The Problem with Psyche as "Soul" or "Life"
The word psyche (ψυχὴν) creates a special problem for translators when they translate Jesus's words because they translate it to mean two very different things: a person's "soul" and his "life.” In the KJV, it is translated 58 times as "soul,” 40 times as "life,” and three times as "mind". Sometimes, the switch between the two is sudden, for example, in KJV Matthew 16:25, it says, "For whoever will save his life shall lose it," translating psyche as "life," but then in the following verse, Matthew 16:26, it says, "For what is a man profited, if he shall gain the whole world, and lose his own soul?" translating psyche as "soul.”
What is interesting is that most of these translations only seem to work as one or the other. For example, in Matthew 6:25, Jesus tells us not to worry about our "life," wondering about what we will eat or drink. It is hard to imagine the word "soul" applying to eating and drinking. However, Jesus also tells us in Matthew 10:28 not to worry about those who would kill the body but not the "soul" using the same word translated as "life" above. This is a "life" that does not die when the body dies. So we have a paradox. A "life" that eats and drinks to survive but does not die when the body dies.
Notice that this is the word translated as "life" in Matthew 20:28 and Mark 10:45 when Jesus say that he came to "give his life" for the ransom of many. I don't think many Christians think that Jesus sacrificed his soul to rescue others. It is also the word used in Matthew 16:26, Luke 9:25, and Mark 8:36 to describe gaining the world and "losing your soul." While "losing your life" works in these verses, this doesn't seem to be what Jesus means to convey.
However, psyche doesn't appear to be a word like the Greek word translated as "judge" that has different meanings in different contexts. Indeed, it would be hard to claim that the context is different in Matthew 16:25 and Matthew 16:26. which are part of the same discussion. Rather it is a concept that is captured well by neither the English "life" or "soul." Of course, given the position of the "soul" in Christian teaching, this creates a problem in following Jesus's ideas when using this word.
A Better Conceptualization
There is an English meaning that does work for the way Jesus uses this word:: the psychological concept of "self,” in the sense of our worldly sense of self. This is a connection point of a mind, flesh, and spirit. In this article, I cover these related words that are also translated as "soul" such as pneuma and "life," such as zoe. so we can understand how they all come together.
How are people different than animals? My sense is that Jesus would agree that animals have minds and spirits and bodies. What they do not have is the organ of conscious awareness of being a specific person in time and place, the psyche. Animals are. We are aware that we area.
This is our awareness that we have a heart, mind, body, spirit, and the temporary life of the flesh. The fact that we know life is temporary is important. From this awareness, we make choices. Animals do not make conscious choices in the same way humans do. Our consciousness, psyche, experiences the thoughts in the mind through the urging of the heart. Jesus joins the psyche, the self, with the life of the body. They are both part of the same life, one of the flesh with a mind and the other, the union of flesh, mind, and spirit. Psyche roots us in time and place because it accesses memory.
The Psyche as Self
So where does this leave the "life" or "soul" of psyche? It is our sense of self as the person we record in our memories in this world. It includes everything else, our flesh, mind, and spirit. The term "self" captures it well because it is our self-awareness but not our pure spirit, our awareness as part of the eternal. Our "self" is how we see the role we play in life. It is the person we are in our memories, playing a specific conscious role in human society.
This is a life that eats and drinks and remembers eating and drinking and remembers that it has all types of needs and obligations. So, this is the life that worries, because it contains mind and heart. This is their personal life, the life of identity, being this specific person at this point time at a specific location. This psyche can be destroyed after death, but isn't necessarily. It is also the "life" that people lose when they die, not because their awareness ceased but because the life they remember ceases when they lose their flesh and body.
One possibility is that it works like this. A human is created by a specific union of spirit/pneuma, a mind/dianoia, and the flesh/sarx. As we grow, we develop our our lives/zoe, our hearts/kardia, and our self/psyche. These three are connected with our eternal spirit/pneuma. When we live a worthy life, all four of these elements of our life, life-heart-self-spirit, can potentially survive. This is our soul. This is what Jesus called "eternal life". We survive knowing our past life.
However, if a life is unworthy, what happens? The elements of this life go into the trash heap of fire. What happens then? The eternal torment of in the traditional hell of Christianity? There is another possibility as well. This life-heart-self are burned off in the fire of the trash heap leaving only the individual consciousness of spirit. In this context, the individual soul that survives is pure spirit, without the taint of an unworthy life. What happens to it? Possibly a rebirth in another life. Jesus makes several references to John (the Baptist) as the rebirth of Elijah.