Monday, January 31, 2011

Philosophers' Carnivals: Now & Next

Philosophers' Carnivals "showcase the best philosophical posts from a wide range of weblogs," as it says on the carnival's homepage. From today, carnival #120 is at nicomachus.net. And carnival #121 will be here in 3 weeks time, so if you find yourself reading something nicely philosophical, posted between now and then, please consider submitting it, via the online submission form, even if you wrote it yourself: "Don't be shy, we want to hear from you, that's the whole point of this project! Your post doesn't need to be anything earth-shattering - it just needs to be something that other philosophically-minded people might enjoy reading."
......As for what you can submit, there are No Rules, except: "No self-help, mysticism, marketing spam, etc." Of course, marketing spammers are unlikely to have bothered reading as far as this, so telling them not to bother submitting seems pointless. And I wouldn't rule out what some academic philosophers like to call 'mysticism', e.g. Mathematical Platonism, Substance Dualism, Open Theism and so forth (since such is just realistic metaphysics). Nor shall I reject whatever formalized craziness such academics work on instead, of course (since I should be unbiased in my hosting). Indeed, since the number of the carnival will be 121 (which sounds like "one-to-one") there's even some hope for self-helpers (and Continental Philosophers) whose positive thinking has carried them thus far, because insofar as their posts describe how the ideal of the Socratic Dialogue relates to their brand of self-help (or Derrida) I shall look upon them kindly.
......Here's a cautionary tale about rule-following: Many years ago, a port on the east coast was industrializing. To its north and south were two large estates, the country houses of two progressive squires, who built factories and docks in the port, and cheap housing for their workers there. Peasants to the west of the port flocked there, to earn more and to be free from their old-fashioned and relatively oppressive squire. As his peasants deserted his lands, that squire soon found himself with cashflow problems, and eventually he was reduced to opening his mansion to the public. He even built an inhumane zoo in its overgrown grounds; but things got no better. He got more and more depressed. One day he became quite deranged, and smashed up his zoo. Then he climbed onto the back of a huge hippopotamus and rode it towards the port. Now, the two rich squires heard of him crashing through their workers' slums, but they were unable to stop him because he had the law on his side, the law which states that the squire on the hippopotamus is evil to the slums of the squires on the other two sides.

Tuesday, January 25, 2011

Liars, Divine Liars, and Semantics revisited

Divine Liar arguments aim to show that there’s no omniscient being—that no one knows all that’s true—in the following way. Suppose I say “No omniscient being knows that what I’m now saying is true.” If (as I believe) no one is omniscient, then no omniscient being exists, to know anything. So in that case, what I said was true. What I said was therefore an assertion, whether it was true or not. And if it wasn’t true—if it’s not the case that no omniscient being knows that what I said was true—then some omniscient being knows that what I said was true, despite it not being true, which is impossible (knowledge being of truths). So I asserted a truth; and so either that was a truth that some omniscient being doesn’t know, which is also impossible, or else there’s no such being.
 ......However, resolutions of the Liar Paradox might show that such arguments are invalid, e.g. according to Daniel J. Hill (2007: ‘The Divine Liar Resurfaces’, The Reasoner 1(5), 11–12) and my earlier article (2008: ‘Liars, Divine Liars and Semantics’, The Reasoner 2(12), 4–5). So, suppose I say “What I’m now saying isn’t true.” If what I said was true then, as I said, what I said wasn’t true. Does it follow that what I said wasn’t true? The paradox is that if so, then since that’s what I seem to have said, I seem to have said something true. The resolution defended earlier by me (2008) takes my utterance to have been meaningless, so that I didn’t really say anything. But we may then wonder how it was that it seemed so clear what my utterance would have meant had it been true; and my Divine Liar utterance was even more obviously meaningful. Another popular resolution would regard my Liar utterance as equivocal, with the word ‘true’ naming many different predicates in Hill’s (2007) Tarskian hierarchy. But formal languages can only be defined via natural language; and my informal Divine Liar utterance wasn’t obviously that equivocal.
 ......Questions of truth are essentially questions of how well our words are describing the world. So insofar as my Liar utterance wasn’t meaningless, it was asserting that it wasn’t describing itself very well, not well enough for it to have been true. And since it was nothing if not self-contradictory, it certainly wasn’t describing itself very well. But therefore, in view of what it was asserting, it seems to have been describing itself quite well after all. Was it describing itself well enough for it to count as true? I’m reluctant to call it ‘true’ as follows. If it was true because it wasn’t, then it was true and not true, but surely something’s only not some way if it’s not the case that it is. Nor do I want to say that it was neither true nor not true, as that’s just to say that it was not true and also true. Nevertheless, my utterance wasn’t describing itself very well, and was therefore describing itself quite well; so perhaps it was only partially true. If so then calling it either ‘true’ or ‘not true’ would both be inaccurate, would both be only partially true.
 ......We naturally focus upon whatever truth we can find in what people say, or upon an obvious untruth. And things are usually described accurately enough for some obvious purpose, or not accurately enough. But would it be unrealistic to think of truth (descriptive accuracy) as a matter of degree? The classic example is that of Vann McGee (1991: Truth, Vagueness, and Paradox, Hackett, 217): If “Harry is bald” is true insofar as Harry is bald, ‘true’ should be at least as vague as ‘bald’. And quite generally, why should we believe that our words are much better defined than our purposes have required them to be? Maybe natural language has a ubiquitous—since usually unobtrusive—vagueness. (That would explain why the discovery of a contradiction so naturally triggers an attempt to clarify our terminology.) And in particular, the Liar Paradox might be revealing this ordinarily obscure vagueness of ‘true’. That’s because if my Liar utterance was only partially true, then it would follow from what I said only that it was also partially not true, which clearly coheres with it being only partially true. There’s no inconsistency—no more paradox—and it seems that much the same could be said of any Liar sentences.
 ......And if that is how the Liar Paradox should be resolved, then my Divine Liar utterance would have been only partially true if there is an omniscient being. My Divine Liar argument was therefore fallacious, because arguments should have premises that are unequivocally true enough to count as true under all relevant hypotheses. But if you asked an omniscient being whether my Divine Liar utterance was true, she might say that it contained an element of truth. That might be a more informative—more true and less misleading—answer than a simple ‘yes’ or ‘no’.
 ......Similarly, the best answer to the question “Is this colour blue or not?” could be to say that it’s vaguely bluish. Ordinary objects are almost always either blue or not, but colours don’t really divide into those that are blue and those that aren’t. On the two sides of any such line, between the blue and the other colours of some spectrum, would be colours that were indistinguishable. So there’s no such division; and so there’s some colour of which, rather than saying that it’s blue, or that it isn’t, we ought to say that it’s bluish. Note that such a colour might look blue against a background of colours that weren’t blue, or even if you just wondered whether it belonged to that class of colours, and so postulated it amongst them (cf. what we find paradoxical about the Liar Paradox).
 ......Incidentally, some formal work on ‘true’ as a vague predicate is well described as Fuzzy Logic.

Saturday, January 01, 2011

Liars Are Fairly True

Suppose I say “what I’m saying isn’t true.” If what I said was true, then as I said, what I said wasn’t true. Does it follow that my words weren’t true? The famous paradox is that if so, then since that’s what I seem to have said, I seem to have said something true. A fairly popular resolution takes my words to have been meaningless, so that I didn’t say anything. But if my words had been meaningless, you could hardly have known what they would have meant had they been true. Is our ordinary conception of truth shown by such Liar-style sentences to be deficient? Let’s see why not.
......To begin with, such sentences are in some ways like Truth-teller-style sentences. If I said “what I’m saying is true,” for example, what would I be saying? Not much. Questions of truth are essentially questions of how well our words describe the world, and “this is a good description” isn’t much of a description. Still, it might not be too bad a self-description, precisely because there isn’t much to describe. If someone saying “what I’m saying is true” intended to be speaking the truth, should we deny that she was telling the truth? It may be hard to say, but therefore it might be that such sentences are not so much vacuous as vague. Since “what I’m saying isn’t true” also addresses nothing but its own descriptive power, might it also be, in its own way, rather vague? Consider the following analogy.
......If I said of some colour, “I wouldn’t say that it’s blue,” I might not be saying that it wasn’t blue, because colours don’t divide into those that are blue and those that aren’t. To see that, consider a spectrum: On the two sides of any such line, between the blue and the other colours, there would be colours that were indistinguishable. So there’s no such division; so there’s some colour of which, rather than saying it was blue, or that it wasn’t, I’d prefer to say, more precisely, that it was bluish but not very blue. (Since the perception of colour is subjective, you might say it was blue, or that it wasn’t.) Our perception of colour is also context-sensitive, e.g. it’s affected by surrounding colours, and by our preconceptions. So if I wondered if our colour really was blue, I might thereby see it as not blue, while if I then wondered if it was therefore not blue, it might seem pretty blue (even to me).
......And similarly, it’s when “what I’m saying isn’t true” has been thought of as definitely not true that it seems most clearly to be true. More precisely, while those words aren’t giving us a very good description of their own meaning—they’re self-contradictory—we therefore have a description that isn’t too bad, insofar as it’s saying that it’s not a very good description. In short, they’re rather nonsensical (and false), but therefore fairly true (and false). And that’s basically how Liar-style sentences are compatible with our ordinary conception of truth. We need a bit more clarification, but it should soon become clear that while we can always be more precise, there’s no threat to truth here.
......What is truth, if not a sufficiently accurate description? Usually we describe things accurately enough for some obvious purpose, or else we don’t, so we tend to assume that truth is black-or-white. But it’s really a matter of degree, in a context-sensitive way. E.g. the table at which I’m writing this is flat enough for that purpose, so “this table is flat” is true enough, but might be false were I writing about geometry. And in general, our words tend not to be much better defined than our purposes have required them to be. So natural language has a ubiquitous—since ordinarily unobtrusive—vagueness (whence the way to resolve paradoxes, and uncover other fallacies, usually involves clarifying some terms). Of course, the words of “what I’m saying isn’t true” have clear enough meanings, so there’s no simple equivocation to discover. But it should help us to resolve the paradox if we don’t demand anything too unrealistic. (Similarly, we shouldn’t demand that colours be either blue or else not blue.)
......Liar-style sentences present themselves as misrepresenting themselves, so their meaning is self-undermining. And they can be read (or heard) in two basic ways—each a necessary part of the other’s context—because their meaning self-undermines in a loopy sort of way. Insofar as Liar-style sentences are true they’re also false, and they need concern nothing but their own truth, so they can certainly be read as nonsensical. But they’re not just senseless, and hence not at all true, because insofar as they’re not true they’re easily read as true. So they also have that sense. But they can’t be nothing but partly true and hence partly false, because that would leave nothing for them to be true or false about.
......This resolution—that Liar-style sentences are fairly true, in that loopy way (they’re fairly true because they’re rather nonsensical, and they’re rather nonsensical because insofar as they’re true they’re also false)—is a strengthened version of the resolution that takes them to be nonsensical. So for those who believe that an omniscient being is logically possible, it allows a similar reply to Divine-Liar-style sentences. E.g. the problem with “no omniscient being knows this” is that it can’t be true if there’s an omniscient being, but if it isn’t true then, since no one could then know it, it would seem to be true. My new reply is that if it’s only fairly true (in this loopy way) then no epistemically perfect being would have to know it, except to know it for what it is. And note that “no omniscient being knows any of this” is simply false, e.g. such a being would know those words. (Similarly, “what I’m saying isn’t at all true” is fairly false.)