I finished For Auld Lang Syne a long time ago, but just recently read that Arcade should have talked to me about whether or not he should fight. This never happened to me, he just stayed my companion, and so I was wondering if there were any console commands or something to fix this. Thanks.

You were supposed to let him talk to you about the Remnants after getting each member, so it might be your fault if that happened, but look here for some fixes:
http://fallout.wikia.com/wiki/For_Auld_Lang_Syne

The bug is described on the page, but there is no fix listed.