thought. But in any case the Tractarian line does not seem to help much with the Gödelian worry. Moreover, consider the question of what essences can possibly exist (in mind or reality). The story we have so far is that something is possible provided its existing is not contradictory to the truths encoded in those essences that exist. This, however, seems to let in so many essences that a certain amount of skepticism is engendered. For instance, it seems that there will be a possible world w which is just like this one, with this exception. The essence of human beings does not exist at w, but instead there are entities that physically behave just like human beings, except that instead of being a single natural kind, they are divided up into two natural kinds defined by different essences: there are those who have an even number of hairs on their bodies and there are those who have an odd number of hairs on their bodies. As soon as one of these beings gains or loses a hair, it perishes, and a new being comes to exist, physically and psychologically just like it, apart from that hair. Otherwise, everything is as it is in our world. After all the existence of such being and such essences does not seem to contradict the truths encoded in any of the essences that exist, such as the essence of the live oak or the photon. But once we allow that w is possible, do we have good reason to suppose that it isn’t our world, that in our world there aren’t different essences for people with even numbers of hairs and for people with odd numbers of hairs? The problem, thus, is with what constrains what essences there could be. One answer, inspired by the static character of Aristotle’s universe, would be that all the essences that can exist in fact do exist, or at least existed, exist or will exist. However, a crucial difficulty remains as to what “can” could mean here. What constrains which essences can exist?
there is no being b such that it is a necessary truth that b satisfies D. However, such quantificational states of affairs are not causes, just as disjunctive states of affairs are not causes. Hence, once again, we get to a necessary being. If, furthermore, we think that causes can only function through the causal efficacy of a being, then we get a causally efficacious necessary being, a first cause. The Taxicab Problem here takes the form of asking what causes C to cause M, and this question has already been discussed in Section 3.3. We can also modify the argument by only assuming a CP for positive wholly contingent states of affairs. Assuming the cause of a positive state of affairs is found in a positive state of affairs, we can again get to a necessary being. 4.2. The CP for chains We assume in this argument that we are dealing with a kind of causation such that the causes relation is transitive (if x causes y and y causes z, then x causes z) and irreflexive (x does not cause x). A causal chain of items is a set S of items totally ordered under the causes relation. In other words, if x and y are members of S, then either x=y, or x causes y, or y causes x. The relata of the causal relation can be concrete things or events or concrete states of shall call these relata “items”. The relevant CP now states that if S is a causal chain of contingent items, then there is a cause of every item in the chain. If S is a finite chain, this follows from a CP for individual items—we just take the first item in the chain and ask for its cause, which cause then is the cause of every item in the chain. Theorem 1. Assume the above CP, assume that causation is transitive and irreflexive, and assume the Axiom of Choice. Suppose there is a set U of all items. Then, for any contingent item e, there is a necessary being G such that G causes e.