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Forecasting and recursive Inhibition within a decision cycle

1 Clarity 20 December 2015 05:37AM

When we anticipate the future, we the opportunity to inhibit our behaviours which we anticipate will lead to counterfactual outcomes. Those of us with sufficiently low latencies in our decision cycles may recursively anticipate the consequences of counterfactuating (neologism) interventions to recursively intervene against our interventions.

This may be difficult for some. Try modelling that decision cycle as a nano-scale approximation of time travel. One relevant paradox from popular culture is the farther future paradox described in the tv cartoon called Family Guy.

Watch this clip: https://www.youtube.com/watch?v=4btAggXRB_Q

Relating the satire back to our abstraction of the decision cycle, one may ponder:

What is a satisfactory stopping rule for the far anticipation of self-referential consequence?

That is:

(1) what are the inherent harmful implications of inhibiting actions in and of themselves: stress?

(2) what are their inherent merits: self-determination?

and (3) what are the favourable and disfavourable consequences as x point into the future given y number of points of self reference at points z, a, b and c?

see no ready solution to this problem in terms of human rationality, and see no corresponding problem in artificial intelligence, where it would also apply. Given the relevance to MIRI (since CFAR doesn't seem work on open-problems in the same way)

I would like to also take this opportunity to open this as an experimental thread for the community to generate a list of ''open-problems'' in human rationality that are otherwise scattered across the community blog and wiki. 

We won't be able to recognise the human Gödel sentence

5 Stuart_Armstrong 05 October 2012 02:46PM

Building on the very bad Gödel anti-AI argument (computers's are formal and can't prove their own Gödel sentence, hence no AI), it occurred to me that you could make a strong case that humans could never recognise a human Gödel sentence. The argument goes like this:

  1. Humans have a meta-proof that all Gödel sentences are true.
  2. If humans could recognise a human Gödel sentence G as being a Gödel sentence, we would therefore prove it was true.
  3. This contradicts the definition of G, which humans should never be able to prove.
  4. Hence humans could never recognise that G was a human Gödel sentence.

Now, the more usual way of dealing with human Gödel sentences is to say that humans are inconsistent, but that the inconsistency doesn't blow up our reasoning system because we use something akin to relevance logic.

But, if we do assume humans are consistent (or can become consistent), then it does seem we will never knowingly encounter our own Gödel sentences. As to where this G could hide and we could never find it? My guess would be somewhere in the larger ordinals, up where our understanding starts to get flaky.