The Big Bang and Determinism
The idea of the big bang, as I understand it, was that time, space an matter did not exist beforehand. There was nothing. However, the idea of determinism is that one event follows another. The big bang could not have followed another event (by definition). Therefore, is the big bang an example of inderminism? If so, are there other examples of inderminism and is finding one example of inderminism enough to say free will is possible?
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Generations A's - decisions are influenced by the decisions of prior generations and so on and so on. Is there a regression of these decisions by prior generations that ends at some - un influenced decision ?
Nope. Big bang cosmology says nothing about "beforehand", and it is likely the entirety of empirical science will never be capable of saying anything about "before the big bang" whatsoever.
Rather than asserting "there was nothing", it's closer to"everything we can observe was at one point condensed into an imperceptibly small space, and because we have no empirical access to that initial moment (the radiation we see only comes well after the big bang, and our theoretical models which infer what happens as we approach time-zero breakdown entirely when we actually get there) we can therefore say nothing about "before the big bang"..
If time as we know it did not exist prior to the big bag (if the statement "prior to the big bang" is incoherent), we can still imagine our universe as an effect situated within and caused by a greater universe, though, the nature of time, cause, and effect in such an inaccessible greater universe could be absolutely anything.
What is important though is to not to jump to any conclusion about the beginnings of the Big Bang. As VagabondSpectre said, there's not much we know thereof. Whether the Big Bang was caused or uncaused, this knowledge is likely to remain hidden from us for a long time or, may be, forever.
You actually don't need to go as far back as the Big Bang to entertain the possibility of free will. Quantum physics is supposedly indeterministic and so provides better grounds for freewill.