The phrase "finite creature" refers to something, usually living, that has a limited lifespan or existence. It can be used to describe beings that are mortal and have boundaries or limitations in various aspects of life. Full definition
The problem arises because, as finite creatures, we inevitably see the world from some particular point of view limited by culture and history. (religion-online.org)
We, being limited, finite creatures make many mistakes, but we are called to learn from them. (redeeminggod.com)
Whereas, for Hartshorne, it is a metaphysical necessity that there be a world of finite creatures, though not that there be just the one we have. (religion-online.org)