I wonder what Hyman R's son would think about the matter. In fact, one would rather expect 'shed light' to mean 'to get rid of light'. I'm sure confusion (or mere sloshiness) among these is due to the fact that 'cast' in the sense of 'cast doubt' is rare in modern English, and 'shed' as in 'shed light' is essentially nonexistent.

Filed by Mark Liberman under Words words words.

Perhaps some day, your word processor's collocation engine will have a user-settable collocational bizarreness knob, running from 'conventional' through 'unremarkable' to 'odd' and on up to 'WTF?'… But that's an aesthetic judgment – the problem in such cases is usually not that the writer knows what the common collocation is, and decides to blaze a new trail. Of course, people who favor jarring prose may wish to point the advice in the opposite direction. This is also a good example of the kind of writing advice that modern statistical NLP could in principle provide. This raises the usual question about collocational association: Are these collocational differences random and unpredictable facts about lexical attraction and repulsion? Or do they follow in some way from the meanings of shed and doubt and cast and light?

'casting doubts' or 'sheds light' would be counted.) (The square brackets mean that I inquired about sequences of lemmas, so that e.g. Judging from the frequencies in COCA, 'shed doubt' is indeed the most improbable cell in the table of pairwise associations:

Correcting a student's paper I came across: 'This behavior seems to shed doubt on treatments which always regard V2 as head.' 'Shed light', 'cast doubt (on)', OK, but 'shed doubt (on)' doesn't quite compute for me.

Cast shadow of doubt