Truth Functional (TF): Has a true/false value which can be completely determined by the truthfulness/falsefullness (?) of the input's values (got that?).
Question: Show that "It is likely that __" is not a truth functional operator (where the blank, the "input", is filled with a simple sentence with a true/false value).
We can prove "likely" is not TF by finding a single counterexample. How do we find a counterexample? For any simple sentence I create which has a true/false value, I already know if it's likely or not.
For example: $A \equiv$ "The Yankees won the world series", is True. It's also likely. Now I need another sentence, $B$, which is True, but is unlikely. Right? Would like explanation and example (or explanation by way of example). Thx.
Edit: P.S. You cannot answer by saying "likely" is a prediction which is not TF. I want to know why "likely" (or even any prediction) is not TF