Did Paul say shit?

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In Philippians 3:8, Paul compares his past successes to σκύβαλα (skubala). This is usually translated as rubbish, but some translations prefer "dung".

There's arguments that this could even be closer to "crap". So how objectionable is the word Paul uses?

The short answer is that this word is the same word that a scholar would use. Skubala isn't used in rude contexts in the body of Greek literature we know today. "Rubbish" is the best translation.

It is sometimes used for feces, but in medical texts. It's used by geographers, philosophers, and historians. The answer here is no.