There is nothing stopping you from defining an analytic theorem of a formal system to be one whose derivation requires appeal to at least one member of a designated subset of axioms. But on what basis are you deciding to single out that particular subset of axioms? If you say you're being guided by the fact that those particular axioms express truths about meanings, whereas other axioms express substantive truths about the world, then you owe an explanation of what that distinction amounts to -- and arguably, that will be no easier to give than an outright analysis of "analytic". (You might also look at W.V. Quine's discussion of Semantic Postulates in his paper "Two Dogmas of Empiricism.")

I don't know what you mean by: "One can create axioms that make statements like 'all bachelors are married' true". I assume that by 'married' you mean 'unmarried'. But I still don't understand. Perhaps you mean that one can write down obviously true principles from which the truth of every analytic sentence, and no other sentence, follows. But we can't.


Not yet anyway.

The tricky thing about this issue is to decide what the issue is. Some people seem to want to say that all facts are constructed, but I've never really understood what this is supposed to mean. Let me yank at a few threads and see if any of them are connected to the worry.

Some facts depend on our conventions, institutions and so on. A well-worn example: I have a shiny round bit of metal in front of me. As a matter of fact, it's a quarter; it's worth $.25. That really is a fact, but it wouldn't be a fact if we didn't have certain practices, institutions and so on. In at least some sense of "constructed," it's a constructed fact.

We also classify things in various ways. Some of those classifications grow out of our interests, beliefs and so on. Classifying music according to genre is relatively benign; classifying people according to the racial categories of apartheid-era South Africa or the antebellum American South is anything but benign. Sometimes we take our classifications to mark deep distinctions in nature when all they really reflect our our own shallow points of view. But it may be, all the same, that some ways of classifying things "cut nature at its joints," as they say. Protons and electrons are arguably real kinds, and among the basic things from which nature is built. Charge and mass may be basic, perfectly natural properties.

Some philosophers -- nominalists of various sorts -- reject the very idea that some ways of classifying things are more true to the world than others. Others -- David Lewis is an important recent example -- would say that we can't get around presupposing that there really are natural properties, even though there's room to fight over just what sort of beast a property is. If this sort of view is right, then there are facts independent of any theories.

Interpretation is a slippery concept. Sometimes my interpretation of a situation is just plain wrong. I may have seen you through the window and interpreted the expression on your face as deep sorrow. In fact, you may have been laughing hysterically. My interpretation was wrong. On the other hand, when what we're trying to interpret is an artifact, "better" and "worse" are sometimes more useful ways of judging interpretations than "right" and "wrong." (Is Hamlet a story about a man with an Oedipus complex? That interpretation got a good deal of mileage, but it's not clear whether there's any hard fact of the matter.)

Here's a view. (It's a crude version of what David Lewis believed.) At bottom, there are perfectly natural properties, distributed in space-time in some particular way. There are facts about all that, whether we know them or not. And everything else is fixed by those facts; there couldn't be any differences at the level of ships, shoes, food fights and French literary theory without differences at that basic level. If Lewis was broadly right (and I've never seen any good reason to think that he was wildly wrong), then the idea that it's interpretive mush all the way down is a mistake.

In connection with Professor Stairs' last two paragraphs, you might also read Question 997 and some of the further entries referred to there.

Let's start with an analogy and see how far it gets us. Suppose I consider a proposition about some distant place. Suppose I consider the proposition that the population of Woodstock, New Brunswick (my home town in Canada) is over 6,000. [To keep things simple, assume that I mean the population today, August 5 2007.] I'm contemplating this "here" in Washington DC. But it's a proposition about some other place -- "there," not "here." And now consider the question: "Does this proposition about Woodstock have to be true or false here in Washington?"

The question seems a little odd. What the proposition asserts refers to a particular place, but the idea that the truth of the proposition is, as it were, tied to the place where it's being contemplated seems off. We might put it this way: the proposition picked out by my use of the sentence "Woodstock has a population over 6,000" is true if the population of Woodstock really is over 6,000 and false otherwise. Asking if the proposition is true here is asking a bad question.

So one might argue that we should say much the same thing about a proposition such as "The President of the USA in 2033 will be a Democrat." I'm contemplating it at a particular time, different from the one that the proposition refers to, but that doesn't give us a reason to tie the truth of the proposition to the time when someone is considering it. On analogy with our previous example, we might say that the proposition I consider when I ask "Will the President of the USA in 2033 be a Democrat?" is true or false depending on whether the American president in 2033 is a Democrat, in the timeless sense of "is."

We might argue this way. But it inevitably feels odd to many people. That's because we don't think of space and time in the same way. Most of us have no doubts about the reality of distant locations. Distant times, and especially, future times provoke a different response. We tend to think of the future as "not yet real." We may think that while there is a fact of the matter about Woodstock's population ("Now," we might add), there is no such fact about the Presidency in 2033.

We've now landed in the middle of a larger metaphysical debate. We're inclined to take our talk of past, present and future (McTaggart's "A-series") as having ontological bite, and to think of the world as a place of "becoming." However, many philosophers argue that this point of view is untenable for very general reason, and that in particular it's hard to square with the view of space and time that Special Relativity seems to embody. In relativity, there's no privileged answer to the question "What is simultaneous with event x?" That makes it hard to single out some ontologically privileged "now" that carves propositions up into ones with truth values and ones that, so to speak, await the arrival of their truth-values.

There's a lively debate about all this; you might look for a copy of Craig Bourne's A Future for Presentism. But to get to the second part of your question, suppose we accept the view that propositions about the future have definite truth-values. Do we then end up having to say that all propositions about the future are necessary?

I would say no. Here again, an analogy might be useful. As it happens, right now there are 4 coins in my pocket: two quarters, a dime and a nickel. But that pretty clearly seems to be a contingent fact. It might very well have turned out otherwise. And whether there will be the same collection of coins in my pocket an hour from now depends on what I do in the meantime. If I leave things as they are, I'll still have just these coins in my pocket. If I buy that $.65 pack of gum from the vending machine, I won't. Even if it's true that in an hour from now, there will be no coins in my pocket, it may be true because of a contingent fact about what I do in the next few minutes.

We could add more detail here, and spelling all of this out really carefully would take quite a few words. But the short version is something like this: one possible view is that the universe just consists of a certain totality of events. Which propositions are true depends on which events, arranged in what way. But that the universe consists of one set of events as opposed to another might well be (plausibly is) a contingent matter and indeed, what later events there are may depend causally on contingent facts about the things we do here and now.

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.

'All statements are false' is necessarily false, so there is at least one true statement.

It's important to avoid a certain confusion here. One might say, about Alex's argument, that if there does not exist at least one true statement, then of course "There is a pen on my desk now" is not itself a true statement; hence the argument is circular. Of course, the first part is true; but the conclusion does not follow. For the argument to be circular, the claim "There is at least one true statement" would need to be used in that argument, but it is not. What is used in the argument are simply (analogues of) the following two premises: (i) snow is white; (ii) if snow is white, then "snow is white" is true. Alex claims to know (i) by observation; it's less obvious how we know (ii), but one who claims to know it seems on pretty firm ground. From (i) and (ii), then, it follows that "snow is white" is true and so, by a simple logical inference, that there is at least one true statement (viz, "snow is white"). To challenge this argument, one must either challenge (i) or (ii) or one must find fault with the reasoning used.