Cognitive Science (CogSci) and AI are addressed from the perspective of inductive inference research, specifically as applied to language learning. Language so represents intelligence that results bridge gaps between the fields. We give examples of rigorous results intractable for AI machines and humans; AI results humans find satisfactory; and AI-Hard problems with "good enough" solutions, adaptively obtained. We conclude that lack of "the human experience" may preclude machines from human thinking, but CogSci can help AI produce human-acceptable results. Conversely, CogSci can benefit when researchers study human processes to improve AI machines. We see no competition: cooperation will advance both fields.