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Is truth binary? Can there be degrees of truth? Must we say a statement is either true or false? In everyday conversations we do say things like “The story is only 30% true.”

### I'd say yes, truth is binary.

I'd say yes, truth is binary: there are no degrees of truth in between 0 and 1. For two reasons, I think that every proposition has exactly one of two truth-values, true or else false . (1) I'm not aware of any problem in logic or philosophy whose solution really does require positing fewer or more than two truth-values. (2) To my knowledge, every system of logic or semantics that accommodates other than two truth-values has consequences that are deeply implausible. These systems include three-valued logic, infinite-valued logic, supervaluation semantics, and others. In light of (1), I see no reason to flirt with those implausible consequences. When solving a problem seems to require other than two truth-values, the real trouble lies somewhere else. Or so it seems to me.
Now, to say that every proposition is true or false is not to say that every sentence is true or false, not even every grammatically correct declarative sentence. For instance, the self-referential Liar sentence "This...

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