The phrase "to avoid this conclusion" means taking an action or making a decision in order to prevent reaching a certain result or outcome. Full definition
The artist avoids conclusion and psychological resolution in his abstract narratives that combine the techniques of film with drama, music, experimental theater, and dance. (art.thehighline.org)
The positivist, according to this account, can avoid this conclusion only if he can consistently make good the claim that the term «God» is meaningless, which is a way of saying that God's purported existence is not a logical possibility in any sense. (religion-online.org)