You know no non-sentences don't imply the lack of many real nothings of the same silences.

...my head hurts.

All words that mean a direction on a spectrum (or a discrete binary choice) imply that the opposite direction or binary exists. But when you string together a phrase with lots of these binary choices, that only implies that any one word can be replaced by its opposite and still describe something that exists, not necessarily that all of the words can be flipped towards their opposite.

So logically:

1. Calling a dog big implies that there are smaller dogs.
2. Calling a dog mean implies that there are nicer dogs.

So a "big, mean dog" implies that there are small mean dogs and big nice dogs in existence, but does not necessarily imply that there are small nice dogs.

Or, let's say another example. Imagine a group of three siblings: a tall sister, a short sister, and a tall brother. If I say "hmm let's call the tall sister over," I did need to use both words "tall" and "sister," because each word eliminates one of the choices, but that does not imply that there is a short brother in the mix.