Back on to SRH - coin flip contradictions

Quickly first: what has SRH got to do with poverty? (if I'm going to try and unify the topic of this blog). SRH was the name given to an insight that self cannot support self, and that "self" implies "other". This was to contradict and suggest there was a contradiction in the belief of a "self contained" self. At least in human mind, "self" appears to imply a "unit self" that can be unplugged from "other" and exist by itself. This flavour of "self" conception infect science and logic in the belief that there is a "truth" or "axiom" that can exist independently, upon which everything else is based but which itself is not based. In essence this is the same idea as God, that there is a single, irreducible entity which is the source of all things, but itself has no source. SRH was just a much needed name "Self Reference Hypothesis" for this insight that ultimately nothing exists by itself. Now the relationship with poverty, is that poverty can only exist if things can be isolated. But since everything depends upon everything else there is no poverty.

Back to blog.

Create a coin toss scenario:

Heads: decide the meaning of this coin toss by coin toss.

It comes down heads. We apply the rule, and it says apply the rule.
It comes down tails. We look at the rule to see what this means, and it says don't use the rule. Problem is we already did, and if we didn't then we can't resolve the coin toss.

Simple liar paradox in coin flips.

Interesting to explore tho, because the problem arises because we are already committed to the meaning before we read the contradiction. These are temporal SRH where we commit to one state, only to find it asks us to uncomit.

--- Addendum 26 May

Another version is:

Heads: should I use coin flips to make decisions?

Result heads: I should use coin flips to make decisions.
Result tails: I should not be using coin flips to make decisions.

Normatively we'd just stop using coins from this moment on. But logically you could say we've run into a problem because we just made a decision by a method that said we should use that method. In other words how valid was this decision?

The point from SRH perspective is that we already made a decision to use coin flips to make make decisions. So setting the next decision to be "should I make decisions this way" gives an insight into what "should" means in English rather than anything else. In logic we would say something like "are decisions made by coin flip true?" And there is the liar paradox. But in English we fudge this out by saying "should" to mean "it is correct" but we aren't going to do it this time. So when we coin lands on tails, despite already having made a decision with the coin, that we are taking as valid, we now think that decisions made by coins is no longer valid - decided by the coins!

What this illustrates is the complexity of "prior" which is what SRH has been struggling with. In this case "temporal prior". In fact we have always aready made the decision to use coins to make further decisions, and when we decide to rest the decison on a coin of "shall I use coins?" we are not contradicting what has gone before, i.e. the prior, but determining the future.

But removing the dimension of time: "is it ALWAYS a good idea to use coins to make decisions?" CANNOT be decided by a coin! And this is SRH. We are then contradicting the prior, in this case a logical prior. If the "prior" is a decision to use coins, then we cannot ask those coins whether we should use coins, because we already did. SRH does exist, but defining how the prior binds us is provide complex (as argued before I suspect there is a contradiction in even defining rules about the relationship of prior to a state of affairs... and infinite regress of priors of priors... would being able to define the limits of freedom of a system with priors, define priors to those limits?). It is quite possibly undefinable what the limits of a system based on SRH are! That SRH is itself a contradiction, but a peculiar one where it must be a contradiction to be true (Godel style).

However we can ask the softer question "is there ever a time that coins can decide?", but if we use a coin to decide this we cannot know the validity of the answer. If it comes down heads (yes), then we don't know if this is one of those times, and all other outcomes undermine the validity of the outcome.

As a friend pointed out we have a "third" way here: true/false/undecided. And this 3rd option is "outside" the system of true/false. Every system (which is complex enough to have self referemce) must have a "outside the system" outcome. This is SRH.

Now a classic case of self reference which is generally considered valid is the definition of the natural numbers by induction:

We take a starting number "1" as an axiom which belongs to set N.
We then define a successor S(n) to define a new member of N, where n is a member of N.

Then S(1) -> 2, S(S(1)) -> 3 etc

Now from an SRH perspective the interesting thing here is N. We already created the set N prior to the rules of membership. Can we define these axioms without pre-defining the domain of the function S.

I need do some reading and thinking on this. But induction is considered probelematic by some as it looks like things are being degined by themselves, in other words there is no definition occuring and the prior was already there...

to be continued...