1.
various theories; multiple accounts; different opinions
A collection of different theories, opinions, or explanations about a topic. Often used to indicate that the truth is uncertain or debated.
Very frequently appears in the set phrase 諸説あり or 諸説ある (there are various theories), used as a disclaimer when presenting information that is not definitively established. 諸説紛々 means "opinions/theories are in wild disagreement." The prefix 諸 means "various/many" and appears in other compounds like 諸国 (various countries) and 諸問題 (various problems).