PHIL 105 Lesson 3

What kind of structure does the argument in the question above have?

None of the above. If we do not break the either-or sentence into parts, then there is only one premise and one conclusion, so the structure cannot be linear, branching, or joint.

The challenger in this election is likely to win, since EXPERTS AGREE that more women support him.

Remove. The assuring phrase "experts agree that" can be dropped because it is not their agreement that makes the Democrat likely to win. It is the support of the women.

THE MOST SURPRISING NEWS OF ALL is that Johnson dropped out of the race because he thought his opponent was better qualified than he was for the office.

Remove. Whether or not such news is surprising does not change the truth of the premises or the force of the argument, and thus it can be dropped.

Every argument with a false conclusion is unsound.

True

Some valid arguments have true premises and a false conclusion.

False. If the premises are actually true and the conclusion is actually false, then it is at least possible that the premises are true and the conclusion is false. So the argument cannot be valid, according to our definition of validity.

CONTEXT: A boat sank, and authorities have been searching for survivors for over a week. ARGUMENT: There must not be any survivors, since, if there were any, they would have been found by now.

No survivors have been found by now. The answer is (C) No survivors have been found by now. (A) approximately repeats the conclusion, so it cannot show the path from the explicit premise to the conclusion, as a suppressed premise should. (B) Plus, the explicit premise would not support the conclusion. Indeed, (B) would refute that conclusion. (D) is clearly false, but we should avoid adding clearly false suppressed premises, if possible.

Mercury is the only common metal that is liquid at room temperature, so a pound of mercury would be liquid in this room. Can this premise be broken up into (a) and (b)? (a) Mercury is the only common metal. (b) Mercury is liquid at room temperature. ____________________________________________ ∴ (c) a pound of mercury would be liquid in this room.

No. Breaking up the premise in in this way turns a true premise ("Mercury is the only common metal that is liquid at room temperature") into a set of premises with one member that is false ("Mercury is the only common metal"). Thus, this division distorts and weakens the argument.

Since he won the lottery, he's rich and lucky, so he'll probably do well in the stock market, too, unless his luck runs out. Can this conclusion be broken up into (c) and (d)? (a) He won the lottery. ______________________ ∴ (b) He's rich and lucky. (c) His luck will not run out. _______________________________________ ∴ (d) He'll probably do well in the stock market.

No. The arguer does not actually say that his luck will not run out, so it distorts the argument to include premise (c).

Mary is either a junior or a senior, so she is almost ready to graduate. Can this premise be broken up into (a) and (b)? (a) Mary is a junior. (b) Mary is a senior. ________________________________ ∴ (c) Mary is almost ready to graduate.

No. The person giving this argument does not claim that Mary is a junior and also does not claim that Mary is a senior. All the arguer claims is that Mary is either one or the other. Thus, it distorts the argument to include these claims as separate premises.

CONTEXT: We want to figure out whether Mildred is older than the other candidate for a job. ARGUMENT: Mildred must be over forty-three, since she has a daughter who is thirty-six years old.

Parents must be more than seven years older than their daughters. The answer is (D) Parents must be more than seven years older than their daughters. (A) is clearly false, but we should avoid adding clearly false suppressed premises if possible. (B) is too vague to make the argument valid, but suppressed premises should make the argument valid if possible. (C) claims more than is needed to make the argument valid, but suppressed premises should not claim more than is needed to make the argument valid.

Philadelphia is RICH IN HISTORY, but it is not now the capital of the United States, so the United States Congress must meet somewhere else.

Remove. The fact that Philadelphia has a rich past is irrelevant to the conclusion about where the United States Congress meets at present.

I know that my wife is at home, since I just called her there and spoke to her. WE TALKED ABOUT OUR DINNER PLANS.

Remove. The fact that the husband and wife talked about dinner plans is an irrelevant tangent. What matters to the argument is only that she spoke from home, not what they spoke about.

Married people are happier, so marriage must be a good thing, OR AT LEAST I THINK SO.

Remove. The guarding phrase "or at least I think so" can be dropped, because what makes marriage good is that it makes people happy, not whether the speaker thinks so.

Not everybody whom you invited is going to come to your party. SOME OF THEM WONT COME. So this room should be big enough.

Remove. To say that some won't come is the same as to say that not all of them will come. Thus, the second sentence repeats the first, so it can be removed without weakening the argument.

Since many newly emerging nations do not have the capital resources that are necessary for sustained growth, they will continue to need help from industrial nations to avoid mass starvation. Can this premise be broken up into (a) and (b)? (a) Adequate capital resources are necessary for sustained growth. (b) Many newly emerging nations do not have adequate capital resources. ___________________________________________________________________________________________ ∴ (c) Many newly emerging nations will continue to need help from industrial nations to avoid mass starvation.

Yes. Here (a) and (b) make independent claims, since either one can be true without the other being true, so it does not distort the argument to separate them.

James is on the chess and football teams. Football is a team sport. So James plays a team sport. Can the first premise be broken up into (a) and (b)? (a) James is on the chess team. (b) James is on the football team. (c) Football is a team sport. _____________________________ ∴ (d) James plays a team sport.

Yes. To say that James is on both teams is to say both that he is on the chess team and also that he is on the football team. The argument is not distorted by breaking these parts into two separate premises. Indeed, breaking them up shows that only one of them (the one about football) is really relevant to the conclusion.

CONTEXT: You are trying to decide whether to visit a sick friend in the hospital. ARGUMENT: You promised to visit her, so you should visit her.

You should keep your promises.(A) is enough to make the argument valid and show how and why the premise supports the conclusion. (B) and (C) might be true, but they do not mention promises, and this explicit argument is about promises. (D) is clearly false, but we should try to avoid adding clearly false suppressed premises.

What kind of structure does the argument in the question above have?

branching structure. In Answer (D) in the previous question, (1) is a reason for (2), and (3) is another reason for the same conclusion.

If you find a reconstruction that is not sound, then the argument that you reconstructed:

could be either sound or unsound. The fact that ONE reconstruction is unsound does not show that ALL reconstructions are unsound. There still might be ANOTHER reconstruction that is sound, even if you find one that is not sound. Admittedly, the goal is to find a sound reconstruction, if there is one, but one still might find a reconstruction that is not good in that way, because it is not sound, even though another reconstruction is better because it is sound.

If you do NOT find a reconstruction that is sound, then he argument that you reconstructed:

could be either sound or unsound. The fact that you fail to find a sound reconstruction could show only that you lack imagination and skill, so the argument that you were trying to reconstruct still might be sound, even though you could not figure out how.

All my children are students. All teenagers are students. Therefore, All my children are teenagers.

invalid and unsound

What kind of structure does the argument in the question above have?

joint structure. The premise "Gold is a metal" would not be enough by itself to show that "Gold must conduct electricity" if it were not also true that "All metals conduct electricity." Similarly, the premise "All metals conduct electricity" would not be enough by itself to show that "Gold must conduct electricity" if it were not also true that "Gold is a metal." Thus, the argument needs both premises to work together in order to support the conclusion. That mutual dependence makes this a joint structure.

Which kind of structure does the argument above have?

linear structure. In Answer (C) of the previous question, (1) is a reason for (2) which is in turn a reason for (3).

All my children are teenagers. All teenagers are students. Therefore, All my children are students.

valid and sound

All teenagers are my children. All my children are students. Therefore, All teenagers are students.

valid but unsound

I took lots of mathematics, so I know that 81 is not a prime number, because 81 is divisible by 3. Indeed, 81 = 3 to the fourth power. Any idiot knows that.

(1) 81 is evenly divisible by 3. (2) 81 is evenly divisible by 1. (3) 81 is evenly divisible by 81. (4) 1, 3, and 81 are three different numbers. ________________________ ∴ (5) 81 is evenly divisible by three different numbers. (from 1-4) (6) Every prime number is evenly divisible by no more than two different numbers. (7) Three different numbers is more than two different numbers. ________________________ ∴ (8) 81 is not a prime number. (from 5-7) Reconstruction (A) is valid, but it is still not adequate, because it lacks suppressed premises that show how to get from the premise to the conclusion. Reconstruction (C) is also inadequate, because it claims that "I know that 81 is not a prime number" is the same as "81 is not a prime number," although these are not equivalent, since the latter can be true when when the former is not.

ARGUMENT: Gold is a metal, so it must conduct electricity, since all metals do.

(1) Gold is a metal. (2) All metals conduct electricity. ____________________ ∴ (3) Gold must conduct electricity. (from 1-2) Arrangement (A) cannot be accurate because the conclusion contains an argument marker "since" that joins two parts that need to be separated. Arrangement (B) cannot be accurate because the fact that gold is a metal is no reason to believe that ALL metals conduct electricity in the step from (1) to (2) in (B). Arrangement (C) cannot be accurate because the premise "Gold is a metal" would not be enough by itself to show that "Gold must conduct electricity" if it were not also true that "All metals conduct electricity." Similarly, the premise "All metals conduct electricity" would not be enough by itself to show that "Gold must conduct electricity" if it were not also true that "Gold is a metal." The two premises need to work together.

His natural talents were not enough; he lost the match because he had not practice sufficiently. You need either great natural talent or hard work to become a winner.

(1) His natural talents were not enough to win without practicing. (2) He had not practiced sufficiently. (3) People lose matches if they do not either practice sufficiently or have enough natural talent to win without practicing. ___________________________ ∴ (4) He lost the match. (from 1-3) (A) is not a good reconstruction because "His natural talents were not enough" is not a reason why "He had not practiced sufficiently." (B) is not a good reconstruction because the passage suggests that inadequate natural talent is not enough to explain the loss if one practices sufficiently, and inadequate practice is not enough to explain the loss if one has enough natural talent.

Joe is not a freshman, since he lives in a fraternity, and freshmen are not allowed to live in fraternities. He also can't be a senior, since he has not declared a major. And he can't be a junior, because I never met him before today, and I would have met him before now if he were a junior. So Joe must be a sophomore.

(1) Joe lives in a fraternity. (2) Joe is allowed to live where he lives. (suppressed premise) (3) Freshmen (first-year students) are not allowed to live in fraternities. ______________________ ∴ (4) Joe is not a freshman. (5) Joe has not declared a major. (6) All seniors (fourth-year students) have declared a major. (suppressed premise) ______________________ ∴ (7) Joe is not a senior. (8) I never met Joe before today. (9) If Joe were a junior (third-year student), then I would have met him before today. ______________________ ∴ (10) Joe is not a junior. (11) Joe is either a freshman, a sophomore, a junior, or a senior. (suppressed premise) ______________________ ∴ (12) Joe is a sophomore (second-year student). (from 4, 7, 10, and 11) Reconstruction (A) merely lists the premises and does not show how they fit together into a structure. Reconstruction (C) falsely suggests that the argument gives three separate reason why Joe is a sophomore, because fact that Joe is not a freshman alone shows that he is a sophomore (in the step from (4) to (5)), and similarly for junior (in the step from (12) to (13)) and senior (in the step from (8) to (9)). However, the argument can conclude that he is a sophomore only after ALL other possibilities have been excluded. That is why this form of argument is often called "process of elimination."

ARGUMENT: Either Jack is a fool or Mary is a crook, because she ended up with all of his money.

(1) Mary ended up with all of Jack's money. _____________________________ ∴ (2) Either Jack is a fool or Mary is a crook. (from 1) The word "because" is a premise marker instead of a conclusion marker, so arrangement (B) cannot be accurate. Arrangements (C) and (D) break up "Either Jack is a fool or Mary is a crook" into the two parts "Jack is a fool" and "Mary is a crook," but either-or sentences should not be broken into parts like this.

ARGUMENT: Our team can't win this Saturday, both because they are no good and also because they are not going to play this Saturday.

(1) Our team is no good. _____________________________ ∴ (2) Our team can't win this Saturday. (from 1) (3) Our team is not going to play this Saturday. _____________________________ ∴ (2) Our team can't win this Saturday. (from 3) Arrangement (A) suggests that both premises are needed to work together to support the conclusion, whereas actually each premise by itself is enough to support the conclusion. Arrangement (B) suggests that "Our team is no good" is a reason to believe "Our team is not going to play this Saturday," but that can't be right, because even bad teams play sometimes on Saturday (unless it is the playoffs, which is not mentioned). Similarly, arrangement (C) suggests that "Our team is not going to play this Saturday" is a reason to believe "Our team is no good," but that can't be right, because even good teams do not play every Saturday.

ARGUMENT: I know Pat can't be a father, because she is not a male. So she can't be a grandfather either.

(1) Pat is not male. _____________________ ∴ (2) Pat can't be a father. (from 1) _____________________ ∴ (3) Pat can't be a grandfather. (from 2) Arrangement (A) fails to break up the premise with the argument marker "because." Arrangements (A) and (B) both fail to capture the role of "Pat is not male" as a premise to support "Pat can't be a father" in the first sentence. Arrangement (D) suggests that "Pat can't be a grandfather" is a reason to believe "Pat can't be a father," but that argument is not valid.

We really got ripped off by that security company. This burglar alarm won't work unless we are lucky or the burglar uses the front door, so we can't count on it. I think we need a new alarm.

1) This burglar alarm won't work unless we are lucky or the burglar uses the front door. (2) We can't count on being lucky. (3) We can't count on the burglar using the front door. (4) We can't count on a burglar alarm that won't work. ______________________ ∴ (5) We can't count on this burglar alarm. (from 1-3) (6) This burglar alarm is the only one that we have. (7) We need a burglar alarm that we can count on. ______________________ ∴ (8) We need a new burglar alarm. (from 1) Reconstruction (B) is inadequate because the explicit argument does not say that we are not lucky or that the burglar won't use the front door. These are risks rather than definite occurrences. Reconstruction (C) is inadequate because neither subargument (from (1) to (2) and from (3) to (4)) is valid, and because "so" is a conclusion marker, so "We can't count on this burglar alarm" is a conclusion rather than a premise.

CONTEXT: You and Susan are working on a project together, and she is not pulling her weight. ARGUMENT: Susan refuses to work on Sundays, which shows that she is lazy and inflexible.

Anyone who refuses to work on Sundays is both lazy and inflexible. The answer is (B) Anyone who refuses to work on Sundays is both lazy and inflexible. (D) is not enough to make the argument valid, because it is too vague. (A) is also not enough to make the argument valid, because the conclusion says that Susan is BOTH lazy AND inflexible. However, suppressed premises are supposed to make the argument valid if possible. (C) is stronger than is necessary to make the argument valid, because it is about ALL days, not just Sundays. However, suppressed premises should not claim more than is needed to make the argument valid.

Susan is smart and strong, so she is smart.

Valid argument. It is not possible for anyone to have both of two qualities without having the first of the two qualities. Notice that it does not matter who Susan is.

SOME students could not concentrate on the lecture, because they did not eat lunch before class.

Do not remove. The guarding term "some" cannot be dropped in this case because it is an essential part of the argument and the speaker is not asserting that "all" or "most" of the students could not concentrate.

Every argument that is unsound has a false conclusion.

False

Every argument with a true conclusion is sound.

False

Washington is in the United States. I live in the United States. So I live in Washington.

Invalid argument. If I live in Texas, then both premises are true, but the conclusion is false. This possibility shows that the argument is invalid.

Sara is either smart or strong, so she is smart.

Invalid argument. If Sara is strong but smart, then the premise is true when the conclusion is false. This possibility shows that the argument is invalid.

Most professors agree that they are paid too little, so they are.

Invalid argument. It is possible for the premise to be true and the conclusion false if most professors believe that they deserve to be paid more than they really do deserve to be paid. This possibility shows that the argument is invalid.

There is no largest six-digit number, because six-digit numbers are numbers and there is no largest number.

Invalid argument. The premises are both true and the conclusion is false. That shows that it is possible for the premises to be true and the conclusion false. Hence, the argument must be invalid, even if it is not clear why.

CONTEXT: You are listening to a lecture in a traditional college classroom, but one person in the audience looks older than the rest. Her name is Mary. ARGUMENT: Mary can't be a student, because she is a professor, and professors must already have degrees.

Students don't already have degrees. The answer is (D) Students don't already have degrees. (A) and (B) do not make the argument valid, because the argument is not about age. Suppressed premises are supposed to show the path from the explicit premises to the conclusion instead of creating a different path to that conclusion. (C) is enough to get us straight from the premise "Mary is a professor" to the conclusion "Mary can't be a student," but then it cannot explain why the arguer went on to add "Professors must already have degrees," so it misses part of the argument. (D) enables us to understand all parts of the argument: Mary can't be a student, because she is a professor, and professors must already have degrees. Then: Students don't already have degrees, so Mary can't be a student. Notice that (D) is false, but it still might be the most plausible suppressed premise to make sense of what the arguer probably had in mind.

Washington is in the United Kingdom. I live in Washington. So I live in the United Kingdom.

Valid argument. There is no possible way for the conclusion to be false when both premises are true. It does not matter that the first premise is actually false, because validity depends on what is possible.

Every argument that is sound has a true conclusion.

True

If you DO find a reconstruction that is sound, then the conclusion of the argument that you reconstructed is:

True. A sound argument has true premises and is valid in the sense that it is not possible for its conclusion to be false when its premises are true, so its conclusion must be true as well.

Washington is in the United States. I live in Washington. So I live in the United States.

Valid argument. There is no possible way for the conclusion to be false when both premises are true. Notice that I can know this relation between the premises and conclusion, even if I do not know whether the premises are true, and even if I do not know whether the argument is about Washington State or Washington, DC.

Some valid arguments have false premises and a true conclusion.

True. Consider this argument: "Our solar system contains fewer than five planets. Therefore, our solar system contains fewer than fifty planets." The premise is false, and conclusion is true. Moreover, the argument is valid because it is not possible for the conclusion to be false when the premise is true.

Some valid arguments have false premises and a false conclusion.

True. Consider this argument: "Our solar system contains fewer than four planets. Therefore, our solar system contains fewer than five planets." The premise and conclusion are both false. Nonetheless, this argument is still valid because it is not possible for the conclusion to be false when the premise is true.

Some valid arguments have true premises and a true conclusion.

True. Consider this argument: "Our solar system contains fewer than seventy-eight planets. Therefore, our solar system contains fewer than seventy-nine planets." The premise and conclusion are both true. The argument is valid because it is not possible for the conclusion to be false when the premise is true.