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...

I tend not to distinguish between a property and a quality. I would say that truth is a property (or quality) of propositions primarily and sentences derivatively: sentences are true when and only when they express true propositions, but propositions can be true without ever being expressed by sentences. It seems odd to me to classify truth as a relation: it would be a relation between what and what else? Some theories of truth say that a proposition's being true depends on a relation, such as a "correspondence" relation between the proposition and a state of affairs in the world. But depending on a relation is different from being a relation. I'm not sure that Locke's distinction between primary and secondary qualities straightforwardly applies to the property (quality) of truth. But I do think that the truth of any proposition is independent of anyone's believing it to be true -- which I suppose makes truth more like a primary than a secondary quality.

Not if they really are necessary truths. By definition, any necessary truth couldn't possibly have been false. It takes some care to state propositions in such a way that they really are necessarily true. For instance, Red is a color asserts the existence of something -- red, or redness -- that arguably doesn't exist in every possible world. If there are possible worlds in which nothing physical ever exists, then nothing is red or (arguably) even could be red in such worlds, making it unclear whether there is a color red in such worlds. By contrast, the necessarily true proposition Whatever is red is colored doesn't assert the existence of anything, so it comes out (vacuously) true even in worlds lacking any red or colored things.

It's not clear to me what you're asking, but I'll do my best. Given a particular conclusion, we can, normally, trace it back to the very basic premises that constitute it. I doubt we can do that without seeing the conclusion in the context of the actual premises used to derive it. The conclusion Socrates is mortal follows from the premises All men are mortal and Socrates is a man , but it also follows from the premises All primates are mortal and Socrates is a primate . So which pair of premises are "the very basic premises" for that conclusion? Outside of the actual argument context, the question has no answer. I don't know what you mean by "the root of a conclusion," but you seem to be suggesting that any knowledge is impure if it depends on -- or if it was acquired using -- any reasoning at all. Perhaps the term inferential would be a better label for such knowledge. On this view, even if I have direct knowledge that I am in pain (when I am), I have only...

I can't make sense of the idea that truth could be relative. Suppose that I find some dish spicy, while you find it mild. We might be inclined to say that (R) "This dish is spicy" is true relative to me and false relative to you, but I think that way of speaking is by no means forced on us and, in fact, is misleading. For if R itself were true, its truth would have to be explained in terms of the truth of this non-relative claim: (NR) This dish is spicy relative to my taste but not yours. NR neither is nor implies the claim that truth is relative. Rather, perceived spiciness is. So too with (P) "Polygamy is acceptable" is true relative to culture A but false relative to culture B. P is an avoidable and misleading way of making the non-relative claim that culture A accepts polygamy whereas culture B doesn't. The acceptance of polygamy is relative to culture, and that's a non-relative truth.

I respectfully disagree with your claim that logic doesn't help in the search for truth. On the contrary, we need logic in order to find out what any proposition P implies -- what other propositions must be true if P is true -- which, in turn, is essential for verifying that P itself is true. This holds as much in science as in philosophy or any other kind of inquiry. You suggest that you need a definition of the word truth before you can answer the question whether philosophy can find truth. But if that's a problem, it isn't a problem just for philosophy: it affects science and any other kind of inquiry just as much as it affects philosophy. You could say to a physicist, "Until I have a definition of truth , how can I know whether physics can find truth?" The only difference here between philosophy and physics is that a philosopher will take your question seriously. I don't think you need a definition of truth -- or at any rate not an interesting definition -- in order to see...

None that I can think of, including none of the candidates that I've seen offered by "dialetheists" (i.e., philosophers who say that some contradictions are true). If you have any promising candidates, please let us know!

To my knowledge, no. Ordinary first-order logic quantifies only over individuals (none of which are literally true) rather than over truth-valued things such as sentences or propositions. Thus there's nothing in first-order logic to which the predicate "is true" can apply. For that you need higher-order logic, which is a topic of controversy in its own right. By "set of all true propositions," I take it you mean "a set of all the true propositions there are," i.e., the extension of the predicate "is a true proposition." A Cantorian argument due to Patrick Grim concludes that no such set is possible. It works by reductio . Let T be any set containing all of the true propositions. If T exists, then it has infinitely many members, but that doesn't affect the argument. Now consider the power set of T -- P(T) -- which is the set whose members are all of the subsets of T. It's provable that any set has more subsets than it has members. With respect to each of those subsets in P(T), there is a true...

One reason that it's difficult to define "truth" might be that the word stands for a concept that's too basic, too fundamental, to be informatively defined in terms of other concepts. I myself think that truth is a property of some propositions and therefore, derivatively, a property of some sentences. Which propositions? The true ones! Which sentences? The ones that express true propositions! The proposal that we can't say more than that is sometimes known as "deflationism" about truth. For much more, see this SEP entry .

Perhaps so many philosophical theories of truth exist because the concept of truth is central and fundamental and because philosophers have been discussing it for such a long time. See the SEP entry on truth for a survey of various theories. As for non-philosophers, I doubt that they're as united in their view of truth as you suggest, and I doubt that they're united around the conception of truth that you proposed: "that which is absolutely incontrovertible and not open to debate." I've met many non-philosophers who claim that both sides in a debate can have the true answer to the precise issue being debated: my side of the debate can be true (for me), while your side can be true (for you). I don't accept their claim, but it certainly seems to be popular. And given how strange human beings often are, few if any statements are going to be "absolutely incontrovertible" if that means "beyond any possible controversy." If, instead, it means "not rationally deniable," then the controversy will...