Half as Small? Or Half as Large?

Dan Freiberger in Jacksonville, Florida, writes:

You answered a question about phrases such as “twice as small” and called them mathematically illiterate. (February 21, 2016) In your reply, you commented that a person who says, “twice as small” likely means “half as small.” Half as small? Shouldn’t that be “half as large”?

Marilyn responds:

No, when one uses the term “small,” one indicates that the item (or whatever) is relatively small. Substituting the adjective “large” removes that information and even introduces its opposite: the element of largeness.