A general discussion on Belief

We need to have ideas of some basic terms before we can discuss atheism. I have given a structural definition with the set analogy. I also proposed a definition of knowledge (100% epistemic certainty) and confidence (< 100% either epistemic or psychological or both) using probability here.

What's belief?

Belief is the psychological state in which an individual accepts a proposition or statement to be either true or false. Any particular mental state of a thinking mind has a belief set i.e. A set of beliefs. Consider the set
B= {a, b, c}
Here the Belief set B has some members where,
a = the truth value of the statement a where A person has the belief that a is true or false. Similarly, b = truth value of the statement b where A person has the belief that b is either true or false and so on.

There are some beliefs which are contingent (depends upon evidence) and some beliefs which are non-contingent type. These beliefs are all subsets of the belief set B.
You could have an empty set B ={ } when you lack belief. You lack belief about statement a and statement b which were given in regard to something or someone.

What's Faith?

Faith is the non-contingent belief. Indeed it seems to be the purpose of faith to quite deliberately not be subject to correction or revision based on available evidence. Faith = a belief which is non-contingent. I'd say a person who has this belief (non-contingent/faith) also has a degree of confidence. This degree of confidence generates from psychological certainty and not from epistemic certainty.

I define knowledge as that statement of which we're 100% or close to 100% epistemically certain. Any less certainty will be called "degrees of confidence" and not strictly knowledge. However, due to some philosophical problems (for exp: Problem of Induction), full certainty isn't possible therefore we usually accept something as knowledge for which we have a very high degree of epistemological certainty.

Indeed this means there are three distinct mental states....actually an infinite number of metal states if one takes into account degrees of confidence (which maps very nicely onto probability).

No belief/lack of belief does not need any degrees of confidence. Only beliefs need to have confidence. For rational people this confidence comes from degrees of epistemic certainty (contingent belief).

There is another type of non-contingent belief which rely on little or no evidence. This belief is called Taste or personal preference of something. However, this type of belief is irrelevant to this discussion.

Why we hold beliefs?

A belief is held because of either motivation or evidence or both. Similarly a lack of belief results from lack of motivation or evidence or non-cognizability or all of these reasons combined. Strong desire or motivation could turn out enough of a reason for someone to hold a belief which has an overwhelming evidence against it. For example: if someone accepts the belief that "human beings are intelligently designed by a supernatural entity and not evolved from earlier species via biological evolution" to be true. This is an example of faith.

Evidence?

Philosophically speaking, I'm an empiricist. Empirical evidence is the real evidence which can be obtained via scientific method which is deeply interwined with cause & effect nature of reality. I adhere to the correspondence theory of truth, metaphysical and methodological naturalism.

To learn more on Belief, Certainty, Truth, Evidence etc...I suggest checking Stanford Encyclopedia of Philosophy.