The Extended Mind Thesis holds that we should consider "cognition" to include the process of using external cognitive tools (rather than only considering processes internal to our brain).
The wikipedia page lists some counterarguments. I am interested in the third one:
It uses coarse-grained functionalism about the mind that ignores plausible differences between internal and external processes, such as differences between beliefs and external props and devices; or for creating a notion of cognition too heterogeneous to make up a scientific natural kind.
The main thrust of the Extended Mind Thesis is that treating distinctions between internal and external as not meaningful makes a more useful model. This objection seems (on the surface) to be circular reasoning - it rejects the Extended Mind Thesis because it rejects the Extended Mind Thesis. However, I wonder if maybe I'm not just missing something in the literature - are there alternative definitions of thought, belief, minds, or intelligence which make the distinctions between "internal and external" meaningful, and would motivate this rejection?
I can imagine the flippant answer of "Intelligence is what goes on inside my brain," but this isn't very measurable (it runs into the problem of other minds, makes it impractical to discuss intelligence of animals, etc.).
Are there well-discussed alternatives to the Extended Mind Thesis, which still provide consistent and useful definitions of intelligence?