Exercises for Conditional Chain Arguments

1. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator wins the New Hampshire primary?

He will be elected president.

He'll have a big advantage when it comes to raising money for his campaign.

He'll have a big advantage when it comes to raising money for his campaign, he'll win the nomination, and he'll be elected president.

No valid conclusion is possible.

2. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator is not elected president?

He wasn't nominated.

He had no advantage in campaign fund-raising.

He didn't win the New Hampshire primary, he had no advantage in campaign fund-raising, and he didn't win the nomination.

No valid conclusion is possible.

3. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator does not win the nomination?

He wasn't elected president.

He didn't win New Hampshire and he wasn't elected president.

He didn't have an advantage in fund-raising and he wasn't elected president.

He didn't have an advantage in fund-raising and he didn't win the primary in New Hampshire.

4. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, if the Senator does not have an advantage in campaign fund-raising, can he be elected president?

No.

Yes.

Unknown.

1. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator wins the New Hampshire primary?

You answered,

He'll have a big advantage when it comes to raising money for his campaign, he'll win the nomination, and he'll be elected president.

Correct!

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator wins the New Hampshire primary," which affirms P and--by modus ponens--we can conclude Q, and R, and finally S are also affirmed.

2. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator is not elected president?

You answered, "He didn't win the New Hampshire primary, he had no advantage in campaign fund-raising, and he didn't win the nomination."

You answered:

He didn't win the New Hampshire primary, he had no advantage in campaign fund-raising, and he didn't win the nomination.

Correct!

3. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator does not win the nomination?

You answered,

He didn't have an advantage in fund-raising and he didn't win the primary in New Hampshire.

Correct!

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator does not win the nomination," which negates R and--by modus tollens--we can conclude Q and P are also negated. Thus, we can reach a valid conclusion that "He didn't have an advantage in fund-raising," (not-Q), and that "He didn't win the primary," (not-P).

4. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, if the Senator does not have an advantage in campaign fund-raising, can he be elected president?

You answered,

Yes.

Correct!

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator does not have an advantage in campaign fund-raising," which negates Q and--by modus tollens--we can conclude P is also negated. But we cannot conclude anything about R or S, since that would be a case of negating the antecedent and invalid. So, even though the Senator was not nominated, according to this argument he may or may not be elected president--we simply can't draw a conclusion one way or the other, meaning that he can be elected.

1. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator wins the New Hampshire primary?

You answered,

He will be elected president.

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator wins the New Hampshire primary," which affirms P and--by modus ponens--we can conclude Q, and R, and finally S are also affirmed. So "He will be elected president" is only part of the answer (S)--not incorrect, just incomplete.

1. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator wins the New Hampshire primary?

You answered,

He'll have a big advantage when it comes to raising money for his campaign.

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator wins the New Hampshire primary," which affirms P and--by modus ponens--we can conclude Q, and R, and finally S are also affirmed. So ,"He'll have a big advantage when it comes to raising money for his campaign" is only part of the answer (Q)--not incorrect, just incomplete.

1. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator wins the New Hampshire primary?

You answered,

No valid conclusion is possible.

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator wins the New Hampshire primary," which affirms P and--by modus ponens--we can conclude Q, and R, and finally S are also affirmed. So, there certainly are valid conclusions possible here: whatever Q, R, and S stand for.

2. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator is not elected president?

You answered

He wasn't nominated.

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator is not elected president," which negates S and--by modus tollens--we can conclude R, Q, and finally P are also negated. Your answer, "He wasn't nominated," is only not-R, so it is incomplete.

2. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator is not elected president?

You answered,

He had no advantage in campaign fund-raising.

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator is not elected president," which negates S and--by modus tollens--we can conclude R, Q, and finally P are also negated. Your answer, "He had no advantage in campaign fund-raising," is only not-Q, so it is incomplete.

2. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator is not elected president?

You answered,

No valid conclusion is possible.

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator is not elected president," which negates S and--by modus tollens--we can conclude R, Q, and finally P are also negated. So, there certainly are valid conclusions possible here: whatever not-R, not-Q and not-P might stand for.

3. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator does not win the nomination?

You answered,

He wasn't elected president.

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator does not win the nomination," which negates R and--by modus tollens--we can conclude Q and P are also negated. But we cannot conclude anything about S, since that would be a case of negating the antecedent and invalid. So, even though the Senator was not nominated, according to this argument he may or may not have been elected president.

3. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator does not win the nomination?

You answered,

He didn't win New Hampshire and he wasn't elected president.

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator does not win the nomination," which negates R and--by modus tollens--we can conclude Q and P are also negated. Thus, we can reach a valid conclusion that "He didn't win the New Hampshire primary" (not-P). But we cannot conclude anything about S, since that would be a case of negating the antecedent and invalid. So, even though the Senator was not nominated, according to this argument he may or may not have been elected president, and your answer is invalid.

3. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, what can you conclude if the Senator does not win the nomination?

You answered,

He didn't have an advantage in fund-raising and he wasn't elected president.

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator does not win the nomination," which negates R and--by modus tollens--we can conclude Q and P are also negated. Thus, we can reach a valid conclusion that "He didn't have an advantage in fund-raising," (not-Q). But we cannot conclude anything about S, since that would be a case of negating the antecedent and invalid. So, even though the Senator was not nominated, according to this argument he may or may not have been elected president, and your answer is invalid.

4. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, if the Senator does not have an advantage in campaign fund-raising, can he be elected president? You answered:

No.

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator does not have an advantage in campaign fund-raising," which negates Q and--by modus tollens--we can conclude P is also negated. But we cannot conclude anything about R or S, since that would be a case of negating the antecedent and invalid. So, even though the Senator was not nominated, according to this argument he may or may not be elected president--we simply can't draw a conclusion one way or the other, as your answer erroneously does.

4. "If the Senator wins the New Hampshire primary, then he'll have a big advantage when it comes to raising money for his campaign. If he has an advantage in campaign fund-raising, he'll certainly win the nomination. And if he's nominated, he will be elected president." Given this chain argument, if the Senator does not have an advantage in campaign fund-raising, can he be elected president?

You answered,

Unknown.

The chain argument has the form:

  1. If P (wins primary), then Q (advantage).
  2. If Q (advantage), then R (win nomination)
  3. If R (win nomination), then S (elected president).

You were told, "the Senator does not have an advantage in campaign fund-raising," which negates Q and--by modus tollens--we can conclude P is also negated. But we cannot conclude anything about R or S, since that would be a case of negating the antecedent and invalid. So, even though the Senator was not nominated, according to this argument he may or may not be elected president--we simply can't draw a conclusion one way or the other. If the question were, "Will he be elected president?", your response of "unknown" would have been fine. But the question is, "Can he beelected president?", and because we can't draw a valid conclusion, we cannot rule out that possibility.

Congratulations! You have finished the exercises on conditional chain arguments.

You can finish the week now with a short quiz on conditionals, by clicking on "Quiz" above.