Originally Posted by Quaggas
What, like a system of axioms is either incomplete or inconsistent? So, like, Bertrand Russel spent a lifetime chasing a castle in the sky? Goedel, Escher, Bach (Hofstadter?) is a good read on this.
Originally Posted by Redbacks
In my opinion: the theorem brings about the rationale for post-modernist thought. A potential defining moment where Western academia give up on the theory that basic logic could be used to describe the world, based on the fact that we now had mathematical logic showing itself to be inconsistent. From base assumptions you cannot build a system which is consistent. It stemmed on Russel’s Paradox which he laboured over for many years:
‘The Set of all sets which is not a member of itself’
a) If this set is in the Set, then contradicts its own rule.
b) If the set is not in its own set then it passes its rule, but then because of this it does belong in the ‘set of all sets not a member of themselves’ and fails, making it a paradox.
Gödel determined this was a sentence that could be constructed from any logical system.
Hence, any logical theory which aims to describe consistently the ‘ultimate truth’ of a human set for morality/ethics can go no further than this, you cant logically use certain axioms to provide a basis for human action. What develops from Gödel’s theorem is the fact that closed logical systems could be developed. i.e. religions, philosophies, idiosyncratic rules of a profession etc. that can remain consistent from their own view, but ultimately this proves they are inconsistent also, hence empiricism is maybe the best thing we’ve got and rationalism needs to be put to one side.
Now you start to interpret a history of ‘progress’ that had been in the minds of enlightenment thinkers, and had justified: Colonisation via improving the lot of poorer nations and helping ‘primitive cultures’ to progress to more enlightened ways. Suddenly there is a final realisation that ‘there is no such thing as progress’ each culture/tribe is no further advanced or closer to any inherent innate truth than that of another, we can no longer hide behind a rebadged idealism of progress (i.e. rationalism) to justify imperialist conduct.
Take for example ‘third wave feminism’ and its more recent interpretations of the head scarf. It moved from “Our reference frame” which said you must wear it to achieve the standard of female liberation we have achieved in the west’ to ‘you should have the choice as to whether you where it or not’ and ultimately aims to show more respect to the ‘cultural reference frame’ from which each person conducts their decisions and is based more towards results rather that ‘absolute authority’ over a moral high ground. Certain non-negotiables exist like human rights etc. but require discourse to resolve, not cultural hegemony. This at least is the similar path by which Australia is looking towards reconciliation.
Fascinating. Now I'm starting to read the book (GEB) properly after having read it earlier in piecemeal fashion as I'd borrowed a copy from someone.
Another interesting question he has raised in the book is.. consider a source of information such as a book or a CDROM. Does it have any meaning on its own (as a collection or a pattern of symbols) or does any meaning that it contains lie only in the brain of the one who reads it?