Logic/SRH notes

All arguments are double edged. If we take an argument over the things it is meant to apply to and apply it elsewhere we will see that it has the opposite effect. For example "everything is worthless". If this argument is worthless then rather than proclaim that everything is worthless it states that it is worthless to state that everything is worthless - which is probably the source of depression itself realising the worthlessness of this kind of activity it is involved in. If it is worthless to do this then it must be worthwhile doing something else and so we contradict the assertion that everything is worthless. This is SRH.

In the notes I applied it to the statement that "Life is pointless". In which case there is no point to me spending my life coming up with statements like this.

So a negative statement defeats all sides of an argument, and a positive statement supports both sides of an argument. The note concludes that arguments make no changes.

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The world of difference is itself indivisible. Thus the world we see of many separate entities cannot be separated into a world of many separate entities and a world of one indivisible entity. There can be no difference between these because if there was then that difference would be part of the world of difference.

For the same reason a world of indivisibility cannot be indivisible from a world of indivisibility.

There is a meta level here (by SRH) that is neither divisible nor indivisible. But it is neither the same nor different from Derrida's Differance ;-)

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§ open set + neighbourhood SRH, complement s in R3 = all points not in s, p on boundary if neighbourhood contains both s & s'

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There is a contradiction in the idea of "self-replication". One can replicate "like" features so that one's child is "like" oneself, but one cannot replicate "oneself" for two identical copies are still two and not one.

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In a processes each step of the process must change the state of the machine. Each step thus exists in the state space of the machine (the set of variables that hold the computation).

Now to get a self-referential system the whole state of the machine at any one point must be present as a point within its state space and so a reference to this state must either create a change of state, or to fix the state of this system the self-reference must be recorded as a state outside the system.

For example I can work out that this sentence has forty six words while the sentence itself can't because I can step outside the system complete the sentence count the words and then change the system from outside, as indeed I am thinking of doing now. I knew that most numbers between 21 and 99 have two parts so just added 2 to the word count of the sentence. Now in true Turing style I could not count the state of the system (the sentence) before it was written because how did I know when the sentence was going to finish without actually creating the sentence first. The sentence can't work out itself if it will finish so can't decide how long it will be.

So it is only because the author can decouple from the sentence after writing that it looks self-referential. It never was able to refer to itself. What it refers to is something that I made, and I am part of that essential state system that the sentence can't exist without namely the English speaking world and actually the Universe in general.

Now for exercise can I create a state machine that runs into the problem above? It seems easy to create a machine that outputs an apparently self-referential number like one that is hard-coded to output 5 which happens to be the count of variables, or a Quine even. What has alluded me so far in the SRH quest is a definition of a machine that is "authentically" processing a self-reference and one that just happens to do so either by design or by accident. Of the set of all possible state machines obviously some will appear self-referential. My question is to find the meaning of a difference between Quines - that simply have self-referential output - and "Ruines" which have a self-referential process that has self-referential output. And what would the difference be?