Is there a term for someone who proclaims they don't believe in an afterlife but they are not sure whether the supernatural exists?
I don't mean agnostic. Atheists don't believe in a deity, but an atheist could believe in an afterlife.
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Spiritual would be the best way to describe yourself.
There is a movement to try and differentiate the terms spirituality vs religion (Sources are numerous, here's one)
Also, there is a belief system being adopted called Spiritual but not religious (SBNR) that is used to self-identify a life-stance of spirituality that rejects traditional organized religion as the sole or most valuable means of furthering spiritual growth.
However, there are several beliefs that you could identify with.
Thanatism (as pointed out by another user) where the basis of belief is life comes before death, not after it (no afterlife). The term Thanatism comes from thanato, which means death. After an individual dies, their soul becomes one with nature. Thanatism is type of spiritual belief and not a religion.
I'm a thanatist. I live life to its fullest.
Esotericism or esoteric, which means that you believe in something that few others do. The term translate to 'inner-circle' and is used to define a small group of individuals that believe in the same thing.
I don't subscribe to any mainstream religious thoughts. My beliefs are esoteric.
Theosphical whereby you use your own beliefs to justify certain facts for your spiritual or religious benefit. One example of this is Christians trying to justify dinosaurs existing during the early history of the world.
I believe in everything the Bible says except about heaven and an afterlife.
I don't believe in an afterlife for the soul because I'm a mystic.
Someone needs to redefine atheism or come up with another term to describe those who believe in the soul and/OR an afterlife type existance/persistance but not in an all powerful, all knowing, God-creator. Maybe Taosim comes closest and Buddhism comes in second, but each has it's own strict tenets of belief and structure as do most religions.
I'd go with "Taoistic" for now.