How do you become an Atheist?

[theVOID]

Also, science (probably) can't establish values, so philosophical theories of value (moral and common) are likely to be irreplaceable by any empirical methods, you can determine the relationships between sets of values in competition a priori.

But if there is no free will, then at least in principle an advanced version of neuroscience that incorporate models of the effects of the interaction between changes in neurological state and the physiology and physical environment can establish a priori how the philosophical theories of value will be formulated and how the competition amongst the values will be resolved. So the philosophy of value is illusory to exactly the same degree as free will is illusory. If will is in principle externally determinable by empirical means then values too can be determined the same way.

If we have to incorporate neuroscience then it cannot be a priori by definition, all science is a posteriori. I can prove a priori that all values exist as relationships between sets of desires and states of affairs or objects simply by examining the language used in expressing subjective value statements, all science can contribute is a higher level of accuracy in determining the precision of these relationships. In other words, we have to decide what sort of relationships give rise to 'value' before we try and learn about value interactions at a precise and analytic level, we aren't going to look into the brain and see brain-state x and then determine that this is value, it needs to be compared to what we mean when we use value terms first.

As for comparing philosophical 'value' with free will, it's really a false analogy, values do exist as physical brain states (specifically desires) and free will doesn't(exist). However, if we don't have an a priori conclusion about what we mean specifically by value, our chances of relating that practical concept to a neurological abstract are nil.

And besides, because we don't have a neurological understanding of value at this point it is meaningless to make scientific value claims in the interim, but we have value statements regardless, they all stem from desires, and that gives us a concrete starting point for working out these neurological relationships. It's very much a case of philosophy giving science a starting point, and then feeding off the scientific results to gain higher precision.

The whole concept of a non-contingent and necessary thing is that it isn't dependent on perception and cognition, so improving our understanding of those things won't help in the slightest. They aren't in any way 'artifacts' of somewhat flawed cognition either, we could be cognitively perfect (whatever that would mean) and what is necessary is still necessary and what is not dependent on physical things is still not dependent on physical things. We can possibly improve the methods by which we arrive at these necessary truths, but to say that they will 'lose their appeal' is like saying the law of non-contradiction will lose it's appeal. Really, it's not going to happen.

My approach to this issue is based not on concept of non-contingent truth but on neurological effect of the grasp of the non-contingent truth.

This seems confused to me, the concept of the non-contingent is the neurological component, so if you are going to say anything about our conception of necessary or non-contingent truths you're dealing with neuroscience and whether or not we are accurate in our determining that something is in fact necessary or non-contingent. An example might be William Lane Craig's belief that God's existence is necessary (KCA), you could by all means determine whether or not his brain is functioning correctly in tying together his premises and conclusions, but this says nothing about the non-contingent things that do exist or whether or not his premises are true.

With sufficiently detailed understanding of how neurological artifacts influence interaction with the physical body and between the physical body and the environment, one could at least in principle establish, based on the interaction of their respective neurological effects and physiological and physical environment, which version of necessary truth as comprehended by the human mind would statistically be most unlikely to be overturned by subsequent philosophizing, or will make the most headway towards the objectives for which these concepts are toyed with in the first place.

That's all rather beside the point, if you can establish that the premises are true (which neuroscience can't tell us unless the premises are neurological in nature) and you're correctly using logic (which neuroscience could potentially tell us, but it can also be determined without it) then the conclusion is necessarily true.

Non-contingent things are even further removed from neuroscience, you can't establish truth that is by definition independent of minds and/or physical things by measuring minds and physics. You can't neurologically prove that a =/= not a, only whether or not we are accurate in our application of these concepts.