To be a creature is to be a valuer, i.e., to be one who considers things on an evaluative level.
To be a person at the level on which humans are persons is to be a self-aware valuer, i.e., a valuer whose values exist in a network such that some values exist as a result of a cross-section of values.
A dog, for example, values, but does not have any equivalent to the problem of evil to consider. A dog who existed as a person might have a difficulty in considering whether or not to trust someone who seemed at some times to care for it and at other times not to. For creatures, anything like this problem is played out in living--it acts on a certain answer (trust/don't trust) and that answer may or may not be changed by the results of acting according to it.
A person, on the other hand, is capable of self-reflective evaluation of the evidence, so that the evidence may be considered, whether it points to one answer or the other. This occurs, for instance, in our ability to consider what a person's intent may have been. It also occurs in the case of someone who has encountered evidence that someone is not trustworthy, yet also sees evidence that they have no survivable option but to trust that person, when such a person chooses to trust the person even though they would never do so under normal conditions. A dog might act according to a cost-benefit type analysis, but a person is able to go beyond that to consider some options viable which are not viable at first glance. This lack of ability to consider evidence may account for the remarkable loyalty of tamed animals. (I should note that I am writing based on a layman's understanding of animal psychology)
A person's self-reflective capacity, then, gives rise to the logical side of the person. We begin with some set of values (we value our own good), which must then be ordered in some way or other. This requirement that we order our values, combined with our self-reflective nature, requires us to adopt some standard of coherence for ourselves, i.e., logic.
This forms the basis on which I argue for belief in an external world, other minds, and God, among other things.