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Goedel applied to emergence: Lower-level indeterminism

Goedel's theorum may be good for more than AI-bashing: we may be able to apply it to emergence (understood broadly enough to include my Aristotelian or rather neo-Platonic conception of higher/lower levels of being/operation).

Think of how we can posit a set of mathematical operations and terms and use these operations and terms to formulate rules/algorithms that can be used in term to determine the truth values of the expressions that use those terms. Goedel showed that the set of all possible rules that we might formulate will be able can determine the truth values of SOME BUT NOT ALL of the expressions that could be created using those terms and operations (I'm not sure I said the Goedel thing 100% right but hopefully closely enough)...

If you keep the above in mind, then you might consider how all of that math stuff might have the following analogy in nature: i.e., the laws or properties that attend a lower level of being can somewhat determine many but not all of the possible behaviors/arrangements/interactions at that lower level. These laws of nature attending lower levels of being are like algorithms: they underdetermine the lower level states of affairs in a manner analogous to how the rules/algorithms in a given math system unable to determine the truth values of all of the possible expressions using operations available. In both cases there is something law-like that underdetermines.

Just as mathematical rules within a system can at least exclude some expressions as impossible or false but cannot establish the truth of all equations that could be expressed using those terms, .... so too, lower-level properties exclude certain things as impossible at the lower level but do not comprehend all possible states of affairs. The lower level rules are open ended, open to influence of a possible higher level.

This indetermination is an openness to determination at the higher level.
This indetermination is NOT freedom. But acknowledging that it is there will utterly undercut reductive materialist arguments against the very possibility of freedom.

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