Even though he’d shown that logic has certain limitations he was still so drawn to the significance of the rational and the logical. That he
desperately wants to prove whatever is most important logically even if it’s an alternative to logic. How strange and what a testimony to his
inability to separate himself - to detach himself from the need for logical proof; Gödel all of all people.
Cantor originally had hoped that at its deepest level mathematics would rest on certainties, which, for him, were the mind of God. But instead, he had
uncovered uncertainties. Which Turing and Godel then proved would never go away; they were an inescapable part of the very foundations of maths and
logic. The almost religious belief that there was a perfect logic, which governed a world of certainties had unsurprisingly unravelled itself.
Logic had revealed the limitations of logic. The search for certainty had revealed uncertainty.
The notion of absolute certainty, is, there is no absolute certainty, in human life, in maths, in logic neither in science. The only certainty that
has withstood the test of time to date is; that what we think is certain and true has a limited axiomatic scope, and the conscious mind is the only
force in the universe that can transcend proclamations of truth by virtue of conceptualising and defining its limited scope, thus transcending
certainties to higher values of truth it itself previously set the scope of. In this regard, focussed right by powerful minds, it's self
transcendental, and could maybe eventually (if the trend continues) reveal a realm approaching the maths and dimensions of the infinite, where the
amount of axioms nears the infinite and where logic and turing machine computation as we recognise it simply fails and we end up with a conscious
internal universe of immense complexity, the complexity of which our current maths, computer models and materialistic sciences could not even begin to
Maybe such an immensely universally complex system already exists. And maybe its the field of consciousness everything in the existing universe
shares. We just have to reach a higher state of consciousness and awareness to become aware of the conscious attributes of things we don't typically
ascribe consciousness to. Everything is alive, just at different levels all relevant to each others level of conscious transcendance.
Bzzzzzt. Reality check. Thats the dream (italisized). The optimist in me hopes, my realist side scorns.
But if consciousness in its normal form is indeed non computational, non algorithmic and not based on logic (incompleteness theorem) associated with
turing machines then how are we ever going to try to understand it in terms of them without just tying ourselves up in knots made of the same
paradoxes that drove the aforementioned geniuses mad?
And how can we solve the mystery of consciousness if neuroscientists do indeed have the cause and effect the wrong way round? It seems explaining
consciousness with reductionist examining of brain function is a fruitless, but yet noble, quest many have embarked on. Consciousness is universal.
To finish, applying Godels theorem more vigorously to current dominant paradigms could have such a catalysing effect in developing new, mathematically
sound theories, based on more creative functions of human inspiration.
I revel in scientific unknowns and theories being falsified and replaced by a better theory, personally. I have no pet theory I'm emotionally attached
But some would likely end up having breakdowns comparable to the ones mentioned above, if say the Big Bang theory was proved wrong or statistically
impossible based on the sort of scientific reasoning we would subject to other areas of science, or evolution insignificant in the large scheme of
things, what would the reaction be? I get a lot of religious zeal when I dare argue with cosmologists, always on the attack implying an emotional
attatchment to their theory. I don't know how their egos could handle it ... and if we should be sensitive or blunt.
The problem is that today, some knowledge still feels too dangerous.
Because our times are not so different to Cantor or Boltzmann or Gödel’s time.
We too feel things we thought were solid, being challenged, feel our certainties slipping away.
And so, as then, we still desperately want to cling to belief in certainty.
It makes us feel safe.
At the end of this journey the question, I think we are left with, is actually the same as it was in Cantor and Boltzmann’s time.
Are we grown up enough to live with uncertainties?
Or will we repeat the mistakes of the twentieth century and pledge blind allegiance to yet another certainty?
Thanks for reading
edit on 7-7-2012 by ZeuZZ because: (no reason given)