Is there any synchronic difference between homonymy and polysemy?
As a literate English speaker, I can usually tell when words that are pronounced identically have different etymologies thanks to our wretched but etymologically informative spelling system. I know that "here" and "hear" come from different roots, for example, just as I know that "run" as in "I want to run away" and "run" as in "Dad runs the company now" come from the same root.
But, as most of us know, children acquiring language don't have access to etymological information. So, spelling aside, is there any synchronic difference between homonymy and polysemy?
One possible answer is that morphologically different words are synchronic homonyms rather than polysemous words. Consider "lie" (repose horizontally) and "lie" (use language to deceive). A naive person like me could argue that the two "lies" are synchronic homonyms and not one polysemous word because they inflect differently in past tense (lied, lay).
But couldn't critic counter that "lie" meaning "present tense of lie.deceive" and "lie" meaning "present tense of lie.repose" are still examples of polysemy?
What am I missing?