When we are discussing the physical facts themselves there is general agreement that truth behaves basically classically. For example if it is a fact that X implies Y, and X holds, then Y holds. Moreover, the physical facts are basically complete, in the sense that every physical fact could be checked in principle, by an observer with all the information, against what was really out there to determine if it was or was not true*.
But things are not so simple when we consider truth preservation in the context of language. For one thing language has the ability to talk about the truth of various linguistic statements, and about the rules of truth preservation, within itself. This means that language is “more powerful” than a restricted language which talks about the physical facts alone. A consequence of this is that language is either incomplete or inconsistent. If language was incomplete it would mean that even if you had access to all the basically true things that could be said in language (say every statement that truly reflected the basic physical facts, plus statements that capture the basic semantic/linguistic facts) then there would be some well-formed sentences in that language that could be neither proved nor disproved. On the other hand, if language were inconsistent, it would mean that there would be some well-formed sentences that could both be proved and disproved.
For various reasons, which I won’t elaborate on here, I lean towards the second possibility, that in language there are some statements that can be both proved and disproved. And this means that classical truth preservation rules won’t work as truth preservation rules for language, because under classical truth preservation if you can establish a contradiction, which is to both prove and disprove a statement, then every statement can be proven. Clearly that is unacceptable.
But if the truth preservation rules are non-classical then truth in language won’t match up with truth in the world, that is the truth regarding the basic physical facts mentioned earlier. This is because the physical facts are both complete and consistent, while language is not. A better question to ask is where these mismatches occur. It is possible that language is only incomplete or inconsistent when statements that involve truth or other semantic/linguistic notions are involved, and thus that truth in language when talking about the physical facts by themselves is unaffected.
But I find it more likely that truth in language and truth about the physical facts are generally mismatched, not just because truth is preserved differently in language, but because the concepts expressed in language simply don’t match up to the physical facts perfectly. For example, consider red. We might think that red signified a certain physical fact about which wavelengths of light were reflected off a surface. But that is an incomplete description, because the color perceived can vary depending on the surrounding colors. So really red is a complex physical fact involving an object and a perceiver and the kind of state that the perceiver will be put into when they view the object. But this still isn’t sufficient because we have to distinguish red from the other colors. This distinction does have a basis within the perceiver (there is some fact about the matter that will make them think of one color as red instead of some other color), but the line drawn between one color and other is basically arbitrary. The point of distinction itself does not have a physical basis, and may vary between perceivers and in the same perceiver over time. Thus “red” is only loosely connected to the physical facts. Although it would be wrong to say that red is independent from the physical facts it would also be an error to say that it simply is a short name for some complex collection of them (unless we accept that each person’s red expresses a different set of physical facts, but if this were the case then it would be impossible to communicate accurately about the physical facts using language, which is basically the same problem).
Another way in which truth in language comes apart from truth about physical facts is when dealing with properties and objects. In the physical world the basic components are simple, in the sense that while they have properties they do not have parts (electrons, quarks, ect). Although there are physical facts about larger scale items they are made up of collections of facts about their microscopic components. In contrast an object in the context of language may have parts, and facts about it are not really fact about its fundamental components, as the speaker may be in the dark about what those fundamental components are. For example, consider the property of being red. To say that something is red doesn’t mean that it is entirely red, but that it is at least partially red. But being red is to be not green. And thus something can be both green and not green. Obviously we really mean partially green and partially not green, but again this is the kind of “loose” talk that prevents language from exactly lining up with the physical world.
Now this doesn’t mean that we have no grasp of the truth, or that we can’t get at the truth, or that we can’t deduce truths, or any of those other “postmodern” claims. For starters just because language doesn’t correlate perfectly with truths about the physical facts doesn’t mean that it doesn’t roughly line up with them. In fact we should expect the truth in language to usually reflect physical truth, because if it didn’t then language wouldn’t be very useful. Secondly, we can purposefully restrict our discourse, so that it doesn’t talk about truth or semantic facts, to a language that does obey some kind of classical logic. If we ensure that our premises reflect physical facts in this restricted language then we can be confident that our conclusions will as well.
So if this doesn’t imply that physical truth is unknowable to us what does it imply? One significant conclusion that can be drawn from all this is that even if we have a consistent and coherent linguistic conception of some phenomena there is no guarantee that this phenomena, so characterized, is real (meaning that it may not reflect a “natural” kind of physical facts). And if that is the case then what it means many vary from person to person, and then we are reduced to a matter of convention instead of a matter of fact. Basically this is another way of looking at the conclusion about intuitions I derived a previously. A second consequence is that reasoning through language, and thus natural language philosophy, is simply a bad idea. Just because a chain of inferences can be made in language from a premise to a conclusion doesn’t automatically mean that the conclusion is sound. Of course almost all philosophy is done through such reasoning, even this very discussion, so I clearly don’t mean to throw out all such reasoning. I simply mean that such reasoning isn’t irrefutable, assuming that someone can provide a better analysis of the claims made, which reveals in turn that the original conclusion in fact rested on some ambiguity or equivocation.
* Admittedly indeterminacy adds some complications to this, but not serious ones. One can either accept a three state logic or drop the law of the excluded middle and replace it with one that says ∀φ(φ ∨ ~φ ∨ ∂φ), where ∂φ is understood to mean that φ is indeterminate.