The Ultimate

A brief foray into set theory last week came as an attempt to prove that the Ultimate must be a different type of thing to everything else. Hiding in the wings was the idea that the Mind must be a "given" in any thinking - not in Cartesian sense that there must be a thinker - but in the sense that thought can't hold together without something linking the thoughts etc. Whatever that is it can't be itself a thought. Its the general view that there must be a heirachy in any system where each level cannot access the higher level. Thus for example God cannot Himself a thing in the world He created, or that a Table can't be the same type of thing as its components etc

The form of the proof was that there cannot be a set containing the Universal set.

Let us refer to the ultimate Universal (E), the set of all things, and all sets of things. There is nothing which is not in this Ultimate set. The question is: is there a set containing E?

If there is a set containing E then it must be a member of E. However if there is not a set containing E then E is unlike all things in that it is not a member of any set.

Let us define a set T = {E}

and since T is a set it belongs to E. Now how do we define T'? On the one hand T' is everything else in the universal set E, on the other it is

...

to be completed there is a tricky bit here, creating a set seems to protect us from the problem!!!!


Anyway that has led to Alan Turing and the Universal Turing Machine. The question I seem to have posed myself since a child has been this question of the Ultimate and whether there is anything beyond it, or whether it even exists. Were it to be decided one way or another what the nature of the Ultimate was it seems to have a lot of ramifications. For one it would stop people fighting thinking that they have got the position of ultimate. It would also sort out the body/mind problem because the question there is one of ultimate: some say that matter is sufficient for everything and others mind, and the people in between have got oil and water. It sorts out AI and whether finite machines can experience a "World" it ties a lot that i've struggled for together so I'm interested. Whether it helps with that question of Life remains to be seen, a Life spent searching the answer seems a bad answer and a bad question!

i continue to explore this but realise with some humility that maybe my faculties are not up to it, and there have been some truley great people before me who have not to my knowledge devised any rigorous views of the ultimate. Infact the ultimate seems largely unexplored by most. Maths covers it with Cantor and his theory of infinities, religions cover it with God. The view seems to be that the ultimate is impossible and beyond finite minds.

Now with Turing machines at least we could show that any notion of "the ultimate" either was or was not computable?

The persisting idea for myself is that whatever is done it seems that we lie outside the system being devised. If we ever were to devise an ultimate answer we would lie outside. So I suspect any proofs come in the form that the Ultimate could never contain itself. Turing machines written on Turing machines? that was the plan tonight but its late I'm tired and pumping out "notes" onto this ticker tape for my "system state" to start again at some time in the future.

Stuff here from Daniel Dennett who've I argued against before but am taking more seriously now as a means of seeing if there are any immanent contradictions.

Searle, Strawson, Saussure note to self to consider them...

Its a huge question not least because whenever I try to frame the question the frame itself becomes a limit that needs to be reconsidered. There seems to be no foundation large enough to create a proof that covers everything? I'm looking for a limit of thought that might liberate a world beyond thought, yet even thought is a tricky thing which refuses exact definition.

The undecidability of it, non-computability of it might be the way forward. There is neither a proof of the infinite, nor the finite because it is even more abstract than that. Imagine living in a world which was proven to be infinite. Isn't that as frightening a prospect as one that was proven to be finite? Its an interesting thought. I certainly want to tidy all this up, as said before about narcisism i am tired of doing the same thing, the same tricks, the same questions. Its been the best part of a life now chasing after the Ultimate, the Big Question, the Gold country, but I am tired... and hungry