Is the glass half full?

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Imagine you pour some water onto an empty glass but stop middle way before filling it. Would it be accurate to say that the glass is now “half full”? Common sense and our linguistic intuitions might immediately suggest that yes, it is. But Keefe’s talk yesterday made me think of an argument against this common sense intuition. One can say that it is nonsense to say that the glass is “half full” because the glass is clearly, totally and determinately not full. The glass is not full and this is not something that is half true, or indeterminate or whatever. It is true, period. Thus, it is inappropriate to say that the glass is half full because being full is something that glasses either are or are not and since you did not finish filling the glass, the glass is just not full. It does not matter how close you were to filling the glass, you still failed filling the glass and, therefore, the glass is not full. It is not empty either, of course, but being empty is not the same as being not full. Therefore, it does not make sense to say that the glass is half full.



Bart CC BY-NC 2.0 2011

Yes, there is such a thing of how much water is in the glass (at a given time) and such a thing as how much water fits in the glass. And, yes, we can calculate the ratio between one and the other and we can say that the ratio of water contained to water capacity is of .5 and say that this is what we mean when we say that the glass is half full. And at some descriptive level, saying that would be right. That is how we use the expression “half full”. But the question was whether this use is accurate. And we may want to argue that is this .5 value which makes it accurate to say that the glass is half full instead of say, one quarter full. But, unfortunately, that ratio is not what “full” means. Thus, even if it is true that the ration is .5, that does not mean that the glass is half full. Basically, because fullness is a property, not a quantity. 

The predicate 'being full' refers not to a quantity but to a property because, in order to talk about quantities, you always need to say how much. In other, a little mor technical words, quantities need to be determined in order to be applicable. For example, length is a quantity because in order to talk about the length of something you have to say how long it is. Nothing of the sort is required to say that a glass is full, i.e. there is no ned to say how full it is. It is either just plain full or it is not. Therefore, whatever quantity it is whose value is one half in a half empty glass, it is not its being full. Because it is not full at all.

Notice that the phenomenon is quite widespread in language: you can be half dead without being dead, or three feet tall without being tall. five year old kids are not actually old, just like an assignment that is half done is not done at all. Linguists have known of this for ages and they have devised a standard answer to this apparent paradox (but aren't all paradoxes just apparent? I digress). The basic idea is that, against all appearances, all of these predicates actually denote quantities. The reference of the predicate "full" in English is just the aforementioned ratio between how much water is in the glass and how much water fits in it. This allows for a compositional explanation of why it is accurate to say that the glass in our examples is half full. 

However, something else is required to explain why the glass is also just not full. For this, it is usually postulated a silent determiner. In other words, yes, when we use "full" and similar predicates, we always need to say how full. However, this can be donde implicitly. Thus, when we say that something is plain full, without explicitly saying how full it is, we are implicitly saying that it is completely full. 



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