It was a central goal of Logical Positivism to discover a criterion for meaningfulness. None was ever formulated that satisfied anyone for very long. There are a couple more specific things to be said here. First, it would not follow that "All faces are beautiful" is meaningless even if, as you claim, "beautiful" was meaningful only if "something can be 'ugly'". For one thing, there may well be other things---feces, perhaps---that are not beautiful, and, as you state your claim, it isn't even required that something else should actually be ugly, only that something can be ugly. So it wouldn't even follow from that claim that "Everything is beautiful" is not meaningful, only that "Everything must be beautiful" was. But I don't myself see why the meaningfulness of a word depends upon its applying only to some things and not to all things. On my view, though not on everyone's view, "exists" is a word that applies to everything. You might say that unicorns do not exist, so that the word "exist...

One further point. Toward the end, you write: These seem to be grave problems for theapplicability and effectiveness of FOPL to natural language arguments.(I am not referring to the “limits” of FOPL where extensions such asmodal, tense, or second-order logic might accommodate the richer partsof natural language, but rather to the apparent inability of anylogic(s) dealing with these problems.) Waiving the issue about vagueness, there isn't any problem dealing with such quantifiers in a second-order context. Both of the quantifiers I mentioned, "Most" and "Eq", can be defined in second-order logic, so the caveat at the end kind of gives the game away. That said, what perhaps is puzzling about these quantifiers is that, as is the case with second-order quantifiers, there is, as I said, no sound and complete set of rules for them, with respect to the intended semantics. In that sense, there is no "formal" logic for these quantifiers. But, again, that is not to say that one cannot write down some...

There are a lot of different questions here, and we need to disentangle some of them. First, some of the questions you are raising about "most", "few", and the like have nothing to do with their vagueness. Consider, for example, a quantifier I'll write "(Most x)(Fx;Gx)". This is what is called a binary quantifier (similar to your "restricted" quantifiers): Unlike the usual way of representing "all" and "some", it forms a formula from two open sentences. Now, define the quantifier, semantically, so that "(Most x)(Fx; Gx)" is true if, and only if, there are more Fs that are G than there are Fs that are non-G. (More generally, we'd have to talk about satisfaction, but waive this complication.) It can be proven that this quantifier cannot be expressed by any formula of FOPL. It can also be shown that there is no sound and complete axiomatization of the logic of this quantifier. That isn't to say you can't write down some sound rules. But you can't write down a complete set of rules: No matter...

Many philosophers and psychologists find this argument compelling. I, for example, am a philosopher who finds the argument compelling. (See also Jerry Fodor, The Language of Thought , for an extensive discussion of this kind of consideration.) But not everyone finds the argument compelling, and even those of us who do need to be careful here. The most we can really conclude is that some kind of cognitive activity is present in pre-linguistic creatures. Someone might think that there are important differences between the kind of cognitive activity present pre- and post-linguistically, and one might think that the reason has very much to do with the acquisition of language. One view I have heard expressed, for example, is that language plays an important role by providing a common form of representation that allows otherwise isolated cognitive systems to "talk" to one another. Whether that is so is, presumably, an empirical question. There are some interesting experiments that point in this...

There's an old arugment called the "Cosmological Argument". (I guess it's actually many related arguments.) Roughly: Something had to cause all this stuff; that's God. There are two kinds of objections to this argument. One is that there's just no good argument that something had to cause all this stuff. In this context: How does one know that anything caused the Big Bang? Why can't it just have been uncaused? It's important not to answer: Well, everything has to have a cause. If so, then presumably God has to have a cause, too. The other objection is that, even if there were, the "God" whose existence the argument would prove need not be much like the God of religion. And, indeed, in this case, too, that is pretty clear. Hume pushes both forms of argument in Dialogues Concerning Natural Religion , if I remember correctly.

Yes, philosophers have worried about this kind of question. One place it surfaces is in a debate over whether the notion of a "communal language" needs to play some important theoretical role. Michael Dummett, for example, has argued that unless we all regarded ourselves as speaking a single language, and unless our so regarding ourselves imposed normative constraints on how we used our language, then we could never be sure what other people were saying and so that our beliefs that we understand one another would always have ultimately to rest upon some kind of faith. Others, perhaps most famously, Noam Chomsky, have disagreed. Have a look at the entry on Idiolects in the Stanford Encyclopedia. (Our fearless leader Alexander George has a couple very nice papers on this topic, by the way.)

I think many people have this kind of experience. Perhaps art, at least in certain of its forms, is a response to it. Which is to say: Maybe you should try writing a poem, composing a symphony, or creating a sculpture.

These new coffee beans I just got make very nice coffee. I could try to describe the difference in the taste, but I'm not much of a coffee expert. I'm sure there are people who could do a better job than I could, but, frankly, I don't find the descriptions I read on the bins all that helpful. I mean, I can see why someone would say that this particular roast had a hint of cinnamon, but that hardly captures it. Is there a thought here that cannot be put into words? That's quite unclear, but there does seem to be something here that it is difficult, maybe even impossible, to put into words, except, as John McDowell suggested, by saying simply: that taste. But that's not exactly what one had in mind. Suppose I've tried a lot of coffees, and I find that many of them seem similar to me in a certain hard to describe way. Coffees A, B, and C seem similar to one another in this respect; coffees D and E are similar in that respect, but not to A, B, and C; and coffee F is unique in that respect....

A picture is worth a thousand words, to be sure, and so language is, in a sense, a poor instrument as compared to perception. But perception isn't always what is needed. The very fact that perception makes such fine distinctions of, say, color is what makes it so ill-suited for expressing similarities . Indeed, seeing and expressing similarities is, one might say, precisely a way of being less exact, but certainly for a purpose. I may, for example, want a red pen. I don't care which shade of red it is, so long as it is red. If I had to show you the color of the pen I wanted, I'd have a problem.

I would be surprised if examples like Chomsky's didn't exist in all human languages. The example rests simply upon the fact that "flies" can be either a noun or a verb and "like" can be either a verb or a, uh, what is it in that construction? a preposition? Both sentences Chomsky cites are therefore, in principle, ambiguous, although one reading in each case is so odd that it is often pragmatically unavailable. That is to say, these examples are essentially just examples of so-called structural ambiguity, that is, of ambiguities that arise because of different possible analyses of the logical structure of a sentence rather than because of different meanings a single word can have. Carroll's examples seem quite different. It's not that there is some ambiguity in "I eat what I see". (At least, if there is, it's not relevant to this example.) What that means is: Anything I see, I eat. Similarly, "I see what I eat" means: Anything I eat, I see. These need not both be true. It does not, however,...

I'm no expert on Helen Keller, but I don't think this comment has the kinds of consequences mentioned here, and I'm not sure it should be trusted. Many human beings have the experience of thinking in language. Keller, obviously, wouldn't have had that ability before discovering language, and it may well be that her ability to use language greatly changed her experience of thinking. It may also, and probably did, greatly expand the range of thoughts of which she was capable. One can therefore understand what she might have meant by the remark reported. But it's also clear from what little reading I've just done about Keller that, by her own account, she was, before she acquired language, capable of communicating, in primitive ways, with members of her family, and her biographer, Dorothy Herrmann, speaks of her "frustration" at being unable to communicate better. So it does not seem likely that she was utterly incapable of thought.