Seems right, except I don’t use the word “product” for the multiplicative definition.
I don’t have much to say about the internalizing-externalizing definition philosophically. One thing to say is that I think the condition that ExternalS(C) observes S is a weaker notion of observability, that might actually agree with philosophical intuition more, and the internalizing-externalizing definition might be easier to interpret if you are thinking in terms of this condition.
Seems right, except I don’t use the word “product” for the multiplicative definition.
I don’t have much to say about the internalizing-externalizing definition philosophically. One thing to say is that I think the condition that ExternalS(C) observes S is a weaker notion of observability, that might actually agree with philosophical intuition more, and the internalizing-externalizing definition might be easier to interpret if you are thinking in terms of this condition.