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.
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.