Quantum mechanics is a mathematical formalism that is an attempt to produce as good a description as possible of 'the world'. The key point of the previous sentence is: it is mathematics. Mathematics may allow us to make certain predictions about the physical reality surrounding us, but it is nevertheless an abstraction that does not necessarily have any direct connection with that reality.
Any interpretation of mathematics in physical terms is debatable at best and completely unfounded at worst. Granted, mathematics seems to reflect nature, but this may well be a prejudiced view: phrasing it differently, it seems hardly amazing that something created to describe nature produces descriptions that seem to describe nature very well. Mathematics would be a failure if it wasn't usable to model nature.
Given the deep metaphysical problems surrounding the relationship between mathematics and physics, any attempt at interpreting quantum mechanical uncertainty as the psychological property 'freedom' belongs to 'completely unfounded' category, requiring lots of work before it becomes even remotely believable.
I understand and to an extent agree with the gist of your argument, but I can't agree with this:
> Mathematics would be a failure if it wasn't usable to model nature.
In fact I don't understand why you would make such a statement, unless you have a very different description of nature (or failure, or both) to what I have. Mathematics has many applications beyond modelling physical reality. This topic has the potential to raise many philosophical questions, but even at the most superficial level there is a difference between "describing" and "solving".
This doesn't sit quite well with me either:
> it seems hardly amazing that something created to describe nature produces descriptions that seem to describe nature very well.
Pure mathematics isn't created to describe nature. Physical applications of pure mathematical concepts are usually only found many years after they are devised.
My belief (I call it a belief, because I haven't done rigorous research to confirm it; it is based on what I learned during studying physics) is that all early, 'basic', mathematics was invented (or discovered, I don't want to get into that) to describe nature.
Initially, the natural numbers were nothing but a convention to describe and differentiate between sets of multiple objects that were to be considered equal for the purposes of discussion. IV apples vs. V apples. II rocks vs. VII garments (of course, the Romans didn't invent this, but I find it a distraction to use 'our' Arabic numerals).
Another example: Newton invented differential calculus specifically to describe nature. Shortly after that field was invented, mathematics in it would be done for it's own sake, but that doesn't detract from the fact that originally it was meant to describe nature.
More recently, mathematics has been invented before it was shown to be applicable to physics. What I earlier meant is that this may be a result of the origins of mathematics and doesn't prove what it seems to imply.
Any interpretation of mathematics in physical terms is debatable at best and completely unfounded at worst. Granted, mathematics seems to reflect nature, but this may well be a prejudiced view: phrasing it differently, it seems hardly amazing that something created to describe nature produces descriptions that seem to describe nature very well. Mathematics would be a failure if it wasn't usable to model nature.
Given the deep metaphysical problems surrounding the relationship between mathematics and physics, any attempt at interpreting quantum mechanical uncertainty as the psychological property 'freedom' belongs to 'completely unfounded' category, requiring lots of work before it becomes even remotely believable.
Moreover, it seems it could well be a typical example of a category mistake: http://en.wikipedia.org/wiki/Category_mistake.