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Neither belief in god, nor non-belief in god

Believing nothing means not believing in god, not even believing that there is no god

Some things have non-zero probability of being true, but are unlikely to be true, and therefore are not worth belief. It is an ignorance of truth which creates a desire for belief: when we do not know whether something is true or false, we tend to reject the uncertainty by prematurely accepting a belief as true or false. This is why it is more logical to begin with the premise that things are false until proven true, than to begin with the premise that things are true until proven false.

This is proven by understanding Truth (represented by non-falsehood, zero) is only composed of non-truth
0 = 0+0

Whereas various degrees of falsehood (represented by non-zero, 1) consist of a mix of truth and falsehood:
1 = 0+1

When we presume that what we are observing is composed of an uncertain amount of truth and falsehood, rather than truth, we understand the method of negation: we must prove truth, rather than prove falsehood.

0+1-1=0 (removing the untruth results in truth)

To do this, we have to skeptically test each argument upon which we found our understanding, and reject all beliefs (all uncertainties) until they can be proven.

As there is no definite proof of God, and no definite proof of non-God, logic compels us to reject both premises until evidence can be obtained.

There is a common belief that real phenomenon is perceived by an observer, and this observer exists. This is demonstrably false. Such a premise implies disparity between observer and observed where there is none: you are correct that separation is an illusion, and the existence of self is contrary to a theory of Atman. It is also contrary to the theory of Atman to disbelieve randomness by conflating it with adharma.

Phenomenon cannot be directly perceived for several reasons: foremost, under a theory of interdependence, any observation which is made is made from within the phenomenon being observed, and therefore the observation affects the observed and the observer, altering the phenomenon and the perception of it beyond any ability to truthfully describe it. There cannot be difference between self and not-self. This is the foundation of a theory of conditionality: truth is not fixed or constant, except within parameters and probabilities.

Phenomenon cannot be perceived directly because all phenomenon must be first inaccurately sensed (by eyes, ears, nose, mouth, touch), and then inaccurately conveyed to the mind for interpretation before the conscious act of perception occurs. Such a theory of inaccuracy requires considerable skepticism: after all, if the blind can dream colors, and the deaf can still listen to the memories of music, what does this imply for our own imaginative capacity?

Since Truth cannot be known, we must utilize logic, especially inferential logic, to determine falsehood. Perception is uncertain (due to parameters of probability arising from interdependence), and inaccurate. A premise that real phenomenon is perceived must be rejected.

Randomness is observed by the limitations of observation: inaccuracy and conditionality permit the acceptance of the fact that some data is meaningless. Further, study of the meaningless data indicates patterns which lend credence that such randomness is not due entirely to the process of observation leading to inaccuracy and conditionality, for there are patterns within the chaos.

Adharma is not anatman, nor even atman, but conclusions based in speculation or perceptions which are unreliable. When salt is dissolved and suspended in water, the two may be easily separated, for each possessed identity. Consciousness, being an emergent property of perception, cannot be separated from its perceptions. Fire emerges from the co-dependent conditions of fuel, spark and air, and disappears when one is not present. Fire has no identity, and cannot be said to dissolve into the air, or the ash, or go here or there. In the same way, "self" emerges from atman. Because self is an emergent property of numerous conditions, it cannot be said to exist in of itself. Both the theory of atman and the theory of anatman may simultaneously apply.

In the same way, adharma is not the opposite or contrary to dharma. Criminality is an emergent property of law, strength is an emergent property of weakness. The two, dharma and adharma, are co-arising, co-dependent, and co-terminating - because they are emergent properties of the atman.