Logic quiz 2 – answers

From logic quiz 2,

Choose the least bad answer: If all whales are triangular, then

  1. no whales are triangular.
  2. some whales are not triangular.
  3. some whales are triangular.
  4. all four of these answers are equally bad.

The answers:

  1. In classical logic, “no whales are triangular” is the contrary of “all whales are triangular.” Contrary statements cannot both be true, but they can both be false.
  2. “some whales are not triangular” is the contradictory of “all whales are triangular.” It contradicts the antecedent in both quantity (“some” instead of “all”) and quality (not triangular instead of triangular). Of contradictories, if one is true the other must be false, and if one is false the other must be true. But a false antecedent cannot imply a true consequent.
  3. “some whales are triangular” is the sub-alternate of “all whales are triangular.” In classical logic, if a statement is true, its sub-alternate is true by immediate inference. So in classical logic the if/then could be said to work for this one, but triangularity is not a property of whales, for as the philosopher says, “the swiftest hare cannot be swifter than an isosceles triangle.” Contemporary logicians say that in classical logic, the universal affirmative was understood to have “existential import” – here implying that whales exist, as well as that all of them are triangular. In contemporary logic, only the particular is taken to have existential import, so that “some whales are triangular” would be understood as saying that there are whales, and that there are triangular whales.
  4. If all four of these answers are equally bad, this one is true, and so false. So this one is false.
  5. Though not without a significant flaw, this is the least bad answer.
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