Paul Almond

To Minds, Substrate, Measure and Value Part 2: Extra Information About Substrate Dependence I make his Objection 9 and am not satisfied with his answer to it. I believe there is a directed graph (possibly cyclic) of mathematical structures containing simulations of other mathematical structures (where the causal relation proceeds from the simulated to the simulator), and I suspect that if we treat this graph as a Markov chain and find its invariant distribution, that this might then give us a statistical measure of the probability of being in each structure, without having to have a concept of a physical substrate which all other substrates eventually reduce to.

However, I'm not sure that any of this is essential to my OP claims; the measure I assign to structures for purposes of forecasting the future is a property of my map, not of the territory, and there needn't be a territorial measure of 'realness' attached to each structure, any more than there need be a boolean property of 'realness' attached to each structure. I note, though, that, being unable to explain why I find myself in an Everett branch in which experiments have confirmed the Born rule (even though in many worlds (without mangling) there should be a 'me' in a branch in which experiments have consistently confirmed the Equal Probabilities rule), I clearly do not have an intuitive grasp of probabilities in a possible-worlds or modal-realistic universe, so I may well be barking up the wrong giraffe.

EDIT: In part 3, Almond characterises the Strong AI Hypothesis thus:

A mind exists when the appropriate algorithm is being run on a physical system.

I characterise my own position on minds thus:

A mind exists when there is an appropriate algorithm, whether that algorithm is being run on a physical system or not. If the existence-of-mind inheres in the interpretative algorithm rather than the algorithm-that-might-be-run, then the interpretative algorithm is the appropriate one; but the mind still exists, whether the interpretative algorithm is being run on a physical system or not.

This is because the idea of a 'physical system' is an attachment to physical realism which I reject in the OP.