Contents

Defeasibility

• An argument is defeasible if the premises’ support of its conclusion can be defeated by additional premises.
• Reliability, explanatory, analogical, deontic, and expected-value arguments are defeasible. Deductive arguments are not.

• Consider the arguments:
  • A reliability argument:
    • In 1998 CNN reported that the U.S. had used sarin nerve gas in Laos in 1970 as part of Operation Tailwind during the Vietnam War.
    • CNN is a reliable source of news.
    • Therefore, the US used sarin gas in Laos in 1970.
  • A deontic argument:
    • Abe promised his brother he would take him to the zoo this morning.
    • Promises should be kept.
    • Therefore Abe should take his brother to the zoo this morning.
  • An analogical argument:
    • Three recently purchased houses in the neighborhood sold for an average $250,000.
    • Amy’s house is like those houses in terms of square footage, number of bedrooms, and age.
    • Therefore Amy’s house will likely sell for about $250,000.

• The arguments are defeated by the following facts:
  • For the CNN argument, the fact that CNN retracted the story
    • cnn.com/US/9807/02/tailwind.johnson;
  • For the argument about Abe’s promise, the fact that Abe had to take their mother to the ER this morning;
  • For the argument about the sale price of Amy’s house, the fact that there’s black mold throughout the house.

Defeaters

• A proposition D defeats an argument if
  • the premises of the argument support the conclusion
  • the premises of the argument with additional premise D don’t support the conclusion.
• Thus, for example, the premises of the CNN argument with the later retraction fail to support the conclusion.
  • In 1998 CNN reported that the U.S. had used sarin nerve gas in Laos in 1970 as part of Operation Tailwind during the Vietnam War.
  • CNN is a reliable source of news.
  • CNN retracted its 1998 story about the use of sarin gas.
  • Therefore, the US used sarin gas in Laos in 1970.

Two Kinds of Defeaters

• A rebutting defeater defeats an argument by casting doubt on its conclusion.
• An undercutting defeater defeats an argument by directly nullifying the premises’ support of the conclusion.
• Example:
  • I look at my watch and infer it’s 3:00. The argument:
    • My watch says it’s 3:00.
    • My watch is reliable.
    • Therefore it’s 3:00.
  • A rebutting defeater is that other people’s watches say 4:00, contradicting the conclusion.
  • An undercutting defeater is that my watch has stopped, directly nullifying the support of the conclusion, i.e. without directly contradicting it.

Valid Deductive Arguments Are Indefeasible

• A valid deductive argument cannot be defeated because it remains valid no matter how many premises are added.
• Consider the valid deductive argument:
  1. Only natural-born U.S. citizens are eligible to be president.
  2. John Oliver isn’t a natural-born U.S. citizen.
  3. Therefore, he’s not eligible to be president.
• Let D be any statement. Consider the argument with additional premise D:
  1. Only natural-born U.S. citizens are eligible to be president.
  2. John Oliver isn’t a natural-born U.S. citizen.
  3. D is true.
  4. Therefore, he’s not eligible to be president.
• Since the conclusion follows necessarily from premises 1 and 2, there’s no possible way premises 1 and 2 are true and the conclusion false. But if the conclusion doesn’t follow necessarily from premises 1, 2, and 3, there’s a way premises 1 and 2 are true and the conclusion false, i.e. by adding premise 3. So, the conclusion follows necessary from premises 1, 2, and 3.