scalar adjectives with arguments
Here's a cartoon with a grammaticality judgment as the punchline:
Funny thing is, I concur: 'half empty' can't take an internal argument, although 'empty' certainly can ('empty of meaning', e.g.). 'Half empty' is also clearly fine. 'Half full' is of course fine, and 'half full' can of course take a internal argument. Here's some Google searches which bear out this judgment:
Ghit ratio: 'full':'empty'
1,980,000,000: 133,000,000 (approx 15:1)
Ghit ratio: 'half full':'half empty'
2,070,000: 1,810,000 (approx 1:1)
Ghit ratio: 'half full of':'half empty of"
247,000: 1660 (approx 149:1)
Indeed, about a third of those 'half empty of' cases seem to be typos for 'half empty or half full'; the Ghit return for "half empty of" -"half empty of half full" is only 1080, so the real ratio is more like 247:1. (Note that if you weed out the "half full of water" cases, to avoid that one expression about the glass being half empty or half full of water, you still have 188,000 hits for "half full of", so the ratio's still about 188:1.
Anyway, I don't need Google to tell me that 'half empty of X' is way worse than 'half full of X', but that the difference between 'empty of X' and 'full of X', although sensable, isn't of the same grade at all.
Update: Mark Lieberman at Language Log has pursued this problem considerably farther, in the context of comparing search results between engines and reliable linguistic corpora, and has lots of interesting remarks to make and examples to exhibit. Among other things, he looked even closer at the sixteen hundred or so results for 'half empty of' and finds that not only are those typos mentioned above inflating the numbers, so are hits for strings that match superficially but have significantly different structures, such as "Only the most 'glass half empty' of HR professionals would...". Nonetheless, a few examples of 'half empty' with an internal argument that seem to be both naturally produced and easily interpretable did turn up. I don't myself find them particularly grammatical, despite their clarity, though the tide of opinion (3 votes for to mine against) seems to be against me here.
I should also note that the GoogleFight ratios that I reported above are slightly different than the results you would get if you just typed the strings straight into Google; mostly the Ghit results are a little higher. I don't know why that is, unless GoogleFight is plugged into an older/newer version of Google that is not obvious from their main website.