We have previously discussed the issue of co-existence of 'determinism' and 'free will'. Here we'll take that to the next logical level and examine the coexistence of 'Explainability' and 'free will'.
We are going to define 'explainability' as a true occurrence of the the following statement:
"Everything that happens has an explanation, whether we know it or not." [1]
Here the underlying assumption may be construed as the existence of some kind of intellect that has the ability to understand or process that kind of knowledge. Here we are concerned only with the ability, and not the actualy knowing. Since the entire effort to analyse and study the Ultimate Truth would be futile if this assumption were not true; we'll assume it's existence for the time being.
Now let's consider the hypothesis that an explanation does exist for everything that happens. If that is the case, then our own actions (and thoughts!) should also have an explanation. This logically implies that all our actions (and thoughts!) are constrained by some laws, i.e., we function according to some well-defined rules [2].
Let's examine this fact more deeply. What does this mean? Doesn't it imply that there has to be some area of the (whole!) truth that has the potential to escape our very understanding! ... (Because we are functioning under some set rules ourselves, and these rules constrain us from being completely "free" in our thinking. We can only think according to these set rules.) ... Besides if an ultimate truth exists then there must be an entity that can comprehend it, otherwise it doesn't really have any meaning! The very concept of 'explanation' means that it should be able to make somebody understand a particular event. If it can't make 'anybody' understand anything, then it simply means that it is not an explanation! A very simple fact emerges here, that is equally complex if examined in still more depth.
"In order for an explanation to exist, there must be an entity that 'can' understand (or process) it." [3]
From this statement, after a few more logical steps (which I have skipped here, as they are more or less straightforward) we can make the following deduction:
"If there is no God (or an ultimate intellect), nothing has any meaning, nothing makes sense, and there is no purpose to life!" [4]
Also, referring to [3], if explainability exists, then everything may be explained including the behavior, actions and thought processes of the entity that is trying to understand or analyse it. Because "everything" includes even the entity that is trying to understand it! Hence we can conclude the following:
"There can be no such thing as a true 'free will', if explainability exists!" [5]
However, if some kind of free will doesn't exist, then there's nothing that can understand the Ultimate Truth. So, following from [3], the Ultimate Truth just doesn't exist! Mind it, it's not just about knowing or not knowing, but about the very existence of this Ultimate explanation.
This is a paradox. How to resolve this? Honestly, I have no idea! The most likely reason for this paradox may be the use of an inadequate (i.e., constrained) logic to examine it*. Perhaps the procedure of analysis here is just not good enough! ... The logic in order here is some kind of 'Ultimate Logic', which we may not be familiar with. A logic that is free from the constrains of the various underlying assumptions of time and space ... But which constrains do we need to remove from our existing logical system before it becomes good enough to analyse it?
... I do not know! Nor does anybody else that I've met. So where do we go and what do we do? ... God help us here!
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The other explanation would be that "We can never understand it".