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 sentence is not true" is grammatically correct and declarative, but it cannot be true or false, on pain of contradiction. The sentence has no truth-value at all. It fails to express a proposition (including the proposition that the sentence itself is not true).
So if by "statement" you mean "sentence," then not every statement is true or false. If by "statement" you mean "proposition," then every statement is true or false. Sentences are items of language; propositions are not. Because language is the somewhat haphazard product of many forces, it should be no surprise that some sentences we concoct fail to express propositions.
We do indeed say things like "That story is only 30% true," by which I take it we mean that only about 3 in 10 of the propositions asserted in the story are true. We can say that without having to allow for more than two truth-values.
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 sentence is not true" is grammatically correct and declarative, but it cannot be true or false, on pain of contradiction. The sentence has no truth-value at all. It fails to express a proposition (including the proposition that the sentence itself is not true).
So if by "statement" you mean "sentence," then not every statement is true or false. If by "statement" you mean "proposition," then every statement is true or false. Sentences are items of language; propositions are not. Because language is the somewhat haphazard product of many forces, it should be no surprise that some sentences we concoct fail to express propositions.
We do indeed say things like "That story is only 30% true," by which I take it we mean that only about 3 in 10 of the propositions asserted in the story are true. We can say that without having to allow for more than two truth-values.