Perhaps it is worth taking continuing the conversation just a bit further.

The idea that a proposition (statement, belief) is true if and only if it "corresponds to reality" is -- as I'm sure William would agree -- not entirely transparent. What does it commit us to, exactly?

The deflationist about truth of course says that the proposition that snow is white is true if and only if reality is such that snow is white -- i.e. just if snow is white. So if the correspondence theorist is to be distinctively saying more than that, she needs to spell out what "correspondence" here comes to, over and above what the weak kind of correspondence that is already built into the deflationist view.

Now, there are indeed metaphysicians who do claim to have an "industrial strength" version of the correspondence theory, who postulate the existence of facts as ingredients of the world, facts which are truth-makers whose existence is required to make propositions true (where the worldly constituents of truth-makers are e.g. objects and universals).¹ But it is far from clear that in saying something is true it is part of what we mean that there are such metaphysically weighty truth-makers as ingredients of the world.

For example, in our everyday truth-talk, outside the philosophy classroom, we are as ready to respond "that's true" to the claim that Angelina is beautiful or that slavery is wrong, as to the claim that snow is white. But are we really committed by this everyday way of talking to the existence of facts out there in the world which make true our aesthetic or moral judgments? Arguably not!

In other words, arguably not all everyday true propositions -- such as that Angelina is beautiful or that slavery is wrong (if you don't think they are true, choose your own examples) -- are made true by metaphysically heavy-weight facts, out there in the world. If that's right, then while the "industrial strength" correspondence theory might very well be part of the story about what makes some claims true, it isn't an account of the general meaning of 'true' across the board (indeed, there being or not being corresponding metaphysically weighty facts may be just what distinguishes some classes of truths from other classes).

As to the coherence theory as described by William, that sounds more like an account of how we tell (fallibly, no doubt) what is true, not an account of what it means to say that something, e.g. a theory, is true. Coherence of a theory with observation might well incline us, very reasonably, to think that it is true: but as skeptics love to point out, there seems to be no logical inconsistency in supposing that a theory is coherent but false.

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1. Fine print: strictly this kind of truth-maker theory isn't a correspondence theory in the traditional sense, for it will deny that there is a one-one correspondence between truths and their truth-makers. For example, the same truth-maker, the fact that snow is white, makes true both "snow is white" and "either snow is white or grass is green"; and the fact that grass is green is another, different, truth-maker for the second proposition.

Peter Smith's use of the deflationary theory of truth to answer this question is just one way of approaching it. Another is to use the correspondence theory of truth.

According to (a highly simplified version of) the correspondence theory, truth is a relation between beliefs (or sentences, or propositions) and "reality": A set of beliefs (or sentences, or propositions) is true if and only if they correspond to reality, i.e., iff they "match" or accurately describe reality.

Now, a (scientific) theory is just a set of beliefs (or sentences, or propositions). So, a theory is true if and only if it corresponds to reality.

But how do we access "reality" so that we can determine if our theories (our beliefs) correspond to it? How can we do the "pattern matching" between our beliefs and reality? One answer is by sense perception (perhaps together with our beliefs about what we perceive). But sense perception is notoriously unreliable (think about optical illusions, for instance). And one of the issues in deciding whether our beliefs are true is deciding whether our perceptions are accurate (i.e., whether they match reality).

So we seem to be back to square one, which gives rise to yet another theory of truth: the coherence theory. According to (a highly simplified version of) the coherence theory of truth, a set of propositions (or beliefs, or claims) is true if and only if (1) they are mutually consistent, and (2) they are supported by, or consistent with, all available evidence--i.e., if and only if they "cohere" with each other and with all evidence. (Sometimes this is called a "pragmatic" theory of truth.) Note that observation statements (i.e., descriptions of what we observe in the world around us) are among the claims that must be mutually consistent, so this is not (necessarily) a "pie-in-the-sky" theory that doesn't have to relate to the way things really are.

Note that both Peter and I have been talking about "theories" of truth. So, which of these (or other) theories of truth is true? The answer to that is beyond our present scope! (But note that a correspondence theory must cohere.)

Jack says "The next train to London is at 11.15"; Jill adds "That's true".

Jill's remark in effect just repeats Jack's message. To say it is true that the next train to London is at 11.15 tells us no more about the world than that the next train to London is at 11.15.

Dora witnesses a crime. She gives quite a long statement. "Three boys in jeans and hooded tops came into the shop just before 12. They ... etc., etc. etc., ... And finally they jumped into a red car and sped off." Dick adds "That's all true." Again, Dick is in effect just repeating Dora's statement, but saving breath. You can see why we should have use for such a very handy device in our language. Someone says something, or we read something in a book; saying "that's true" has the effect of saying the same, without all the bother of repeating what is said or written.

And the same handy device is just as useful when what is said or what is written is not so common-or-garden but more theoretical. Alice says "The atomic weight of gold is 196.966". Ben says: "Hold on; I'll check -- [he Googles!] -- yep, that's true". When Ben says it is true that the atomic weight of gold is 196.966 he is just saying that the atomic weight of gold is 196.966.

Likewise, Charles produces a theory about why different people find different effects in holding a certain mobile phone in one corner, a theory that talks (let's suppose) about the different conductivity of different people's skin. Daisy goes off and does some tests, and comes back to report: she talks about the experiments, and concludes (let's suppose) "Charles's theory is true". Her concluding remark is just tantamount to repeating what Charles said in stating his theory, without the bother of saying it all again.

On this view, then, to say that a theory is true is, in effect, to say no more than would be said in repeating the theory.

More generally, what it takes for it to be true that P is no more than that P -- here fill in P by any proposition you care to pick. And that's the same whether P is very short and commonsensical (e.g. about train times), or is a long statement of theory (e.g. a textbook version of the theory of quantum tunnelling).

Of course, if P is long and theoretical it may be very hard to decide whether P is true! -- but that's not because 'truth' is mysterious but because it is difficult to decide whether P. It isn't that there are two tasks here, first deciding whether P, then deciding whether it is true that P: they are just the same task!

(The line I have been explaining is often called a "deflationary" or "minimalist" theory of truth. Of course the devil is in the details, and working out exactly how to present this sort of theory isn't easy. However, the various versions of deflationism/minimalism agree on this much -- the notion of truth functions in just the same non-metaphysical way whether we are talking about train times or quantum tunnelling, whether we are in the realms of common sense or high theory. Putting it crudely, in all cases, the notion of truth just serves as a handy device to enable us to say various things that would take too long without it.)

Some talk about facts is just a stylistic variant of truth-talk. For example, in ordinary discourse, to say 'It's a fact that the fast train to London from Cambridge takes less than an hour' is to say no more than that 'It is true that the fast train to London from Cambridge takes less than an hour'. And, arguably, both those in turn say no more than that the fast train to London to Cambridge does take less than an hour.

However there is also a more substantive notion of fact that has a long history in philosophy and has in recent years made something of a comeback -- this is the notion of facts as not truths but truth-makers. The proposition that the fast train to London from Cambridge takes less than an hour is true. And there is, plausibly, something worldly that makes it true, something that has to exist if the proposition is to be true, a truth-maker in short. And what kind of thing is a truth-maker? It isn't enough for London, Cambridge and trains to exist. And adding in the property of being a fast train and the property of taking less than an hour into your catalogue of existent things isn't enough either. No, the objects and the properties have to be put together in the right way to constitute the right fact to make it true that the fast train to London from Cambridge takes less than an hour.

So on this metaphysical view, there are facts (worldly items) which make propositions true. And of course, such a view has to distinguish facts, in the sense of truth-makers, from truths, meaning true propositions.

You are adopting a pretty radical position, for it seems like common sense for us to recognize as facts (or truths or as actual states of affairs) all sorts of things quite independent of human minds. Most of us would want to say (for example) that it was true that there was life long before there was intelligent life here on earth. Your professor's example is a little odd, partly because very few people have ever believed the earth is flat. (There is a good book on the myth of believing in a flat earth). But you might be able to defend your position as part of a philosophy of language, contending that facts are what correspond to or are referred to as sentences and simply hold the line about not recognizing facts until you have language-users. I believe Fred Stoutland holds that position, and Richard Rorty expresses something like that in The Mirror of Nature. Still, you are not in an enviable position in terms of arguments, as most of us would want to recognize that it is a fact that before there was language there was no language.

Isn't it the other way about? Only a small number of philosophers would not maintain the distinction! For as you remark, lots of truths aren't useful in any ordinary sense (e.g. there is a fact of the matter about whether the number of grains in the rice jar yesterday was odd or even -- but the truth one way or the other is no use now to man or beast); and lots of claims which are strictly false can be useful (quick and dirty approximations that do us well enough.

So to tie the ideas of what is true and what is useful together will need, for a start, bending the idea of the useful into something fairly remote from its common-or-garden sense, and we will also probably have to be pretty revisionary about what counts as true, in a way that few philosophers will be happy with.

Yes, and me.

I'm not sure what the worry is here. I think it's clear that there are some philosophical views that are plainly wrong. There may be some truth in them somewhere, but research over the years has shown that the view is wrong. (Examples: Plato's theory of forms; Hobbes's theory of government.) So who says they're wrong? Well, the people who have done the research mentioned. This is no different from science. There are scientific theories that are wrong, and the people who say so are the scientists who do the work.

If you wanted to say something in favor of this view, you might point to the absence of observed discrepancies between what we all believe and the truth. But, on reflection, this isn't a strong argument because there are observed discrepancies between what is commonly believed now and what was commonly believed at some earlier time. At the earlier time, p was commonly believed. Now not-p is commonly believed. If what's commonly believed were true, then both p and not-p would be true. But p and not-p cannot both be true. Therefore it is not the case that whatever is commonly believed is true.

Now you might say that what you mean is that truth is nothing more that what's commonly believed throughout the ages, the future included. So here is an argument against this revised view. There are lots of propositions about which there is no common belief shared throughout the ages: neither p nor not-p have been commonly believed. Does it follow that neither p nor not-p are true? For example, it has not been commonly believed throughout the ages that the sun is larger than the moon. Nor has it been commonly believed throughout the ages that the sun is not larger than the moon. Would you then want to conclude that neither belief is true: it is not true that the sun is larger than the moon and also not true that the sun is not larger than the moon?

I'm happy to try to clarify: I don't think that philosophers use facts differently from most non-philosophers. Rather, I think that philosophers use the word 'fact' differently from the way most non-philosophers use it. I think that most non-philosophers use it to mean more or less the same as the expressions 'true sentence', or 'true proposition', or 'true belief'. I think that most philosophers use it to mean more or less the same as the word 'situation' or the phrase 'state of affairs', i.e., a bunch of objects having properties or standing in relations. Used in this way, I don't think it makes sense to call a fact "rational" or "irrational", any more than it makes sense to call, say, the number 3 "beautiful" or to call, say, the color red "odd" (in the sense of not evenly divisible by 2).

In this sense, the sentence 'The Earth is round' is true. And the reason that it is true is that there is a fact that corresponds to it, namely, the fact consisting of the object that is the Earth having the property of being round. The sentence might be considered "rational" or "irrational", but the corresponding fact simply "obtains" or "holds".

What might it mean for that sentence to be "rational"? I don't think that there's a standardly accepted definition of "rational" in this sense, but here's one plausible possibility: A sentence is rational if it coheres with other true (or believed) sentences, and it is irrational otherwise. So, given the usually accepted claims of science, the sentence 'The Earth is flat' -- or, better, the belief that the Earth is flat -- might be considered irrational.

The sentence 'We all die' is true. That we all die is a fact. The sentence is not simultaneously a fact. Rather, there is a fact that corresponds to that sentence.

You say that you don't see how a fact can be anything but a sentence. I agree that in the usual non-philosopher's use of the word 'fact', it is usually used in the same way that the word 'sentence' is. But my understanding of the original question and Allen Stairs's original reply was that there was a confusion about how philosophers use the word. If you think that we use it in a strange way, so be it, but there is a distinction to be made between sentences and situations (or whatever you want to call them), and reserving the word 'fact' for the latter is the way some philosophers speak when they're wearing their professional philosopher's hats.

I do agree that the way the world is is one big fact and that the way your room is right now is a smaller fact (which is part of the bigger one). But as I said above, I don't see how such things can be "rational" or "irrational".

How are you using the word "irrational" to apply to situations? Do you mean that the situation doesn't "cohere" with other situations? But what would that mean? A person's actions might be irrational, I suppose. But an action isn't a fact.

I'm not quite sure what dictionary.com's "agreeable to reason" means, but if it means something like what I suggested above, namely, cohering with other true sentences, then it can't apply to facts considered as situations. (By the way, "agreeable to reason" doesn't mean that a reasonable person likes it or finds it "agreeable". A person could like a fact, but that's not what's meant in that definition.)

Boy, we philosophers love to split hairs, don't we? :-)

As it happens, I recently had to update the reading list for the logic paper of the first-year of the Cambridge Philosophy Tripos. One of the topic-headings is "Necessity" (see foot of p. 8 to top of p.10). That's a modest introductory list, concentrating on the notions of logical necessity and analyticity.

Unfortunately, however, this might not be a terribly helpful response, as access to most of the references given will involve you using a university library. Perhaps others will know of useful and reliable free online resources of an introductory kind (and I'd be glad to hear of them to add to the reading list too!).