The word "irreconcilable" means that two things or people are so different or opposed that it is impossible for them to come to an agreement or find a solution. Full definition
On the other hand, in cases of irreconcilable differences with the other parent, or when a parent is trying to get out of paying child support, a judge will not usually grant approval since neither situation is typically in the child's best interest. (wisegeek.com)
Evolutionary theory has two main features that have made it seemingly irreconcilable with traditional theism. (religion-online.org)
Alfred Adler, a psychiatrist in Vienna in the late 1800ʼs, was a member of Freudʼs Vienna Circle until he and several other members of the group left because of irreconcilable differences of opinion. (alfredadler.org)