I’ve always wondered why “paradigm” is pronounced pa-ra-dime, but “paradigmatic” is pronounced pa-ra-dig-ma-tic. Why does that silent ‹g› suddenly become noisy?
This answer, from the user tchrist on the English Stack Exchange, explains it incredibly clearly.
In short: the ‹g› is there because it’s there in the Greek original. We can’t pronounce it because English phonotactics forbid the pronunciation of a /g/ followed by a nasal at the end of a word (hence “align”, “consign”, “foreign”, “phlegm”, etc.). But keeping the ‹g›, rather than spelling it “paradim” or “paradime”, is helpful:
“We tend to keep the written ‹g› in English words like this, even though we ‘can’t’ say it there at the end of the word right before that final nasal. This helps us understand the shared relationship with longer words like paradigmatic that have a vowel after the nasal, which allows the /g/ to ‘reappear’. But we probably no more ever said it in paradigm(e) than we ever said it in phlegm. Our phonotactic rules forbid it.”