One of the things usually taken to be distinctive of mathematical and logical truth is that such truths are in some very strong sense necessary , i.e., they could not have been false. Assuming that it is in fact true that 2 + 2 = 4, how could that have failed to be true? (Or, to take a logical example: How could it fail to be true that, if Goldbach's conjecture is true and the twin prime conjuecture is also true, then Goldbach's conjecture is true?) Presumably, the answer to this question depends upon what, precisely, one thinks "2 + 2 = 4" means, but it is hard to see how one could accept the statement that 2 + 2 = 4 as both meaningful and true and think that it might not have been true. It's important to be clear that this statement does not say anything about how actual objects behave, e.g., that if you put two oranges on a table with two apples and no other pieces of fruit, then you'll have four pieces of fruit. Weird things might happen in some worlds, but that would not make it false in...

Yes, there's quite a good deal of work on this kind of thing. It tends to go under the name "fuzzy logic" or "degree theoretic logic". The Stanford Encyclopedia entry is a good place to start. There's a fairly recent paper by Brian Weatherson called "True, Truer, Truest", if I remember right, that does some work on the philosophical foundations, which have always been a bit unclear.

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.

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...

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...

Truth is a property that some propositions have and some do not. Itcan be hard to tell which a proposition is. But this much we can say.The proposition that Wittgenstein was Jewish is true if, and only if,Wittgenstein was Jewish. The proposition that Frege was Catholic istrue if, and only if, Frege was Catholic. And so forth. Somephilosophers (Paul Horwich, Scott Soames) think that's about all thereis to be said about truth. I'd disagree, but I hope we can all agreethat, even if that's not all there is to be said, it is something that there is to be said. (Note that there is some kind of sense herealready in which what is true depends upon how things are. For example,whether the proposition that Russell was German is true depends upon,well, whether Russell was German, and that's a question of how things are "out there".) So, that said, how can we know that truth is not an illusion?The obvious way to interpret the question is: How can we know, e.g.,that it isn't an illusion that it is true...

The most familiar challenge to relativism is straightforward and, to my mind, has never been adequately answered. It is that the truth of "Truth is relative" had better not be relative. But we can spell the argument out a little more. Question: Relative to what? Now, whatever you tell me, I will introduce an explicit statement of the alleged condition. So, if it's "relative to cultural standards", I'll ask you to consider something like: Lying is impermissible, according to the predominant standards of culture X. I can't even make sense of the claim that that is true only relative to cultural standards. It's like trying to make sense of "It's warm in Texas in Oklahoma". (Afficionados will note the similarity of this argument to Quine's criticism of conventionalism. That's non-accidental.) Note that no such argument could show that truth was not in some interesting sense relative in some particular area. The foregoing does not show, for example, that moral claims are not true only relative...