Dan74-MkII wrote: ↑Tue Apr 16, 2019 3:47 pm
Germann wrote: ↑Tue Apr 16, 2019 3:40 pm
Dan74-MkII wrote: ↑Tue Apr 16, 2019 3:34 pm
Why should it trace out any particular sequence of steps?

This has nothing to do with countability. The set of all infinite paths of this algorithm may be finite or infinite and still not contain a given sequence. Why should it?

So we take every sentient being today as the starting configuration of your algorithm. You run the time backwards and suppose that it goes on for ever into the past. You get a finite set of paths - one for each sentient being alive today, each of infinite length (infinitely many moments each containing a finite combination of dhammas, based on your assumptions). Now why should each one of them, or even one of them contain the magic sequence leading to nibbana??

The infinite set of

all steps of of algorithm still not contain

one of the steps of this algorithm???

Firstly, not one step but a sequence of steps. Secondly, yes, even a step may not be contained. Suppose there is a diamond hidden in a rock since eternity. Why would it be guaranteed that anyone would find it? Maybe no one even got close to it.

Each step is deterministic. Each step is necessarily implemented in an infinite sequence. In order to have at least one step that is not realized, it is necessary that the infinite set of

all possible steps have cardinality, which exceeds the cardinality of the infinite set of steps already implemented. But the infinite set of

all possible steps is a countable set. That isn't possible.

If for an infinite number of steps of a deterministic algorithm a step is not implemented, then this step is not deterministic, it is an impossible event, it is an impossible step for this algorithm.

The manifestation of Nibbana is considered possible. If each step is deterministic, then the step of the algorithm that leads to the manifestation of Nibbana is predetermined. It is necessarily implemented in an infinite set of steps of a deterministic algorithm.