Perhaps the Heisenberg principle applies not only to quantom physics but also to any microscopic endevour that man undertakes. When we get down to the miniutia of any declared statement we hit a nebulous, uncertain and incomplete understaning of what is exactly stated. Do you get my drift guys?
Logical systems have certain premises that must be assumed true. They cannot be proven to be true by other axioms in the set.
If possible to be proven then they are not assumed and cannot be used as a base assumption to derive initial conclusions as they are a conclusion themself. Without base assumptions you have no basis to derive any conclusions on which to build the Logical system and these "must" be indemostratable.
Hence I concurr with your statement: .incomplete understanding
and further propose it is necessary to any system in order for it to maintain a consistancy without infinite regress.
A similar example of the Heisenburg uncertainty principle is the the inexact value of Pi. Since we dont know the exact value of Pi all measurements dealing with circles are approximations. No matter how many places Pi is calculated is still an approximation. We will simply never know the exact value of a circle.
A perfect circle is unknown in nature, could it be that Pi is telling us that we will never know the universe exactly?That the truth will always evade us? Maybe Pi was put there to show our limitations.
If God created everything and set it into motion she would not need to observe. She would know without looking where all of her precious little particles are at all times. It is just a mater mathmatics.
Though Math is incomplete and cannot be anymore than an approximation.
Indeed if it was resolved it would be illogical and invalidate itself.
Kurt Gödel demonstrated that within any given branch of mathematics, there would always be some propositions that couldn't be proven either true or false using the rules and axioms ... of that mathematical branch itself. You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules an axioms, but by doing so you'll only create a larger system with its own unprovable statements. The implication is that all logical system of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.
Whereas Aristotle noticed the inconsistancy far earlier and created foundationalism to escape the self validation problem. Aristotle deduced there would be no system which could prove it's own first axioms. If they are provable from the existing first axioms then they are not first premises and should be removed from the initial set and concluded later. What you end up with are premises you must assume and cannot be proven by the system to arrive at any future conclusions. To prove them within the system you would have to use the conclusions you derived from them and fall into the trap of circular logical validation. Invalidation by internal consistancy.
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