As Price (1996, 278 n.7) puts it in the context of endorsing Horwich's conclusion: "the hypothesis of time travel can be made to imply propositions of arbitrarily low probability.
The proof of Theorem 1 can be adapted to imply Proposition 1.
Under the compatibility reading of $N$ this condition says that every world $Y$ is incompatible with is also a world $X$ is incompatible with, if proposition $X$ implies proposition $Y$.
A last type of inference is called contraposition and is produced by the fact that some propositions imply the proposition that results from the original proposition when both of its term variables are negated and their order reversed.
Finally, we turn to the set of attraction (cf. Sect. 2.4) of Model 3. As implied by Proposition 1 (Proposition 2), the set of attraction of Model 2a (Model 3) is a subset of S A2a (S A3).
The meaning of "implies" is that "of ordinary inference and proof" (1912, 531) according to which a proposition implies another proposition if the second can be logically deduced from the first.
A term is said to be distributed in a given proposition if that proposition implies all other propositions that differ from it only in having, in place of the original term, any other term whose extension is a part of that of the original term i.e., if, and only if, the term as it is used in that occurrence covers all the members of the class that it denotes.
The principle that a necessarily false proposition implies any proposition, and that a necessarily true proposition is implied by any proposition, was apparently first propounded in twelfth century Latin logic, and came to be widely, though not universally, accepted in the fourteenth century.
Proposition 5.2 implied the following propositions.
In contrast, the sign of β2 implied by Proposition 2 is significantly positive.11.11
