The Quotation is not the Referent — LessWrong
In classical logic, the operational definition of identity is that whenever 'A=B' is a theorem, you can substitute 'A' for 'B' in any theorem where B appears. For example, if (2 + 2) = 4 is a theorem, and ((2 + 2) + 3) = 7 is a theorem, then (4 + 3) = 7 is a theorem. This leads to a problem which is usually phrased in the following terms: The morning star and the evening star happen to be the same object, the planet Venus. Suppose John knows that the morning star and evening star are the same object. Mary, however, believes that the morning star is the god Lucifer, but the evening star is the god Venus. John believes Mary believes that the morning star is Lucifer. Must John therefore (by substitution) believe that Mary believes that the evening star is Lucifer? Or here's an even simpler version of the problem. 2 + 2 = 4 is true; it is a theorem that (((2 + 2) = 4) = TRUE). Fermat's Last Theorem is also true. So: I believe 2 + 2 = 4 => I believe TRUE => I believe Fermat's Last