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In “Two Dogmas”, Quine indicates that Carnap’s Aufbau fails “in principle” to reduce our knowledge of the external world to sense data. This is because in projecting the sensory material to reconstruct the physical world, Carnap gives up the use of operating rules and switches to a procedure informed by general principles. This procedure falls short of providing an eliminative translation for the connective “is at”, which is necessary for the reduction. In dissecting Quine’s objection, I argue that Quine has at best proven the claim that the use of general principles essentially fails the task of radical reductionism. However, in order to establish the conclusion that the Aufbau fails in principle, Quine needs to further vindicate two other claims. They are: first, a switch from operating rules to general principles is necessary; second, the set of general principles Carnap adopts is the best alternative. By disambiguating the notion of “explicit definition” and examining the concept of definability in the Aufbau, I explore the possibility of justifying these two claims that Quine overlooks in his objection. The result suggests that Quine’s objection stands in tension with his radical reductionist reading of the Aufbau.