Author Topic: Semantics of negation  (Read 4458 times)

Offline Daniel

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Semantics of negation
« on: December 18, 2013, 04:45:06 PM »
I've been thinking (rather abstractly) about how semantic notions like modification and quantification work, and I feel that I have a fairly strong understanding of the basics. Modification involves assigning a property to an object (think of it visually if you want: painting an object with a property), while quantification involves talking about a set and distributing descriptions across that set.

But then perhaps the hardest meaning to conceptualize is "negation". Let's just (for simplicity) focus on the general case of "It-is-not-the-case-that" as an operator (the ~ or ¬ symbol) as in the English sentence "John is not happy." => ¬[John is happy].

Intuitively it seems simple enough, but then most paraphrases end up being circular. In the end I feel completely lost with this. It seems like, perhaps by definition, the absence of meaning, yet it clearly contributes to truth conditions.

The closest I can come to any intuitively sensible meaning is by thinking of negation as a type of modality. Modals act as quantifiers across sets of possible worlds ("must" = in all worlds, or at least those of a certain type like those in which everyone follows the rules; and "can" = in some of those worlds, at least one)-- these then look a lot like the basic quantifier logic that deals with sets and generally makes intuitive sense once you wrap your head around it. And there are also time adverbials that seem quantificational: "always" and "sometimes". But is "not" also a modal or quantifier?

Perhaps: we do have quantifiers like "no [books]" and time adverbials like "never". But those are counterparts to positive expressions. In the case of negation, it doesn't see to have an overt positive polarity counterpart. (Actually, I think this might be a really rare but attested typological variant, where negation is default, unmarked structurally and positive-polarity [positivization? indication? declaration?].) So... does that work? Is "not" a modal/quantifier?

In terms of processing, that's where this seems so odd. If I tell you "John is happy" or "There's a house. It's green", you can build up representations intuitively (formal representations aside) without any trouble. But if I add in negation, it feels like I'm not actually adding any meaning at all. It's as if I'm just telling you to make a footnote for yourself to remember that something isn't the case. "John isn't happy" doesn't give you any information about the world, except that whatever else is going on, the one thing that isn't true is that John is happy. But that's not really informative, at least not intuitively. I could also tell you many, infinitely many things that aren't true and would have no impact on your representation of the world! Certainly in a particular pragmatic context I might want to know that something isn't true, but that only works intuitively in the sense of imagining a different world in which it would be true then being happy that that world isn't the real world.

So in the end, this seems like a great argument in favor of possible world semantics: negation contributes just as much as positive-polarity information, because it reduces the number of possible worlds. (On the other hand, one might argue that it typically reduces the number much less significantly-- "John has a hat" is very specific and I'd think signals a much smaller set of worlds than compared to "John doesn't have a hat".) And while possible world semantics is useful as a formal model, it doesn't strike me as intuitive (or processing-friedly) at all.

So... what is the meaning of negation?

Just wondering if you have any thoughts or if you know of any literature that addresses this abstract, strange, and confusing point.
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Offline isauk

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Re: Semantics of negation
« Reply #1 on: June 12, 2014, 11:09:51 AM »
i think the problem you're running into has to do with the fact that you're treating languages like it's a representation of situations in reality. and so, a sentence like "john is wearing a hat" could almost be summed up with a drawing of a guy with a hat on his head (and maybe some sort of arrow or something to show the relation between john and the hat, which is that he's the wear-er and the hat is the wear-ee). it seems like such a drawing would make sense because it's got all of the different components, "john", "hat", and "wearing", and it ties them together into a single idea of "john wearing a hat". by contrast, how on earth would you draw a picture of "john /isn't/ wearing a hat"? simply having a hat-less man wouldn't fly, and while it's almost conceivable that you could capture the meaning "isn't wearing" with an arrow that's been X-ed out or something, you'd still have to have a drawing of the hat that he isn't wearing (but then, if would have to be an abstract hat that doesn't even really exist). and so, i can see what you mean.

really though, i (personally) don't see language as a representation of the situations around us. rather, i see /thought/ as a representation of those situations, and then language as a representation of though. -- it might sound like a pedantic distinction, but i think it's really necessary if you want to avoid running into problems like these. i think that the typical way that linguists go about thinking about this stuff is by drawing a sharp line between semantics and pragmatics, and then saying that some aspects of language have a semantic function (which is to say, they attempt to describe real life) and that other aspects have a pragmatic function (which is to say that they try to capture all of the little extra thoughts that speakers inject a sentence regarding information tracking and personal perspective etc). personally, i'm just kinda against this whole analysis (though, if you happen to be into it, then feel free to make an argument as to why it makes good sense), and prefer instead the "reality --> thought --> language" analysis that i described above. (but, maybe then you could say that "not" functions kinda like how other pragmatically oriented words, like "the", do.)

anyhow, if we think of language as only being a representation of thought, then we shouldn't be trying to think in terms of drawing pictures (which,,, maybe no one else beside me ever thought anyway). if a word like "hat" seems like it could code for an actual hat, then that's really only incidental. (really though, how could it? the word "hat" is totally abstract. it has no size or color or anything. but there are no abstract color-free hats in real life.) the word "not" then is just a way to indicate negation (like the examples you showed using logic symbols), and in some cases it actually works backwards from how we might expect (for example, a sentence like "i doubt he's coming" is technically not a negated sentence in any way, but it ends up having the same meaning as a sentence like "i think he's not coming", which /is/ negated). and i'd say that that's really no different from the sort of thing that other logical operators (such as "or") do. and in fact, that's another good one. how would you draw a picture of a sentence containing the word "or"?

really though, i think there might be a whole bunch of examples that have the sorts of problem that "not" does. for example, it would probably be difficult enough to draw a picture of "if that mug falls, it will shatter", but then, what about "if that mug had fallen, it would have shattered"? what's more,, even if you could figure out a way to draw those two sentences, how on earth would you distinguish them? ------ but if these sentences are representations of thoughts, instead of real life, then our only job would be to draw the /thoughts/. now,,, i wouldn't know how to go about doing that, and i'm not quite sure what the "components" of a thought are (although, then again, i'm not really sure what the "components" of real life are either), but i think it's reasonable to assume that the though "he isn't wearing a hat" is every bit as substantial as the thought "he is wearing a hat" (whereas, the event of "him not wearing a hat" is not nearly as real as the event of "him wearing a hat"). --- another question to ponder over is how thoughts relate to real life, but that of course then would be outside of linguistics and i don't know that there's really anyone who has any good ideas on the subject.