In my opinion the definition of intelligence is a machine that has an input and an output. It covers all the intelligent systems you can imagine, but also things like thermostats. I think it is too human centric to think that a thermostat is not intelligent because it doesn't have legs and it can't do much. It is very stupid (if you think it is possible to rate intelligence), but still, it can be viewed as an intelligent system. Intelligence really means many, many things and I'm not really that interested in a strict mathematical definition. It reminds me of all the philosophers who have debated for thousands of years on the definition of love, art and such. In the end, no definition is more correct than any other. You can build an AGI without really knowing what intelligence is, just like you can paint beautiful art without knowing some strict definition of art.
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