Thus if steps 1 and 2 were reversed in the above example, both would have to be denied: As an example of this failure, let p and q be contingent propositions neither of which logically implies the other, and let the respondent know that q is false whereas he does not know the truth value of p. Then: Clearly, positio on Burley's theory is a very peculiar kind of disputation.
Yes, we have won promotion to the top division every so often; but the fact of promotion logically implies an earlier relegation.
The idea of saving or delivering from some dire situation logically implies that humankind, as a whole or in part, is in such a situation.
Indeed, by making Walt a chemistry genius, the show offers an implicit rebuke to the persistent modern conceit that a scientific worldview logically implies liberalism, humanism and a widening circle of concern.
For example, in order to show that a certain formula F logically implies another formula G, one tries to construct in step-by-step fashion a model of the logical system (i.e., an assignment of values to its names and predicates) in which F is true but G is false.
Khayyam's achievement in this topic was not to invent a new definition, but rather to demonstrate that each of the existing definitions logically implies the other.
The implication problem is the most important one in dependency theory, and is the problem of determining if a set of dependencies logically implies another dependency.
Deductively, e logically implies h if h is true in every model for e. Degree of confirmation is thus a metrical generalization of first-order logical implication.
One might, for example, appeal to some closure principle about causal power, claiming that if A causes B and B logically implies C, then A causes C.
In contrast to the case of physics, where one could never hope to show that the data logically implies the theory, in the case of the search for new axioms this is in fact possible.
