I'm reading W.V. Quine's Essay "The Two Dogmas of Empiricism", and in it he gives a page or so treatment of Carnap's Aufbau. Carnap was a radical reductionist at the time, and was actually proceeding to break all statements down into some language where all statements would either be true or false based on sensory data. Not actually having read Aufbau, I don't know much about the language other than what Quine mentions, which is that it is essentially the whole body of mathematics (including logic). My problem is at the part where he (Quine) is talking about the problem Carnap had with assigning everything a quadruple of real numbers (x,y,z,t). Quine says that Carnap only got so far as to say "Quality P is at point-instant (x,y,z,t)". His language had no way to define 'is at', and so remains an added undefined connective. It seems to me that a solution is readily available. You would simply let all point-instants represent a class whose elements are precisely all of the qualities previously described as 'at' that particular point-instant. Like I said, this solution seems too easy, and Carnap ended up rejecting radical reductionism because he was unable to do this. Why is it that my answer does not work?