 Reichenbach’s 1925 essay “The Causal Structure of the World” (1925d) is also an early attempt to account for the direction of time in terms of causal and probabilistic asymmetries. Reichenbach there introduces the notion of a “probability implication” with 10 axiom schemes on propositional variables involving both material implication and a new 2-place probability implication connective. The axioms are evidently meant to supplement those of propositional logic. No rules of inference are specified, but substitution and modus ponens are used. The axioms do not guarantee that a probability implication, a ⊇  b[2],  is the conditional probability of b given a, or even that the consequents of a collection of probability implications with a as antecedent satisfy the axioms of finite probability. Interpretation is difficult, since Reichenbach both asserts that the probability of the consequent in a probability implication can be between 0 and 1 inclusive (1925d, 1978, vol. II, p. 89), but then disallows a probability implication because the consequent has probability 0 (p. 92). Reichenbach’s thought seems to be that a ⊇ b asserts that in circumstance a, b has a well defined probability, that is, a specifies something like what Ian Hacking (1965) later called a “chance setup,” or as Reichenbach might have put it, implies the existence of a probability function for {b, ~b}. Reichenbach uses the operation very much in that way in his 1925 discussion of the direction of time, which he thinks can be founded on cases in which a ⊇ b is true but b ⊇ a is false. Even under this reading some of his axiom schemes have false instances, e.g., (a ⊇ b) ⊃ (a.c ⊇ b), where the dot is ordinary conjunction. (The claim that b has a probability distribution in context a does not necessarily imply that b has a probability distribution in context a conjoined with context c, since c might make a distribution impossible.) Revised, probability implication later became a foundational notion of Reichenbach’s theory of probability and the central concept of his approach to inductive logic. 