President Bush
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I don't need to 'know' this. It is the axiom of choice.
A choice occuring without a choice mechanism is not possible because that would also be a mechanism - namely the mechanism that behaves in a manner that is not like any other mechanism. It is excluded from the discussion by virtue of paradox.
You can call it circular if you like but then it would show up your understanding of logic as limited to only parroting fallacies without understanding the formulation of logical systems under which they are valid.
It is quite simple: in the study of 'choice' we formulate our logic with:
1) Sets of possible choices
2) Mechanisms by which choices are selected
You are free to disagree with this if you want but then you are just going to have to tell me what you mean by 'choice' - that word won't attain meaning through its six letters alone you know.
I'm no mathematician, but I'll give it a shot:
According to Wikipedia, "choice" is:
... the mental process of thinking involved with the process of judging the merits of multiple options and selecting one of them for action.
Is it possible to demonstrate a proof requiring the axiom of choice to produce a simple answer of either yes, it does or no, it doesn't... that the subject of axiom of choice has something to do with the subject of free will (to be a necessarily true statement)?