Trialism
Trialism in philosophy was introduced by John Cottingham as an alternative interpretation of the mind-body dualism of Rene Descartes. Trialism keeps the two substances of mind and body, but introduces a third attribute, sensation, belonging to the union of mind and body. This allows animals, which do not have thought, to be regarded as having sensation and not as being mere automata.
Christian trialism is the doctrine that humans have three separate essences (body, soul, spirit), based on a literal interpretation of 1 Thessalonians 5:23 And the very God of peace sanctify you wholly; and I pray God your whole spirit and soul and body be preserved blameless unto the coming of our Lord Jesus Christ. This doctrine holds the soul to belong to the union of the body and the spirit, which makes it roughly compatible with philosophical trialism. However, the evangelist Kenneth Copeland came under fire by critics such as Hank Hanegraff for extending trialism to each Person in the Trinity, for a total of nine essences.
Sources
Cottingham, J. Cartesian Trialism, Mind, 1985.