General intelligence, of the kind that underwrites the full range of human cognitive achievement, is not a property of computational architecture alone. This paper advances a single thesis: the structural constraints on general intelligence occupy distinct levels of description and are mutually non-reducible, in the sense that the special-sciences tradition gives to that term. It follows that no single architectural advance, and no continuation of the scaling programme by itself, can produce artificial general intelligence (AGI), and that research programmes must be evaluated against the full constraint profile rather than against performance on any one benchmark. The thesis is developed through a method that reads general intelligence through four evidential lenses, AI systems research, anthropology, law, and economics, each anchored to a distinct level of description, supplemented by speculative fiction used as a disciplined heuristic in the context of discovery rather than the context of justification. Applying the method yields a taxonomy of twenty-three structural constraints organised into eight clusters; six are examined in depth and ordered as an ascending ladder of levels, with explicit bridges showing why progress at one level cannot carry to the next. The argument issues in five falsifiable predictions, each stated with a named benchmark family and a disconfirmation condition, converting a descriptive framework into a research programme with a longer horizon than the scaling hypothesis implies.

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