I don't find it to be an inherently religious question at all. Sure, it has become the preoccupation of a number of high profile religions (and those who ascribe to those religions can add to this discussion), but that does not, in and of itself, tie the question or the concept of 'the soul' to religion. In fact, the question of the soul (it's components, make up, feasibility, purpose, etc.) has been discussed for ages without tossing religious beliefs into the mix.
Here, you can see a quick summary of Plato's tripartite theory of soul as written about in his Republic:
Quote:
Plato argues that the soul is composed of three parts: the appetitive, the rational, and the spirited. These three parts of the soul also correspond to the three classes of a just society. Individual justice consists in maintaining these three parts in the correct balance, where reason (aided by spirit) rules, and appetite obeys.
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You seem to be operating under the assumption that the spirit or something that is spiritual is automatically religious in nature. While this is often the case, it is not always so. Technically the only discussion that necessitates that religion be brought in in order to make the discussion fruitful or worthwhile is a discussion on religion itself (either in the broad sense or in a more specific sense).