Total Systems & The Ultimate System

It occurs to me this w/e gone that a reductio ad absurdum argument might win the day for SRH. What the SRH is arguing against is the existence of Total System.

A Total System is one in which we can make a statement of the type "All ...". In particular it is the idea that there is a ultimate Total System in which all things are accounted for -- call this an Ultimate System.

Some interesting things about Ultimate systems. If they exist there is just one of them because if there were two they would defeat each others Ultimate status. We are part of The Ultimate System (US), if it exists, because if we stood outside it then we would stand as evidence that it was not ultimate. The US is thus a hermaneutic circle which we must accept, being born into it, which cannot be justified by anything outside it because having anything outside contradicts its ultimate status. US is also a joke because the United States more than any existent system believes itself to be the Ultimate System of human beings.

In order for a system to be classed as a US it must be able to show:

1) that no alternative system can exist.

2) that no possible entity exists that is not accounted for in the system. Such an entity would enable a new system to be created which was more comprehensive than itself.

3) that there is no meta system, or way of talking about the elements of itself, that it can't do itself. That is to say all elements only map onto themselves, and all relations between elements only map onto themselves. (problem 1. The power series cannot be expressed within a system)

3.1) that the incorporated meta system respects the use/mention distinction so that the system is able to avoid paradoxes.

4) Must be immune to diagonalisation (or equivalent).

It seems easier to show the absurdity of a US than to prove the SRH!

Some other thoughts toward this. A US would also need to prove that there were no "black swans". In other words once all data has been incorporated into a theory it must be able to prove that there is no possible event that would contradict the theory to be classed as a US. The relevance of data is deternmined by the theory so it is possible for a theory to determine what data would constitute a refutation. A US would have to show that no further data would cause a rejection of the theory, or that there was no possible further type of data. Even the smallest black swan not accounted for in the theory would create a bigger more ultimate system.

One possible line of enquiry was this: A TS that was complete (TS1) would be broken if we could step outside it and speak about it. But in doing this we would occupy a new, more powerful system (TS2) which was now complete since it incorporated TS1 and the system of speaking about TS1 (the meta system). But then once we start to speak about TS2 we would have entered a new system TS3 ad infinitum. To know that the TS we occupy is the US we need to prove that there is no way of talking about it that is not present within the TS. A possible break in this loop would be if we could show that talking about TS2 was isomorphic with talking about TS1, so that the language of talking about TS1 mirrored any language needed to talk about TS2.

The first observation is that any thinking that goes along the lines of rejecting thoughts is actually fashioning a smaller and weaker system. The US obviously needs to incorporate everything! This would be a way of describing the weakness of dogma ... since the establishment of dogma is done from a perspective already outside the dogma, the very perspective that sees the dogma as correct and other positions as wrong! So the dogmatist needs to establish that the various dogmas in their view cannot, any of them, establish the point of view of that dogmatist!!

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If the US could express the notion that it was a/the US then it would be speaking about itself. This would mean that it was outside itself. Now it is the necessity of the US that it either:

1) Doesn't know that it is the US
2) Can resolve the ecstatic paradox (present in humans) of both being something and being able to speak about that something. It was this aspect of self that so fascinated my teenage mind as it explored self-consciousness -- and which it never found a resolution to. This could be evidence that actually humans are not-selves at all and they only speak about a model of themselves (isomorphic to some extent with themselves but not actually themselves). Like looking in a mirror: we think we see ourself but is the person we are looking at looking at us? This is the problem the SRH says provides the limit of self-isomorphism. Our "self" is only ever a "dogma" (see above) that is established within the True Self (the US).