Trialism

Trialism in philosophy was introduced by John Cottingham as an alternative interpretation of the mind–body dualism of Descartes. Trialism keeps the two substances of mind and body, but introduces a third substance, sensation, belonging to the union of mind and body. This allows animals, which do not think like humans, to be regarded as having sensations and not as being mere automata.

Background
Cottingham introduced this term after noting that Descartes' account of sensation and imagination has placed his official dualism under considerable pressure: "Partly as a result of this, we often see the emergence, in Descartes’ writings on human human psychology, of a grouping of not two but three notions – not a dualism but what may be called a ‘trialism’." According to Cottingham, Descartes added the third notion of sensation "alongside thought and extension without proceeding to reify it as a separate substance". Thinkers such as Daniel Garber and Tad Schmaltz supported this by citing a letter in the correspondence between Descartes and Princess Elizabeth of Bohemia, which indicated that he changed his mind from a dualistic view.

Christian trialism
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 was criticized by critics such as Hank Hanegraff for extending trialism to each Person in the Trinity, for a total of nine essences.