H · C

Instructions: Choose the symbolic notation translation of the following statements that captures as closely as possible the logical structure of each statement. Both Lee Ann and Mary Lynn are vegetarians.

L · M

Instructions: Use your knowledge of truth tables to determine if the pairs of statements are logically equivalent. ~ S v ~ R | ~ ( S · R )

Logically equivalent

If "~ (X v Y)" is true, then can one of the disjuncts be true?

No -The statement negates the possibility that either disjunct is true.

Instructions: Use your knowledge of truth tables to identify the following statements as contingent, tautology, or self-contradiction. P · ~ P

Self-contradiction

True or False The compound statement called biconditional is made up of two conditionals: one indicated by the word "if" and the other indicated by the phrase "only if."

True

True or False The experimental group is the group that gets the variable being tested.

True

True or False The experimental variable is withheld from the control group.

True

True or False The joint method of agreement and difference combines two methods.

True

True or False The method of difference looks for what all the instances of an event do not have in common.

True

True or False The method of residues subtracts from a complex set of events those parts that already have known causes.

True

True or False Theoretical science proposes explanations for observations of natural phenomena.

True

True or False We can test a hypothesis by getting it to make a prediction.

True

Truth values 3 Instructions: If P is true, Q is false, R is true, and S is false, determine the truth value of the following: R · ~ S

True

Truth values 3 Instructions: If P is true, Q is false, R is true, and S is false, determine the truth value of the following: S v ~ Q

True

Truth values 3 Instructions: If P is true, Q is false, R is true, and S is false, determine the truth value of the following: [ P v ( Q v R ) ] ⊃ ( S v P )

True

If "X · ~ Y" is true, then which of the following is correct?

Y must be false. -The only way for a conjunction to be true is when both conjuncts are true. Since Y is negated, in order for the negated Y to be true, Y must be false.

If "X v Y" is true, then can one of the disjuncts be false?

Yes -A disjunction can be true when only one of the disjuncts is true.

Translate the following statements into symbolic form by using logical operators and uppercase letters to represent the English statements. If you have a good credit score and no debt, then you can buy a house. Let G = you have a good credit score, D = you have debt, and H = you can buy a house.

( G · ~ D ) ⊃ H -It's important to bracket off the conjunction so that it can function as the antecedent of the conditional.

You can buy a house with a good interest rate if and only if you have good credit and no debt. Let G = you have good credit, I = good interest rate, D = you have debt, and H = you can buy a house.

( H · I ) ≡ ( G · ~ D ) -"If and only if" is your clue that the statement is a biconditional, which means that the complex statements on either side are bound by parentheses. In addition, "with" is translated using a conjunction.

Instructions: Choose the symbolic notation translation of the following statements that captures as closely as possible the logical structure of each statement. If it walks like a duck and talks like a duck, then it's a duck.

( W · T ) ⊃ D

Instructions: Choose the symbolic notation translation of the following statements that captures as closely as possible the logical structure of each statement. If it does not walk like a duck and does not talk like a duck, then it's not a duck.

( ~ W · ~ T ) ⊃ ~ D

Instructions: Choose the symbolic notation translation of the following statements that captures as closely as possible the logical structure of each statement. If Carly works hard and is not distracted, then she will get done on time.

(W · ~ D ) ⊃ T

~ Q · P

. (and) -Remember that the operator that has in its range the largest component or components in a compound statement is the main operator.

Which fallacy best fits the following passage? Doctor: I can't find the cause of your illness, but frankly I think it's due to drinking. Patient: Then I'll come back when you are sober. Anonymous-used by many comedians

Amphiboly -The patient has confused who is being said to be drunk: himself or the doctor.

Which fallacy best fits the following passage? I always said the only failure is when you fail to try. I guess the other failure would not be giving your best effort. And I did both. Martina Navratilova, quoted in Telegraph.co.uk

Amphiboly -Two problems: 1. "The only failure" is mentioned, so there is only one kind of failure; but she goes on to say, "the other failure." 2. She then says, "And I did both," so are we to conclude that she failed to try and failed to give her best effort?

Which fallacy of ambiguity or diversion best fits the following passage? Just waiting to be eaten, he noticed the cake in the corner.

Amphiboly -Who is waiting to be eaten, him or the cake?

Which fallacy best fits the following passage? I do not have much information on this case except the general statement of the agency that there is nothing in the files to disprove his Communist connections. Richard H. Rovere, Senator Joe McCarthy

Appeal to ignorance -Lack of disproof is not proof.

Which fallacy best fits the following passage? These are the times that try men's souls. The summer soldier and the sunshine patriot will in this crisis shrink from the service of his country; but he that stands it now deserves the love and thanks for man and woman. Tyranny, like hell, is not easily conquered; yet we have this consolation with us, that the harder the conflict, the more glorious the triumph. What we obtain too cheap, we esteem too lightly; 'tis dearness only that gives everything its value. Heaven knows how to put a proper price upon its goods; and it would be strange indeed, if so celestial an article as freedom should not be highly rated. Britain, with an army to enforce her tyranny, has declared that she has a right (not only to tax) but "to bind us in all cases whatsoever," and if being bound in that manner is not slavery, then there is no such thing as slavery upon earth. Thomas Paine, The Crisis

Appeal to the people -To the extent that Paine is making an argument, he is urging Americans to fight against British rule; however, he offers mostly flowery language to demonize the British and glorify revolt.

Which fallacy of unwarranted assumption best describes the following passage? Grades should not be based only on regular attendance. If that were the case, then someone could pass a class just by showing up often. And that's just wrong.

Begging the question -The issue is whether grades should be based on attendance only, so this argument begs the question by simply assuming it is wrong.

Which fallacy best fits the following passage? Dear Friend, a man who has studied law to its highest degree is a brilliant lawyer, for a brilliant lawyer has studied law to its highest degree. Oscar Wilde, De Profundis

Begging the question -Why is he brilliant? Because he is brilliant.

Which fallacy best fits the following passage? For the natives, they are near all dead of the smallpox, so as the Lord hath cleared our title to what we possess. John Winthrop, governor, Massachusetts Colony, 1634

Coincidence -Lots of people dying from disease doesn't establish divine intervention (though many people have thought this and continue to think so).

Which fallacy of unwarranted assumption best describes the following passage? The Dow Jones industrial average surged by two hundred points today. This proves my theory that the stock market is sensitive to solar activity, since there was also substantial solar flare this morning.

Coincidence -There is no obvious mechanism and no substantial evidence for a causal link between the sun and the stock market, so this is best classified as a coincidence.

Which fallacy of ambiguity or diversion best fits the following passage? I know for a fact that the acrylic paints that Vincent van Gogh used to create this portrait were very inexpensive. So even though his painting is hanging in a museum, it can't be very expensive.

Composition -An individual grain of silicon may not be expensive, but putting it together into a smart phone might make the whole expensive.

Instructions: Pick out the premises and conclusion for each of the following arguments. Argument 3 Paris is called the "City of Lights." Las Vegas is also called the "City of Lights." So, there must be at least two cities with the same nickname. There must be at least two cities with the same nickname.

Conclusion

Instructions: Use your knowledge of truth tables to determine if the following sets of statements are contradictory, consistent, or inconsistent. A v ~ B | ~ A v B

Consistent

Instructions: Use your knowledge of truth tables to determine if the following sets of statements are contradictory, consistent, or inconsistent. P ⊃ Q | P v ~ Q

Consistent

Instructions: Use your knowledge of truth tables to determine if the following sets of statements are contradictory, consistent, or inconsistent. S = U | S v U

Consistent

Instructions: Use your knowledge of truth tables to determine if the following sets of statements are contradictory, consistent, or inconsistent. ~ A · B | A · ~ B

Inconsistent

Determine whether the truth table is correct for the following compound proposition. ​ A B C (AvB) & C t t t T t t f T t f t F t f f F f t t T f t f F f f t F f f f F

Incorrect -There are mistakes in the second and third lines.

Determine whether the truth table is correct for the following compound proposition. ​ P Q P v (P LaTeX: \supset ⊃ Q t t t...T...t t f t...T...t f t t...T...t f f f...F...f

Incorrect -There is a mistake in the fourth line under the conditional.

Instructions: Use your knowledge of truth tables to determine if the pairs of statements are logically equivalent. P = Q | ( P ⊃ Q ) v ( Q ⊃ P )

Not logically equivalent

Instructions: Pick out the premises and conclusion for each of the following arguments. Argument 2 Soy bean curd has no taste. The fat in hamburgers is what gives them their great taste. The fat in pizza is what gives it great taste. Food without fat tastes bland. Soy bean curd has no fat. Soy bean curd has no fat.

Premise

Instructions: Pick out the premises and conclusion for each of the following arguments. Argument 4 Paris's Eiffel Tower is three times as tall as the one in Las Vegas. The Luxor Pyramid in Las Vegas is half the size of the original in Egypt. The Statue of Liberty in New York is four times the one in Las Vegas. Thus, every object in Las Vegas is smaller than in other cities. Paris's Eiffel Tower is three times as tall as the one in Las Vegas.

Premise

Instructions: Pick out the premises and conclusion for each of the following arguments. Argument 3 Paris is called the "City of Lights." Las Vegas is also called the "City of Lights." So, there must be at least two cities with the same nickname. Las Vegas is also called the "City of Lights."

Premise

Instructions: Pick out the premises and conclusion for each of the following arguments. Argument 3 Paris is called the "City of Lights." Las Vegas is also called the "City of Lights." So, there must be at least two cities with the same nickname. Paris is called the "City of Lights."

Premise

Which fallacy of ambiguity or diversion best fits the following passage? My mother wants me to take piano lessons because studies show that early music training helps students in math. But pianos cost a lot of money, and even if we could afford one, our apartment is too small.

Red herring -The speaker ignores the mother's reason and changes the topic instead of replying to her argument. This is question 17 in the book.

Instructions: Analyze the following case studies by picking out the hypothesis, experiment, and prediction. Determine whether the evidence offered in the case study confirms or disconfirms the hypothesis. Case study 4 Barbara began sneezing and had bouts of dizziness for 4 consecutive days. She remembered that the day before the symptoms began she had bought a new flowering houseplant. She decided to take the plant outside to see what would happen. The next day the symptoms disappeared. What is the experiment?

Take the plant outside.

Instructions: Use your knowledge of truth tables to identify the following statements as contingent, tautology, or self-contradiction. P v ~ P

Tautology

For the following case, construct a chart based on the information given for each case. Use that chart to determine which of Mill's methods apply to that case, and to determine the conclusion that can be derived from the method: Sam had $250 in his wallet on Friday afternoon. By Sunday night he had only $10 left. He recalled spending $60 on a dinner and a date Friday night. Then he spent $70 on groceries, $40 on gas for his car, and lent $50 to a friend. He didn't recall spending any more money, so the only thing he could think of was that he must have lost the $20 somewhere.

The method of agreement; conclusion: Losing the money is probably causally connected to the missing $20. -The following chart displays the method of agreement. We can conclude that losing the money is probably causally connected to the missing $20.

TreShawn boiled an egg for 3 minutes. Opening it, he found that it was quite runny. He tried boiling another egg for 4 minutes; it was a little thicker, but still not what he wanted. He boiled another egg for 5 minutes, and it was exactly what he wanted. He then decided to try to get a hard-boiled egg. After adding an additional minute of boiling to each subsequent egg, he determined that the hard-boiled egg he liked took 10 minutes of boiling.

The method of concomitant variations: conclusion: The number of minutes boiling an egg is probably causally connected to the hardness of the egg. -The following chart displays the method of concomitant variations. We can conclude that the number of minutes boiling an egg is probably causally connected to the hardness of the egg.

Two tomato plants were started from the same batch of seeds. They were all placed in the same kind of soil, given the same watering schedule and same amount of water, and had the same access to sun. Only one of the plants was sprayed with a fertilizer once a week; the other plant never received the fertilizer. The plant that received the fertilizer produced twice as many pounds of tomatoes as the nonfertilized plant.

The method of difference: conclusion: Spraying the plant with a fertilizer once a week is probably causally connected to producing twice as many pounds of tomatoes. -The following chart displays the method of difference. We can conclude that spraying the plant with a fertilizer once a week is probably causally connected to producing twice as many pounds of tomatoes.

(R ⋅ ∼ R) ⊃ (S ν ∼ S)

The statement is a tautology. -The truth table reveals that the main operator is necessarily true.

∼ (R ⋅ ∼ R) ν ∼ (S ν ∼ S)

The statement is a tautology. -The truth table reveals that the main operator is necessarily true.

Instructions: Analyze the following case studies by picking out the hypothesis, experiment, and prediction. Determine whether the evidence offered in the case study confirms or disconfirms the hypothesis. Case study 4 Barbara began sneezing and had bouts of dizziness for 4 consecutive days. She remembered that the day before the symptoms began she had bought a new flowering houseplant. She decided to take the plant outside to see what would happen. The next day the symptoms disappeared. What is the prediction?

The symptoms should go away.

True or False A causal network is the set of necessary conditions that bring about an effect.

True

True or False A conjunction is a compound statement that has two distinct statements (called conjuncts) connected by the dot symbol.

True

True or False A correlation is a correspondence between two sets of objects, events, or sets of data.

True

True or False A disjunction is a compound statement that has two distinct statements (called disjuncts) connected by the wedge symbol.

True

True or False A good hypothesis provides an explanation of facts and gives us a way of discovering new facts.

True

True or False A nontrivial prediction requires reference to background knowledge, which is everything we know to be true.

True

True or False A simple statement is one that does not have any other statement as a component.

True

True or False A statement form is a pattern of statement variables and logical operators.

True

True or False An abnormal state is a drastic change in the normal state.

True

True or False In inference to the best explanation, we reason from the premise that a hypothesis would explain certain facts to the conclusion that the hypothesis is the best explanation for those facts.

True

True or False Predictions are either true or false, and the results are used to confirm (support) or disconfirm (refute) the hypothesis.

True

True or False When someone makes an argument on the assumption that all members of a group are like some members of another group, even though that smaller group is different from the larger group, they are committing the fallacy of biased sample.

True -This is another way of describing the use of a non-representative sample as the basis of a generalization.

True or False Any argument that tries to persuade exclusively by making the audience feel sorry for someone is a fallacious appeal to pity.

True -An appeal to pity only on pity for support.

True or False Arguments that beg the question are often convincing because, in many cases, the conclusion is assumed in the premises.

True -Premises that legitimately support a conclusion do so by providing reasons independent of the conclusions claim. Begging the question does not.

If you have neither a bad credit score nor debt, then you can buy a house. Let B = you have a bad credit score, D = you have debt, and H = you can buy a house.

~ ( B v D ) ⊃ H -Pay very close attention to how the parentheses affect the negation.

Instructions: Choose the symbolic notation translation of the following statements that captures as closely as possible the logical structure of each statement. It is not the case that either Lee Ann or Mary Lynn is a vegetarian.

~ (L v M)

[ (M ν P) ⊃ (Q ν R) ] ν (S · ~ P)

ν -In this case, it is the third "ν" connecting [ (M ν P) ⊃ (Q ν R) ] with (S · ~ P).

(P · Q) ν ~ R

ν -Remember that the operator that has in its range the largest component or components in a compound statement is the main operator.

L ⊃ (~ P ⊃ Q)

⊃ -In this case, it is the first ⊃ symbol. Remember that the operator that has in its range the largest component or components in a compound statement is the main operator.

Identify the main operator in each of the following WFFs. Choose the correct answer. L ⊃ ~ P

⊃ -Remember that the operator that has in its range the largest component or components in a compound statement is the main operator.

~ K ⊃ ~ P

⊃ -Remember that the operator that has in its range the largest component or components in a compound statement is the main operator.