THEOREM. If three objects are ordered for all states of affairs in a world containing a finite number of facts, they cannot have the same logical form (Assuming the Tractatus). Outline of Proof. There are six different possible orderings of three objects but 2n states of affairs for a world with n facts. Since 2n is not divisible by six, there is an asymmetry in the way states of affairs get mapped on to orderings. This asymmetry is exploited to create a predicate which picks out a particular object independently of the state of affairs. This immediately implies that the objects cannot have the same logical form, for if they did they would be indistinguishable. Proof. There are six possible ways for three objects to be ordered so let Pi, 1 6 which implies that n > 3. Let Ai be the number of distinct states of affairs which result in the order asserted by Pi. Then