From the POV of this traits reproduction, the bat predation is a random factor that stopped the beneficial mutation spreading.
No - it's non-deterministic with respect to the mutation. To say
it is random - as I have been trying to get across - is a stronger claim that cannot be supported.
As far as the player's in the game are concerned this is a deterministic problem with respect to the environment - i.e. the bats have to deal with the fact they are being preyed upon. It is this deterministic relationship that is important if you are modelling it. If not you can compensate by simply encoding it as a 'disaster' probability for the population.
Think of it like differentiation - I could differentiate some complex polynomial with respect to y and get a chaotic behaviour or differentiate it with respect to x and get a more simplistic behaviour. What we are doing here is teasing out the correlations then promoting them to causations.
Predation is a simple concept is it not? You get caught, you get eaten - pretty deterministic. Yet we can see how in nature it can lead to quite chaotic systems - but nonetheless we can tease out this complexity into a more deterministic model if we wish and explore deeper facets of the effects of evolution in life-like systems.
Or we can ignore it if we don't need that sort of fine grained detail. But we should NOT be making strong claims based on ignorance.
Identical conditions, produce identical outcomes in deterministic* systems, even if they are chaotic.
Unfortunately we lack the ability to roll back time. Therefore we will be forever unable to decide on things like whether quantum mechanics acts in a truly random manner or as the result of massive entanglement - we cannot step outside the system to confirm it so we are stuck with being entangled either way.
And yes I do accept that there are systems with complex feedback loops that are deterministic; but which can be modelled by probabilities. However I don't think natural selection is one of these. (It depends on whether quantum effects are truly random).
I really don't think it does - for the reasons I have already outlined. It
seems very important because it
seems that random and non-random are fundamentally and diametrically opposed concepts. They are not really but we have to assume as much in order to get useful work done.
As long as you keep in mind that they are, and always will be, useful lies you will remain flexible. As such I have been arguing for the usefulness of my lies.
A probabilistic (or stochastic) treatment works and I would argue it also reflects reality.
Well duh - of course it
reflects reality - if it did not then we would not use the model would we?
Have I at any point said otherwise? No I have not. I have merely been pointing out - and in fact I pointed this out very early - the problem with, what is essentially, the strong claim of randomness and relating that to how it might be best to think of evolution. Hence why I introduced the most basic terminology I could that would unambiguously separate the important concepts without in fact making a strong claim either way vis-a-vis randomness.
Hence it is not sufficient to simply talk about random and non-random: you must talk about it WITH RESPECT TO some variable - just like differentiation.