0

In Classical Mathematical Logic: The Semantic Foundations of Logic by R.L. Epstein, he says the following:

Which declarative sentences are true or false, that is, have a truth-value? It is sufficient for our purposes in logic to ask whether we can agree that a particular sentence, or class of sentences as in a formal language, is declarative and whether it is appropriate for us to assume it has a truth-value. If we cannot agree that a certain sentence such as ‘The King of France is bald’ has a truth-value, then we cannot reason together using it. That does not mean that we adopt different logics or that logic is psychological; it only means that we differ on certain cases.

  1. Does he intend to ask which declarative sentences are either true or false, but not both?

  2. Is he saying that when we work with sentences in classical logic, we all agree they are declarative and have exactly one truth value?

  3. Since France has no king, one can neither agree the sentence is false nor true. This is because for the sentence to be false, the king of France must not be bald, and for it to be true, the king of France is actually bald. Is this interpretation valid?

R004
  • 1,023
  • Re: "The King of France is bald." That sentence is vacuously true since there does not exist a King of France at present. It is trivial to prove $\neg \exists x: King(x) \implies \forall x:[King(x) \implies Bald(x)]$. Likewise, $\neg \exists x: King(x) \implies \forall x:[King(x) \implies \neg Bald(x)]$. Note: These statements will be true regardless of whether or not there is at most one King of France. – Dan Christensen Mar 24 '25 at 17:24

0 Answers0