The view that there is something which makes true a statement or something in virtue of which the statement is true is usually referred to as the conception of truth as correspondence. It presupposes that the something which makes true the statement - say the statement that the cat is on the mat - and which is is "out there" in the world, i.e a cat being on a mat, or some sort of "fact" or "truthmaker". This view is often considered problematic because we do not know exactly the nature of the "facts" in question, which seem to be arbitrary depending upon the language wxho use to describe them. For instance is "the cat is on the mat" is made true by the presence of *several* cats on the mat ( in which case it is false to talk of "the" (unique) cat, or by an animal who is boardline for a cat (say a lynx)? Some facts seem to be identical although the descriptions differ ( for instance that I gave you 100 $ is the same fact as that you received 100 $ from me, but not quite) We feel that in this case it's a matter of language, hence of choice of description, and that descriptions are relative. In the case of historical truths, we also feel that they cannot be made true by historical facts, since a) these are long past, hence difficult to confront to our present day statements, b) these facts are most of time human actions, which can be relative to human interpreters ( a battle can be understood as a victory for one camp, as a defeat for another). So the temptation of relativising the facts to our descriptions of the facts, hence to reject the correspondence conception of truth for historical statements is very tempting. But we should resist this temptation. That a fact can be vague or precise depending upon our language of description is often a feature of our language and of our ignorance rather than a feature of reality. The difference between a mountain and a valley is often vague, or the baldness of a man may be evaluated with respect to different standards of loss of hair, but there is a difference between mountin and valley , and between a hairy person and a very un-hairy one. That truths are often relative to our language of description, including metaphorical ones ( if Mother tells to Child that he is a pig when he eats does not mean that Child has a snout and makes piggish noises) does not mean that they are not truths. We may pick up the facts, but ignore exactly how the world is sliced.
The matter is difficult in legal contexts, where aguably interpretation is very present and sometimes essential. There is a whole school of though in legal theory who claims that there is no objectivity in law. But there are also good reasons, from a realist camp, to believe in objectivity and truth in legal matters too.
To say that facts could be decided by authorities is to sucribe to a for of the argument from authority. But this kind of argument is usually considered invalid, even though some authorities ARE reliable. Arguably a Nobel Prize in physics is more reliable about the physics of the universes than Homer Simpson.
A famous article by the philosopher of law Ronald Dworkin , "Objectivity and truth: you'd better believe it" (http://philosophy.fas.nyu.edu/object/ronalddworkin) is very useful in this respect.
I think you raise one of the strongest objections possible to relativism, one so strong that it renders relativism impossible to formulate in that way (i.e., "All truths are relative"). But I do warn you that things get stickier as your get into relativistic theories. What makes them compelling? Here are a couple of general strategies that I've run across.
1. Negative Proof: Negatively, non-relativistic theories of truth seem, at least in the view of many, to have irresolveable problems of their own, arguably greater problems. So, if non-relativistic theories can't be right, some kind of relativism must be correct.
2. Positive Proof: Positively but indirectly, relativism seems (1) to answer serveral questions about the way the meaning of language and the designation "true" is determined and correlatively (2) it seems to be the consequence of investigations into matters concerning topics like whether a body of evidence can determine only one conclusion (answer: no), whether a word can have a single, clear, univocal meaning (nope), whether hypotheses are testable individually (no again), and whether any unique sentence or set of sentences can represent independent reality (no way). Then, of course, there seems to be the facts of sociology and history that exhibit countless and forever changing truth-claims.
3. Shown, Not Said. Some who are influenced by Wittgenstein, might argue that something like relativism can be "shown" by certain manipulations of language usages and certain investigations into the way language works, but it can't be proven. So, if you don't see the relativism, look again, look harder.
4. Biting the Bullet. Some might just embrace the idea that relativism is relative, too. Of course, that would seem to make it impossible for the relativist to criticize absolutists or to assert that absolutism is wrong (after all the absolutists might just say that, "well, absolutism is true for me or for my society, and that's supposed to be enough for you"). But watch it here. The relativist might then try to bring the absolutist to change her or his mind and accept relativism--but NOT by maintaining that relativism is "true" (where there can only be one truth or perhaps where truth is thought somehow to depict "the way things are") but by maintaing that relativism seems to be morally or politically preferable, that it seems more felicitous, the best explanation for our present social purposes, that it seems to work better, that it yields more pleasant consequences, that it produces more agreement, etc.
So, while you're right that relativism of the form you describe hoists itself on its own petard (as Schick & Vaugh like to say) and therefore is self-defeating, don't assume that all relativists would formulate their positions in just that way--at least not without a fuss.
I would not say that necessity is defined by our powers of imagination. Maybe some people are better at imagining things that others, but necessity doesn't vary. Like many philosophers these days, I find it helpful to think about necessity instead in terms of 'possible worlds', in terms of different ways the world might be. To say that a statement is necessarily true on this way of thinking about these things is to say that it holds in all possible worlds. Those worlds are not defined by imagination, so neither is necessity.
This is not to say that imagination isn't important here, because we use our powers of imagination in order to try to work out whether a statement is or isn't necessary. For example, I may convince myself that something is not necessary because I can imagine it being false. But on this view imagination is a fallible guide to necessity, not the definition of necessity. I might just that something is necessary because I can't imagine it being false, but in fact that's only because I'm not clever enough at thinking of possibilities. And I might think that something is not necessary because I think that I can imagine it being false, but in fact I am fooling myself. On this view, imagination is part of the epistemology of necessity, not part of its nature.
Most philosophers today in the English-speaking tradition agree with you that truth is not just subjective. But there is a lot of room between thinking that there is a single, complete true description of all reality and thinking that truth is just what we make it. For example, you might deny that truth is just a matter of opinion (even collective opinion) and ALSO deny that reality is what it is entirely independently of us. (I think that Wittgenstein would deny both.) So, I don't think that we have to choose between 'the truth [independently of us]' and 'truth-for-us'.
I think that this is a deep and fascinating question.
The past can't change, but what happened in the past affects what will happen in the future. Suppose that you didn't water your plant yesterday. If you believe this, then you will water your plant today and it will be fine. But if you falsely believe that you did water your plant yesterday, then you won't water it today and it will die. So the truth about the past matters.
I think the idea in the book was that anything that is possible is actually true somewhere: It is not that anything one does imagine becomes true, but that anything one can imagine is true, somewhere or other, the assumption being made that, if one can imagine it, it must be possible. (Whether that is true, whether "conceivability implies possibility", is a much contested issue.)
It seems unlikely that the Universe is actually as described in the Hitchhiker's Guide,if only because the universe is finite and it would seem that there areinfinitely things that are possible. But David Lewis has held a view that is in some ways similar: Reality consists of ever so many universes, all of which are spatio-temporally disconnected from one another, and anything that might have been true is actually true in one of those universes. So, for example, since it is possible that I should explode, leaving nothing but a pile of gold in my chair, there is a universe somewhere in which not I, since I live in this universe, but someone otherwise exactly like me explodes, a pile of gold being all that is left not in this chair, since it is here, but in a chair otherwise just like this one. Poor guy.
It's only a rough analogy, but just as the fact that we can see things without understanding how vision works does not remove the interest of a theory of vision, so I would say that the fact that we can know things without understanding the nature of truth does not remove the interest of a theory of truth. Maybe discovering a good theory of truth would not help us discover more ordinary truths, but the fortunately the value of philosophy does not depend entirely on it technological applications.
Yes and no.
But seriously, now. First, a "conjunction" (an and sentence) might have a true part and a false part: "2 > 1 and 7 > 9". But the usual view of logicians is that a sentence like that is simply false despite having a true conjunct: its truth requires precisely that both conjuncts be true, which is simply not the case. Similarly for "all natural numbers are either less than or greater than 3"---it's simply false, even if there's only one exception among the infinitely many natural numbers.
Second, a sentence can be ambiguous, and true on one way of understanding it, but not on another. "Bill Gates contributes generously to charities," for example, might be true if by "giving generously" we mean "giving a great deal of money" but false if we mean "giving so much as to make for a significant sacrifice on the part of the giver". I suppose that if we use this sentence without intending one of those meanings rather than the other---so that it remains ambiguous---it might be called "partially true", or "true in a sense", or something like that. Or it might just be called "too unclear to evaluate".
Probably a better candidate for partial truth and partial falsity is a sentence involving the application of vague terminology to a "borderline case". It might be that "Monterey is in Northern California" is a good example: it seems not quite true, and not quite false, because, to speak metaphorically, "Northern California" doesn't have clean boundaries, and the city of Monterey is covered by the smudge. But it's a big controversy among philosophers how to apply the concepts of "true" and "false" to sentences like that. Some horses in the race:
- Degrees-of-truth Theorists: the sentence is true to a certain degree and false to a certain degree---perhaps 50-50 or 60-40.
- Nihilists: the sentence is not true to any degree nor false to any degree. "Northern California" is too ill-defined to be used in true or false sentences.
- Epistemicists: the sentence is completely true, or completely false; it's just that we don't know (and probably could never figure out) which, because the (clean!) boundary that delimits Northern California is an elusive little bugger.
- Supervaluationists: we simply haven't bothered to settle on where exactly the clean boundary should be; still, we've narrowed it down to a limited neighborhood of okay ways of slicing it. The sentence is true if it would come out true however we slice it, false if false however we slice it, otherwise an intermediate status that we might call "indeterminate". Monterey, being included by some okay boundaries of "Northern California" but excluded by others, therefore makes for an indeterminate case.
The buzz-word for this issue is "vagueness"; it's a playground (or is it a morass?) for logicians, metaphysicians, and philosophers of language.