Actually is that is... if there is always a meta level by the diagonal lemma and these can be shown to compund indefinitely then by a wierd sort of induction there is no ultimate-system.
The other thing to develop is the difference between formal and computable systems and human thought. Following Turing's insight, human thought must be finite because we use discrete things and ideas - an infinite system can't carry information... that said an ordered infinite system can like the Natural Numbers can can't it? Dennett also has the idea that what we call human thought is really just a "computer" being run like software within the brain hardware. Hofstadter also makes this point that human thought is not done on the brain hardware - we don't think in neurons and synapses. Rather this level of organisation has emergent properties that have emergent properties, and the levels are not stacked on one another but intersect with strange loops. So what we (and Turing when he designed the computer, which was based upon how a human would compute in their head) what we are conscious of is actually caught up in the levels of human brain activity.
An insight as a child was that we do not experience objective reality. What science says is the truth and what we see must be different - reference the blog entries on vision and brain activity. It is quite obvious that for us to see anything light must "enter" our eye. The object doesn't enter the eye, only the light. We see light then and not objects. This is why cinema and TV works. Objects are thus made up by the brain from the light that enters. Yet when I look around this room in which I sit everything looks normal and solid. The problem is then to ask well what is a "real" object like, that is the ones the light is bouncing off and going into our eyes, the ones that are being recreated in my brain? We can never know! You can't get outside your brain. This kind of blew my mind as a kid. This is the noumenal level as opposed to the phenomenal level.
Some ways of dealing with that are:
- The Cartesian approach: the existence of perceptions is proof that a brain exists, so the brain's existence is a different level from the perceptions of that brain (SRH) and is logically prior to those perceptions: it makes them possible. Thus our existence is not the existence of a perception of ourselves but the fact that a perceieved world exists at all. Had that realisation washing my hands before a big staff meeting in the Food Giant in Wathamstow in 1995 of all wierd places.
- The Hegelian/Buddhist approach: the idea of a real world is just that, an idea. The true reality we infer objective things to have is just an idea. Phenomenon are all that exist.
- Holistic approach: Our perception of things is not like an arrow hitting a target, rather it is the whole process taken as one. The arrow must be mounted in the bow, fired, make the journey and hit the target for it to hit the target. Any break in the process is a failure. To see something is not the light getting to the eye or the electrical stimulation hitting a part of the brain. So to see something requires the whole process and it is not just brain activity that is important but everything. I always thought as a child that we place too much importance on "brains" they are material like anything else so why focus only on them when we talk about perception?
- A recent innovation is this view. The noumenon is rather a "potential". We only know what the noumenon is when it has become a phenomenon, or when the mind has categorised it, but we can categorise it many ways so the noumenon is not only One way. Rather it is a "potential" to be many things. Systems of phenomena are not random however and have logic like the idea of "harmonic structuralism" (see blog).
So if it can be shown that human thought is finite and computable then it is fairly easy to show that human thought has no limits.
This is all hugely self-referential now because human thought is just a thought itself and if we can show that human thought has no limits then the question of what is reality (which is also a thought) has no limits either. This then would be the SRH with icing on top and an eternal candle.
It is kind of obvious, but there are those of the belief that we are progressing toward a certain truth, which may be true but the point of the SRH is that we can never arrive because the diagonal lemma (I believe this is the active ingredient) means we will always break out of any theory that tries to go for totality.
NOTE: correct the blog on Tarski - he does use self-reference. It is by self-reference that all the problems and inability to become complete and total arise. The Aboslute will always escape computing for this reason, so there will always be God outside the theory - hence the rather grand name for the SRH the God Principle. Put another way God cannot be brought into the theory by definition and he can't be pinned down by definition - chasing God is like a dog chasing its tail and all those "in the know" will see people who try to theorise on God involved in such a pointless activity. Most up for the scaffold in my opinion are the growing number of people who assume God to have been refuted, who don't realise that in the same breath they are saying that Man (whatever that is) or Reality (whatever that is) are sufficient concepts to explain the universe. It is their self imposed narrow mindedness that I find self-defeating. Why if you wish to know about things and have opinions on things would you take a dogmatic position that actually limits your outlook? I can only imagine it is the poor image if "religion" that has emerged where people focus on the failing on churches but I note always while ignoring the immeasurable good they have done. It is interesting that war is often cited in connection with religions - yet a better case for war is put down in this blog that really it is just people vying for power and too often religious divisions are exploited for this purpose, rather than the religions actually being the cause.
Islam for example is being used at the moment to incite division between powerful Arab leaders and Western leaders who (I agree) interfer too much in Arab affairs. But this has gone on for centuries, Britain did win some important wars in Arabia a century ago which is the deal when you fight and the Arabs are rich because of the oil sold to the West so it is all very incestuous. If America and Britain became Islamic I bet the Arab leaders would just find another way to fight for power in the Middle East. Bin Laden is a complex character he is on the surface fighting for power in Saudi-Arabia but I wonder to what extent he is so caught up in U.S. foreign policy that he is actually working for the Americans now. If congress wish to cut funding to the terror war the military just need a need produce a video from him. Entirely speculative but this is what i would do. I imagine that Mohammed understood the importance of battle to protect his nation, but I doubt very much if he wished to spread his wisdom at the end of a sword - hardly wisdom if you have no choice but to accept it! The other great error in the minds of people who wish to use violence on behalf of God (or believe that people do) is the simple question: if God wants something why do I need to do it for Him? He made the universe and Man I'm sure he would remove the infidels off the face of the Universe by Himself if he wanted. When people for world gains like power and land (on Earth or Heaven) it is the act of a Man - only when they act for sublime purposes is it inspired by God. For the meaning of sublime see the SRH.
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