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I'm not sure the GIT applies here, it is my understanding that the GIT says that for any formal system (i.e. sentences derived by repeated application of rules
by improv32 13y ago
I'm not sure the GIT applies here, it is my understanding that the GIT says that for any formal system (i.e. sentences derived by repeated application of rules of derivation to axioms) that is able to represent the Peano arithmetic, has no deterministic decision procedure, due to the ability of a sentence to self-reference. Is that accurate, or is GIT broader than I thought?
- lutusp 13y agoI mentioned the GIT as an example of the risk of invalidation by self-reference, but whether they formally apply depends on how we state our hypotheses. They certainly apply in some degree to any effort to define strict deterministic criteria by which one might conclude that the universe is a simulation, carried out from within that same universe. The more formal and detailed the criteria, the more likely we are to be trapped by self-reference. > Is that accurate, or is GIT broader than I thought? I think the ambition of the simulation question offers enough similarity to a complex logical system that one needn't assume any greater scope for the GIT than they're known to have. I'm not claiming that the GIT obviously applies, only that the possibility needs to be taken into account on a list of issues that attend this question.