 Even the weak principle P3 faces some difficulties. Consider a true universal proposition, say the proposition that every finger of my right hand is less than 1m long. It seems that unless some controversial assumptions are made (like Wittgenstein’s view that universal propositions are conjunctions), to countenance P3 involves accepting that there is something like the fact that every finger of my right hand is less than 1m long and claiming that its existence-set is identical to the truth-set of the proposition in question. Following Wittgenstein (TLP), many reject such universal facts. In the other camp are e.g., Russell (PLA) and Armstrong (1997; Armstrong invokes certain totality facts, which have indeed a universal component.).